determination of retinal thermal hazard and blue light photochemical hazard protection

Determination of Retinal Thermal Hazard and Blue Light Photochemical Hazard Protection Needed by Automatic Welding Filters

Bestämning av Skyddsbehov för Automatiska Svetsglas Gällande Riskerna för Termisk och Fotokemisk Skada på Näthinnan

AKOTO CHAMA LEONEL

Degree Project Mech. Engineering 2009 Nr: E 3726 M

Determination of Retinal Thermal Hazard and Blue Light Photochemical Hazard Protection Needed by

Automatic Welding Filters

Change the Thesis No. E xxxx M using the Document Properties box

Akoto Chama Leonel

Page 0(128)

EXAMENSARBETE

D-Nivå Maskinteknik

Program Reg nr Omfattning

Maskinteknik – produkt- och produktionsutvecklling,

30 ECTS E 3726 M 30hp

Namn Datum

Akoto Chama Leonel 2009-09-20

Handledare Examinator

Roger Johansson

Företag/Institution Kontaktperson vid företaget/institutionen

3M Svenska AB / Research and Development Department Kristna Magnusson

Titel

Bestämning av skyddsbehov för automatiska svetsglas gällande riskerna för termisk och

fotokemisk skada på näthinnan.

Nyckelord

Termisk, blått ljus, fotokemisk, risker, skydd, automatisk, svets, filter

Sammanfattning

Nya resultat inom den biologiska forskningen har visat att de tidigare gränserna för högsta

tillåtna exponering (MPE) av artificiell optisk strålning för skydd av arbetare, var strängare än

nödvändigt. Utgående från färska gränsvärden för artificiell optisk strålning har det här arbetet

fokuserat på att undersöka vilken nivå av dämpning av det synliga ljuset som är nödvändig när

ett automatiskt svetsglas fallerar att slå om vid svets. Resultat från jämförelse mellan olika

standarder för maximal exponering användes som utgångspunkt för att undersöka behovet av

krav på Vis/IR- och blåljustransmittans för automatiska svetsglas. Verkliga och antagna

spektralfördelningar användes för att simulera olika fall av artificiell optisk strålning. Ett

excel-diagram för att beräkna exponeringsvärden från olika ljuskällor samt att beräkna viktade

transmittanser utgående från spektrala transmittansmätningar på svetsfilter togs fram under

projektets gång. Excel-diagramet utvecklades och testades utgående från kända

produktegenskaper för att verifiera tillförlitligheten. Slutsatsen från det här projektet är att det

behövs dämpning av det synliga ljuset i ljusa läget om täthetsgraden i det mörkaste läget är 11

eller högre. Det visades också att ett befintligt automatiskt svetsglas med stor marginal ger

tillräckligt skydd även om produkten fallerar att slå om vid svets.




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DEGREE PROJECT

Magister Thesis Mechanical Engineering

Degree Program Reg number Extent

M.Sc. Mechanical Engineering - Product and Production

Development, 30 ECTS

E 3726 M 30 ECTS

Name of student Year-Month-Day

Akoto Chama Leonel 2009-09-20

Supervisor Examiner

Roger Johansson Company/Department Supervisor at the Company/Department

3M Svenska AB / Research and Development Department Kristina Magnusson

Title

Determination of Retinal Thermal Hazard and Blue Light Photochemical Hazard Protection

Needed by Automatic Welding Filters

Keywords

Thermal, Blue Light, Photochemical, Hazard, Protection, Automatic, Welding, Filters

Summary

Recent developments in biological research, has shown that the initial maximum permissible

exposure (MPE) limits for protection of workers from risks associated with artificial optical

radiations were more stringent than needed. Using the most recent MPE limits for artificial

optical radiation this piece of work was focused on the investigation of the level of visible

light attenuation needed by automatic welding filters in case of switching failure. Results from

the comparison of different exposure standards were employed in investigating the need of

Vis/IR and blue light transmittance requirement for automatic welding filters. Real and

arbitrary spectra were taken into consideration for the worst and best case scenarios of

artificial optical radiations. An excel worksheet developed during the execution of this project

took into consideration the exposure from different light sources and the precision of the

spectrometer used in measuring the transmittances of a welding filter. The worksheet was

developed and tested with known product properties to investigate the validity of its

formulation. The conclusion drawn from this project was that attenuation in the light state will

be needed for products with the darkest state shade 11 or higher. Also shown is that current

welding filter protects the eye well enough even in the case of switching failure.




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Abstract Recent developments in biological research, has shown that the initial maximum permissible


radiations were more stringent than needed. Using the most recent MPE limits for artificial

optical radiation this piece of work has focused on the investigation of the level of visible light

attenuation needed by automatic welding filters in case of switching failure. Results from the

comparison of different exposure standards were employed in investigating the need of Vis/IR

and blue light transmittance requirement for automatic welding filters. Real and arbitrary

spectra were taken into consideration for the worst and best case scenarios of artificial optical

radiations. An excel worksheet developed during the execution of this project took into

consideration the exposure from different light sources and the precision of the spectrometer

used in measuring the transmittances of a welding filter. The worksheet was developed and

tested with known product properties to investigate the validity of its formulation. The

conclusion drawn from this project was that attenuation in the light state will be needed for

products with the darkest state shade 11 or higher. Also shown is that current welding filter

protects the eye well enough even in the case of switching failure.




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Acknowledgements This research project would not have been possible without the support and encouragement of

many people. I wish to express my gratitude to my supervisor, Kristina Magnusson (Senior

Optics Specialist at 3M) who was abundantly helpful and offered invaluable assistance,

support and guidance. Deepest gratitude are also due to the members of the supervisory

committee (The Optic group at 3M) and to all those at the R&D Department of 3M without

whose knowledge and assistance this study would not have been successful. Not leaving out

special thanks to 3M for the financial support throughout this project.

I would also like to extend my gratitude to my teachers, Roger Johansson and Bengt Lofgren

for their support and encouragement.

Special thanks also to all my friends, for their encouragement and invaluable assistance.

I would also like to convey thanks to the University and Department for providing the

possibility of carrying out this research project to a successful completion.

I wish to express my love and gratitude to my beloved families; for their understanding &

endless love, through the duration of my studies, most especially to my mum: Diana, brothers:

Roland, Terence and Derick and to my sister Ernestine.

I am grateful also to the examples of my late father, Eki Thomas. His unflinching courage and

conviction will always inspire me, and I hope to continue, in my own small way, the noble

mission to which he gave his life. It is to him that I dedicate this work.




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Table of Contents Abstract ............................................................................................................................ 2

Acknowledgements .......................................................................................................... 3

Table of Contents ............................................................................................................. 4

1 Introduction .............................................................................................................. 5

1.1 Background ........................................................................................................ 5

1.2 Problem .............................................................................................................. 5

1.3 Objective ............................................................................................................ 5

1.4 Delimitations ...................................................................................................... 5

1.5 Approach ............................................................................................................ 6

1.6 Report Outline .................................................................................................... 6

2 Method ..................................................................................................................... 7

2.1 Introducing the Liquid Crystal (LC) Technology ................................................... 7

2.2 Introducing the Optics of the Eye ..........................................................................18

2.3 Welding and the Emission of Electromagnetic Waves ..........................................25

2.4 Speedglas and the LC-Technology ........................................................................28

3 Execution .................................................................................................................38

3.1 Comparison of Different Standards .......................................................................38

3.2 Study of Filter Characteristics...............................................................................57

4 Result : Determination of Damage from Intense Light Exposure ..............................69

5 Discussion ...............................................................................................................84

6 Conclusion / Recommendations ...............................................................................85

7 References ...............................................................................................................87

Appendices ......................................................................................................................88

Appendix A (Annex) Calculations ...............................................................................88

Appendix A Data Sheet .......................................................................................... 118




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1 Introduction

1.1 Background



radiations were more stringent than they really should have been. These restrictions which

were stipulated in the 1999 Technical Report of the International Electrotechnical

Commission (IEC) were more restrictive than the most recent investigated permissible

exposure limits of the eyes. As a result of this and because the products where standardized

according to initial research reports, it is therefore imperative that the products be investigated

to see if they do not pose any threat to humans even within the limits of recent MPEs.

1.2 Problem

The problem here was to determine whether or not there is any risk involved in using

automatic welding filters for protection against artificial optical radiations according to the

new exposure standards, within 0,5 s of switching failure. If there is, to what extent should

protection be needed?

(Note: Since the blink reflex is often mentioned as 0.25 s, choosing 0.5 s for switching failure

gives some error margin.)

1.3 Objective

The objective of this project is to determine the thermal and blue light photochemical hazard

protection needed by automatic welding filters in case of switching failure. The required

protection in the light state, when welding filter fails to go to the intended darkest state is

searched.

1.4 Delimitations

In this project investigations were made within the Electromagnetic spectral range from

300nm to 1400nm leaving out all other wavelengths of the EM spectrum. This project

stipulated the expected design properties but did not go into the actual fabrication of the

system. Design properties were mainly focused on the blue light and Infrared regions of the

EM spectrum.




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1.5 Approach

In order to determine the thermal and blue light photochemical hazard protection needed by

automatic welding filters in case of switching failure ( i.e. the required protection in the light

state, when a welding filter fails to go to the intended darkest state) and because these filters

use the liquid crystal technology for its operation, the work was carried out as follows:

First of all, a lot of background studies was done in order to understand the following:

- Liquid Crystal Technology

- Optics of the eyes

- Welding and the emission of electromagnetic spectra

- Differences between various standards

After a clear understanding of the problem, an excel worksheet was developed (see

accompanying CD) and used to:

- Understand the behaviour of the filter

- Simulate spectral data

At the end of the analysis logical conclusions were drawn from the results obtained.

1.6 Report Outline

The product under investigation uses mainly the Liquid crystal (LC) technology in its

operation. As a result of this, the report started with a general introduction of the LC-

Technology to introduce the main concepts considered during the investigation. This was

closely followed by an introduction of the optics of the eye(organ of the body directly

affected), welding and the emission of electromagnetic spectra (processes that produce

radiations for which protection is needed) with both limited to areas related to the objective of

the project. After these, a closer look was made on the specific application of the LC-

Technology on the speedglas (product under investigation) and the operations and principles

of its constituent parts. With a good knowledge and understanding from the background, the

next step introduced the preliminary investigation to proffer a solution to our problem, here

different standards were then compared in order to choose a final standard to analyse the

protection needed. With a standard now adopted, it was then employed in the study of the

filter characteristics. With a deep understanding of the product properties and its operation

principles, the damage level from intense light exposure was determined through simulation

on an excel worksheet, followed by a conclusion stating clearly to what extent this project

attained its original objective..




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2 Method The methods used here were both experimental and analytic, but first we start by introducing

the necessary literature to understand the technology behind the product, the source of EM

radiations and how they may affect the eyes.

2.1 Introducing the Liquid Crystal (LC) Technology

2.1.1 Electro Optic Filters

Electro optic filters could be described as electromagnetic wave filters that use the interaction

between liquid crystal molecules and an external electromagnetic field for filtration.

Before the introduction of electro-optic filters, the optics of liquid crystals shall be briefly

introduced since it constitutes the main filtration element.

The main reason for the significant optical effects of liquid crystals is the large optical

anisotropy of these materials (with ∆n typically in the range 0.1 to 0.3) and also because the

optic axis can easily be reoriented by external forces such as electric or magnetic fields or

surface interactions. As the case may be, in the presence of an external field, the molecules

turn to align themselves in the direction of the field with the completeness of the alignment

proportional to the field strength.

The anisotropic nature of liquid crystal molecules and the macroscopic ordering makes the

material birefringent and hence the optical properties depend on the polarization direction of

the propagating light. [1]

In the presence of an electric field, the structure and thermodynamic properties of a dielectric

anisotropic medium changes. These changes include a shift in the phase transition points,

change in order parameters, induced new symmetry, a reorientation of the director bringing

about strong changes in the optical properties of the liquid crystals such as the transmittance,

reflectance, refraction etc.[2]

Electro-optic filters make use of the above mentioned properties of liquid crystals to filter

electromagnetic waves passing through them.

In general there are many different applications of electro-optic filters but for the purpose of

this thesis studies will be limited only to Automatic Darkening Welding filters.




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Automatic Darkening Filters are filters which utilise Liquid Crystal Technology (LC-

Technology) to filter electromagnetic waves. Other applications of electro-optics include:

electro-optic shutter, electro-optic light modulation and acousto-optic beam deflection.

2.1.2 Twisted Nematic Liquid Crystal Cells

In the absence of an external voltage across a liquid crystal sample the molecules turn to bend

around their axis given rise to a twist angle (θ). Depending on the angle we can identify 4

different types of twists:

θ = 90o the standard 90o twisted nematic cell is form

θ < 90o gives rise to the low-twist (L.T.) cell

90< θ ≤ 180 we have high twist cells

θ > 180o we have the super twist cells.

For the purpose of this project we shall be limited only to the standard twisted nematic with a

twist angle of 90o.

Based on the director distribution, it is possible to derive the electro-optical response of

nematic liquid crystal cells (such as birefringence), rotation of polarization plane of incident

light, total internal reflection, or some other important characteristics of the cell [3]. In order

to understand the optical characteristics of a liquid crystal layer in the electrically controlled

birefringence (ECB) effect, let us consider Figure 2.1, with the initial homogenous director

oriented along the x-axis (θ = 00, no twist).




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Fig 2.1[3] Homogenous (S-effect)

If the applied voltage is below the threshold, the nematic liquid crystal layers manifest a

birefringence of

∆n = ne – no = n - n (1)

When the field exceeds its threshold value, the director deviates from its orientation along the

x-axis while remaining perpendicular to the y-axis. Therefore the refractive index of the

ordinary ray remains unchanged no = n, while at the same time, the refractive index of the

extraordinary ray (ne) decreases, tending towards no.

The relationship between the magnitude of ne and the angle of orientation of the director θ (z)

is shown below:

ne(z)= neno/√ (ne2sin2θ(z) + no

2cos2 θ (z)) (2)

Also the intensity of the light passing through the cell depends on the angle(φo) between the

polarization vector of the incident beam and the initial orientation of the director of the

nematic liquid crystal. This relationship is shown in the following formula:

I = Iosin2φosin2(∆Ф/2) (3)




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Where Io = Intensity of plane polarised light incident on cell

∆Ф = Change in phase difference

The effects of phase modulation for an initial planar orientation of the director (along x) with

positive dielectric or diamagnetic anisotropy (∆є, ∆X >0) and with the field applied along the

z-axis (see figure 1.1 above) is called the S-effect because , though a bend deformation is

introduced above the threshold, the initial deformation is a splay deformation.

The applied field causes a phase difference to arise between the ordinary and the

extraordinary rays and the intensity of the light oscillates according to eqn. (3) above.

In the case when the bend deformation is in the initial stages of its development (Fig 2.2) the

corresponding electro optic effect is called the B-effect, and takes place for negative values of

the dielectric anisotropy ∆є <0

Fig 2.2 [3]Homeotropic (B-effect)

However the final orientation of the director is not defined (degenerate), and the sample does

not remain monodomain and contains specific defects (umbifics) [3]. In principle, the

preferred direction of the final orientation of the director can be established and these defects

in the structure eliminated by special preparation of the surfaces with a slight pre-tilt.




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There is also another twist effect caused by a pure twist deformation shown in fig 2.3 below.

The electro-optical or magneto-optical effect corresponding to this geometry is called the T-

effect and is most amendable for theoretical analysis and less suitable for experimental

investigations since the filed induces biaxiality in the nematic liquid crystal.

Fig 2.3 [3]Homogenous (T-effect)

Since the Optic filter in this project operates within the conditions of the S-effect (∆є, ∆X >0)

we shall limit our discussion within this region.

The above discussion about ECB effects leads us to a fundamental problem of switching time.

2.1.3 Switching Time

In order to address this problem we need to specify conditions under which we can have

full switiching from Imax to Imin with minimal response time.

According to (3) such a switching is stipulated when the phase difference ∆Ф is changed as

much as π. When a voltage U is applied across a nematic cell corresponding to a maximum

intensity Imax , then to attain another state with Imin we have to supply an additional voltage Uл

≥ ∆U, where ∆U is the minimum possible value of Uл (see figure 2.4 below)




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Fig 2.4[3] Electrically controlled birefringence in homogenous liquid crystal cell (S-effect).

Polarizer (P) is crossed with the analyzer (A) and set at the angle φo with respect to the initial

liquid crysral director. Below the intensity / of the transmitted light and phase, difference –δ are shown versus the applied voltage. The phase π switching regime is indicated, which result

in the variation of the intensity from Imax to Imin.

Times ζл which correspond to the total intensity variation Imax ↔ Imin decreases with increasing

applied (bias) voltage U, and pass through a minimum at the intermediate voltages U≈1,3US,

where US is the S-effect threshold voltage (see fig. 2.4 above). For large amplitudes of a

switching pulse Uл >> ∆U, the reaction times for a phase lag change by л : ζr(л) can reach the

values of 20 microseconds at room temperature.

As a result of the low-frequency relaxation of є, the three to four orders of magnitude

larger off-times can be decreased to the value of ζr(л), as the dielectric anisotropy of the liquid

crystal becomes negative at a certain frequency. Hence it is possible to address the cell with a

high frequency signal and to force the director to rotate rapidly into the homogenous “off”

configuration. The minimal times of the total switching cycle, Imax → Imin → Imax , obtained in

the S-effect with the double frequency addressing technique, attained 40-50 microseconds at

room temperature. A further decrease of response times is very difficult due to the appearance

of defects in thin nematic cells at high voltages, which hinder fast electro-optic switching in

the S-effect[3].

The main disadvantage of the S-effect for display applications is the strong dependence of

the transmitted intensity on the light wavelength and the non-uniform transmission-voltage

characteristics at oblique light incidence. However, it is possible to avoid them by placing a

compensating birefrigent plate between the liquid crystal cell and one of the polarisers or by

using two nematic S-cells in series that have perpendicular initial directors.




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Special attention should be paid to the so called л cells, when the birefringent intensity is

switched in the last fall of the oscillation curve (see fig. below). In this case, the switching is

attained due to very slight variation of the director distribution within the narrow regions near

the boundaries, thus resulting in a very fast response speed. The corresponding switching

times can be estimated according to the formula [3]:

ζ≈ (∆/л/2л)21/(1 - βUл/Uo)2γ1λ2/K11∆n2 (4)

Where (∆/л)≈1 is a relative phase difference for the last intensity fall and β≈1 is the liquid

crystal material constant. As we may see the response time does not depend on the cell

thickness. Combining л cells with phase retardation plates, both with positive and phase shifts,

it is possible to optimize a contrast and colour uniformity of the liquid crystal cell. The

contrast ratios of 50:1 and more can be obtained for viewing angles of about 20o from normal

to the cell.

We also have some characteristics induced by the B-effect, but will not be discussed in this

project.

2.1.4 Twist Effect

If the directions x and y of the planar orientation of the nematic liquid crystal molecules on

opposite electrodes are perpendicular to each other and the material has a positive dielectric

anisotropy ∆є>0, then when an electric field is applied along the z-axis (see figure 2.5) a

reorientation effect occurs, which is a combination of the S, B, and T deformations.




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Fig 2.5 [3] Diagramatic representation of the twist effect

In the absence of the field, the light polarization vector follows the director and, consequently,

the structure rotates the polarization plane up to the angle characterizing the structure φm = л/2

(see fig 2.5). This specific waveguide regime (the Mauguin regime) takes place when[3]

∆nd / λ >> 1 (5)

When the applied voltage exceeds a certain threshold value

Utw= л[л(4K11 + K33 – 2K22)/∆є]1/2 (6)

The director L deviates from the initial orientation so that the linear dependence of the

azimuthally angle φ (z) disappears and the tilt angle θ (z) becomes nonzero (see fig 2.7). The

qualitative character of functions φ (z) and θ (z) for different voltages is shown in figure 2.6.




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Fig 2.6[3] Distribution of the Director angles θ (z) and φ (z) in the twist effect for different

voltages U : (a) U ≦ Utw ; (b) Utw < U1 < U2 < U3.

Since the director tends to orient perpendicular to the substrate, the effective values of ∆n

decreases and, for a certain voltage (optical threshold of the twist Uopt), the waveguide regime

no longer remains. Let us note that, despite the fact that the director starts to reorient at U =

Utw, a visible change of the twist cell transmission is observed only for U = Uopt > Utw (see fig

2,8)

Figure 2.7 gives the dependence of the optical transmission of a twist cell for both the

conventional geometry PL(0) and when the polarizer P forms an angle 45o with respect to

the orientation of the director at Z = 0.




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Fig 2.7[3] Optical response of the twist-cell between parallel polarizers: curve 1: polarizers

are parallel to the director on the input surface of the cell (conventional orientation); curve 2:

polarizers at the angle of 45o to the director on the input surface (maximum birefringence

intensity); curve 3: phase retardation calculated from curve 2

The deformation threshold, Utw = 6V, determined by extrapolating the linear section phase

delay curve to ∂(U) = 0, coincides with that calculated from (6). The optical threshold for twist

effect increases with decreasing wavelength (Uopt = 8,9V and 10,2V for λ=750 and 450nm

respectively), since the cut-off implied by the Mauguin condition (eqn. 7) occurs at a higher

voltage for shorter wavelengths (eqn 5)

∆nd / λ = (4m2 – 1)1/2 / 2, m = 1, 2, 3, … (7)




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2.1.5 Dynamics of Twist Effect

The response of a twist cell to an external voltage pulse has been studied by a number of

workers:[2]. A typical oscillogram of the switching effect under conditions in which the

external voltage does not greatly exceed the threshold value (2,5 times greater) is shown in Fig

2.8 (curve 2).

Fig 2.8[3] Oscillogram for switching on (A, resolution of 100 ms per division) and

oscillogram for switching off (B, resolution of 1 s per division) for twist effect ( the cell is the

same as in Fig. 2.7). (1) Voltage pulse, f = 1 KHz, U = 25 V ; (2) twist effect, output for the

ray polarized parallel to the director when z = 0; and (3) output for a cell rotated through 450

around the direction of the beam

Another curve (curve 3) is superimposed on the same oscillogram showing the response of

the same twist cell rotated through an angle of 45o ( about the normal) to the light polarization

vector, so that the phase lag for the exit ray with elliptical polarization can be recorded. By

comparing the oscillograms it can easily be seen that the rise and decay times of the optical

response in the twist effect are significantly less than the corresponding times for deformation

of the layer.

However, qualitatively, the times for both the twist effect and the layer deformations are

proportional to the viscosity and to the square of the thickness, and inversely proportional to

an elastic constant. Also the rise times are inversely proportional to the difference (U2 – Utw2)

[2]..

For higher applied voltages, the edge of the twist effect oscillograms develops a

characteristic bounce. This effect is accounted for theoretically by allowing for the backflow.




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The point is that, in the initial stages of relaxation, the maximum elastic torque is found in the

region of rapid change in θm with the z-coordinate in the vicinity of the walls as in the ECB

effect.

The greatest rate of reorientation of the director also occurs in this region, inducing the

maximum associated flow of the liquid. This flow influences the director in the layer centre in

such a way that the angle θm increases (to values above π/2). As relaxation proceeds, the

backflow decreases and the director can return to its initial state (θm ～ π/2) under the elastic

forces. This corresponds to the maximum transmission of the cell (a bounce of the rear edge).

Relaxation then continues until θm = 0.

There is also the possibility of decreasing the twist-effect relaxation times by applying a field

with a frequency greater than that at which the dielectric anisotropy changes sign. The best

earlier result in this dual-frequency addressing scheme [2] were achieved by Rayans and

Shank (a 100% modulation of the light with a frequency of 25Hz). This frequency can be

increased by a factor of 20. However, higher operating voltages and a limited operating

temperature range prevent the dual frequency addressing scheme from finding commercial

application.




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2.2. Introducing the Optics of the Eyes

Since this project concerns hazards caused to the eyes from exposure to harmful radiations, it

is very important to understand those aspects of the eyes that are directly concerned.

2.2.1 Human Factors

Human factors or ergonomics is concerned with the way a product is made for a productive

and healthy interaction between a human being and a machine. Human factor engineers

approach the problem of human interface to a machine by assuming that the human is an

instrument whose complex design is complete and unalterable- a design to which a product

must link in order to get optimum exchange of information [4]. As applied to LCDs and other

information displays, emphasis will be placed upon three areas within the broader discipline of

human factors.

a) Anthropometry

For optimization of product properties, the physical configuration of systems needs to

match the physical capabilities of the users. Anthropometric scientific data is available in the

form of detailed tables and charts indicating the range of human body dimensions from small

female (5th percentile) to large (95th percentile), that can be applied to the products for

optimization.

b) Sensory

Sensory human factors determine the characteristics of the products that output or input

information to the human system with emphasis on visual, auditory and colour applications,

voice I/O, touch panels etc. Available information on sensory capacity is much less complete

than for anthropometry.

c) Cognitive

Cognitive human factors involve the use of human mental capability and capacity to design

systems. Some examples include menu configuration and lay out, error handling and

messaging. The cognitive area has the weakest database. With increasing intelligence of

electronic instrumentation, the demand for more research into the cognitive area also

increases.




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2.2.2 The Electromagnetic Spectrum and the Capabilities and Limitations of the Human

Visual System

We perceive objects by light coming from them and their surroundings into our eyes. Light

is that part of the electromagnetic spectrum (see fig 2.9 on page 19) which has the ability to

produce response in photoreceptors of the human eye and hence visual sensation. Different

individuals have different levels of sensitivity to the electromagnetic spectrum, as a result of

which, there are no precise boundaries denoting the wavelength range of light. For scientific

analysis, this range is commonly taken as 380-780 nm. Under certain conditions some

observers can see an even broader range (i.e. 360nm-830nm) of the electromagnetic spectrum.

However the extremely precise boundary is not very critical as the human eyes has maximum

sensitivity at ~555nm and has extremely low sensitivity outside the 400nm-700nm range.

Different regions of this visual spectrum exhibit different colours (fig 2.9 on page 19).

The human visual system is an incredibly complex optical instrument in which the stimulus, a

constantly changing pattern of light, is transformed into a response, a pattern of electrical

signals that travels along the optical nerve, where they produce the perception we call

seeing[4]. The operation of the eye involves optics, photochemistry, neurobiology and

electrophysiology. Light rays from the object strike the cornea and thereby are nearly focused

on the retina. Fine focusing is achieved by the lens. As the distance between the lens and the

retina is fixed in the human eye, precise focusing is achieved through accommodation

(changing the optical power of the lens). If the light intensity is high, the iris diaphragm

contracts so that the pupil becomes small and only the centre of the lens is used. The central

part of the lens gives the sharpest image.




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Fig 2.9 Electromagnetic spectrum (courtesy of Burle Industries, Inc.)




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2.2.3 Spectral Sensitivity and Hazard Weighting Functions of the Human Eye

The human eye is characterised by different response functions depending on the particular

aspects on investigation.

For the purpose of this project discussion will be only about 3 different types of response

weightings and their significance.

a) Photopic Response Function

A luminous efficiency function represents the eye’s sensitivity to the visible spectrum as a

function of wavelength. Sometimes it is also called a relative luminous efficiency, luminosity

or sensitivity function. Luminous efficiency function forms the basis of present day

photometric measurements. The photopic (V(λ)) relative luminous efficiency function gives

the ratio of the radiant flux at wavelength λm to that at wavelength λ, when the two fluxes

produce the same photopic luminous sensation under specified viewing conditions[4]. λm is

chosen such that the maximum value of this ratio is unity. For photopic or daylight vision λm

is taken as 555nm where the eye has maximum photopic sensitivity (see fig 2.10 (a) below).

Spectral Weight Distribution Function

0

0,2

0,4

0,6

0,8

1

1,2

0 200 400 600 800 1000

λ(nm)

V(λ

)

V(λ)

Fig 2.10 (a) Photopic Relative Luminous Efficiency curve




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0,0001

0,001

0,01

0,1

1

0 200 400 600 800 1000

λ(nm)

V(λ

)

V(λ)

Fig 2.10 (b) Photopic Relative Luminous Efficiency curve (logarithmic scale)

This indicates that the eye is most sensitive at a small interval range for which this is the mid

point, but the sensitivity drops to zero as the wavelength moves further away from this point

on either sides as shown on the graph. Fig 2.10 (b) shows V(λ) plotted on a logarithmic scale.

b) Blue Light Hazard Response Function

This is the hazard response function that describes the hazards caused to the eye within the

wavelength range of 300nm to 700nm. The main type of hazard in this region is the

photoretinitis and affects mostly the eye retina. It is mathematically characterised by B(λ), a

dimensionless spectral weighting function taking into account the wavelength dependence of

the photochemical injury caused to the by blue light radiation[5]. This distribution is shown on

the graph below (fig 2.11 (a)) and it is used in calculating the effective blue light radiance (LB

see eqn 17 of chapter 3) expressed in watts per square metre per steridian [Wm-2sr-1].




Akoto Chama Leonel

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0

0,2

0,4

0,6

0,8

1

1,2

0 100 200 300 400 500 600 700 800

λ(nm)

B(λ

)

B(λ)

Fig 2.11 (a) Blue Light sensitivity curve


0,001

0,01

0,1

1

0 100 200 300 400 500 600 700 800

λ(nm)

B(λ

)

B(λ)

Fig 2.11 (b) Blue Light Sensitivity curve (logarithmic scale)

Observe that the peak of the hazard occurs when λ~440nm. This indicates that more injury is

sustained at a small interval range for which this is the mid point, but the hazard drops to zero

as the wavelength moves further away from this point on either side. Fig 2.11 (b) shows B(λ)

plotted on a logarithmic scale.

c) Visible and IRA Hazard Response Function

This is the hazard response function that describes the hazards caused to the eye within the

wavelength range of 380nm to 1400nm. The main type of hazard in this region is the retinal

burn and affects mostly the eye retina. It is mathematically characterised by R(λ), a

dimensionless spectral weighting function taking into account the wavelength dependence of

the thermal injury caused to the eye by visible and IRA radiation[5]. This distribution is




Akoto Chama Leonel

Page 25(128)

shown on the graph below (fig 2.12 (a)) and it is used in calculating the effective visible and

IRA radiance (LR see eqn 23 of chapter 3) expressed in watts per square metre per steridian

[Wm-2sr-1].


0

2

4

6

8

10

12

0 200 400 600 800 1000 1200 1400 1600

λ(nm)

R(λ

)

R(λ)

Fig 2.12 (a) Visible and IRA sensitivity curve


0,01

0,1

1

10

0 200 400 600 800 1000 1200 1400 1600

λ(nm)

R(λ

)

R(λ)

Fig 2.12 (b) Visible and IRA sensitivity curve (logarithmic scale).

Observe that the peak of the hazard occurs when λ is in the approximated interval of 435nm to

440nm. This indicates that more injury is sustained at a small interval range for which this

interval is a subinterval, but the hazard drops towards zero as the wavelength moves further

away from this range on either sides. Fig 2.12 (b) shows R(λ) plotted on a logarithmic scale




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2.3 Welding and the Emission of Electromagnetic Waves

The arc welding process is usually characterised by the emission of electromagnetic waves

which may cause damage to the human eye or skin if not properly protected. Welding is

essentially the process of unifying two or more pieces of metal at faces rendered plastic or

liquid by heat or by pressure, or by both. In this chapter we shall talk on two types of gas

metal-arc welding processes. Some spectral would then be analysed with respect to the

spectral sensitivity curves in the previous chapter to understand the level of threat they pose to

the unprotected eye.

Generally there arc welding process involves the flow of electrons through an ionised air gap

between an electric circuit and the welding substrate. Due to ionisation, the electrons become

displaced from their mean position with some moving to lower energy levels within the atoms

of the substrate. This change in energy level is characterised by a corresponding release of

energy as electromagnetic waves. The colour intensity of the arc perceived by the human eye

varies according to the frequency of the electromagnetic radiation, which in turn is dependent

on the type of atoms present in the air gap and which varies with different types of gases.

2.3.1 TIG Welding

The generally adopted name for Gas Tungsten-arc welding is TIG welding. In TIG welding an

electric arc is struck between a tungsten electrode and the workpiece, the arc being surrounded

by an inert gas[6]. The electrode may consist of pure tungsten or may be alloyed with

approximately 2% thorium. The arc is initiated through a spark generated by high frequency

voltage across the air gap between the electrode and workpiece. The spark ionises the air gap,

which enables the main arc to be struck without short-circuiting the arc column. The current is

supplied to the electrode via a contact tube within the torch. Filler metal when required is fed

to the arc by separate means.

2.3.2 MIG/MAG Welding

Gas metal-arc welding (MIG/MAG welding) is welding by which an electric arc is struck

between a continuously fed consumable electrode and the work piece[6]. The current is

transferred to the electrode through a contact tube within the welding gun. The contact tube is

connected to the positive pole of the DC circuit. The electrode is continuously fed by means of

an automatic wire drive unit, melts in the arc and is transferred to the weld pool in the form of

droplets.




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2.3.3 Analysis of Some Electromagnetic Spectra with respect to the Sensitivity Curves

In order to give an impression of the variability of the emission spectra of welding arcs in

dependence on the welding material, the shielding gas and the welding current,[7] the

following figures 3 to 6 are shown:

Fig 2.13 Welding arcs [7]

We shall now use the above spectra to understand the meaning of potential hazard level with

respect to the sensitivity weight functions in the previous chapter. Since V (λ) gives the

photopic sensitivity of the eye, that will not be discussed here, since this does not give a

measure of the potential hazard from electromagnetic radiations.




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A) Wavelength Range 300nm to 700nm:

On average, all four spectra show a significant amount of electromagnetic radiations (blue

light) in this region which implies that they pose a potential threat to the unprotected eye. In

this range, figure 4 shows very strong emission spectra when steel is welded with covered

electrodes. Observe that at approximately 440nm (or some small interval for which this point

belongs), the spectral emission is strong enough, hence according to the blue light hazard

response function (chapter 2), they eye is likely to be damaged. The extent of this damage will

be understood more clearly as we go through the chapters ahead. Figure 3 exhibits a line

spectrum in the whole spectral range due to aluminium and magnesium emission, thus

portraying an almost equal radiation level within this range. Because B (λ) drops to zero as we

move away from 440nm, the potential threat will likewise reduce in the same manner, but the

high sensitivity at 440nm makes it a candidate for investigation. Figure 5, shows a slowly

increasing line spectrum. As B (λ) is maximum at approximately 440nm, this implies that they

eye will also be affected by this spectra. And finally figure 6 shows a significant increase in

spectral irradiance at very low wavelengths but drops at we move to 700nm. At 440nm, the

spectral irradiance is low compared to the proceeding wavelengths though still high enough,

and because of the behaviour of B (λ), there is a likely hood of a potential threat, hence should

be investigated.

B) Wavelength Range 380nm to 1400nm:

Similar as in section (A) all four spectra show a significant amount of electromagnetic waves

in this region, thus posing potential hazards threats to the unprotected eye. Figure 4 shows an

initial strong line emission but gradually becomes a line spectrum. According to R (λ) the eyes

has its maximum sensitivity within the approximate range of 435nm to 440nm. And because

this spectrum is significant within this sub interval, it poses a potential threat to the

unprotected eye. The high and almost equal spectral irradiance of figure 3 across the entire

interval and the maximum sensitivity of R (λ) within the subinterval also make it potentially

hazardous to the unprotected eye. Within the subinterval of maximum sensitivity as shown by

R (λ), figures 5 and 6 still stand as potentially dangerous because though within this interval

the spectra is not maximum, it is still high enough to attract attention and a further

investigation.




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2.4 Speedglas and the LC-Technology

2.4.1 Automatic Darkening Welding Filters

Fig 2.14 (a) Welding Helmet Fig 2.14 (b) Filter Unit

Shown above left (fig. 2.14 (a)) is the welding helmet with the filter integrated on it and on the

right (fig. 2.14 (b)) is the filter unit showing the electric circuitry that supplies the external

field to the glass laminate.

This shows a product that utilizes a particular application of LC-Technology. The basic

principle of the filter unit could be described simply as:

Utilizing liquid crystal cells in combination with polarizing sheets (fig. 2.16) to filter

electromagnetic waves. The filtering unit serves as an optical shutter which can be rapidly

switched between a light and a dark state upon application of a stimulating voltage.

The light wave detectors(optical weld detectors), (Fig 2.20 ) positioned around the unit serve

as sensors for the incoming radiation. When incoming radiation is detected by the sensors, the

electric circuit is triggered to produce an electric field which in turn alters the optical

properties of the liquid crystal molecules, thus affecting the transmittance of the unit. In the

absence of any radiation the unit switches back to the light state.

In the place of the conventional fixed shade welding filter which consists of a robust piece of

coloured glass hand-held or fastened in a helmet design in front of the eyes[8], the automatic

darkening welding filter based on LC-Technology is today gaining more grounds in the

welding process. This is because the former has got many limitations, some of which include

the prior adjustment or positioning of the working material. In order for the welder to have a

good vision of the working material, the filter must be moved away from the line of sight.

This movement may pose little or no problem for the hand-held filter, however, filters




Akoto Chama Leonel

Page 30(128)

attached to the helmet may achieve this either by having a dual lens with one part possessing a

high optical transmission and the other part being very dark, or by having a lens that can be

pivoted away when not in use. Some limitations with the fixed shade welding filter include:

the welder must change his/her view point of the substrate in order to bring the dark part of

the lens into the line of sight or the usage of one hand to either hold or adjust the equipment

already in place, thereby releasing the work material. One other limitation of these type of

filters is that they are unable to provide complete protection against accidental weld-flush or

the radiation emitted from neighbouring workers as is the case in lager working areas where

several welders and simultaneously based.

Some of the advantages of the automatic darkening welding filter over the conventional fixed

shade welding filter are enumerated below:

This unit is integrated in the helmet and displays a high transmittance level prior to welding;

enabling the operator to position his work correctly. [8]

When the welding arc is ignited, the electronics detect the presence of harmful radiations, and

consequently switches the unit into a pre-set dark protective state within a switching time

around 0.1ms to prevent any eventual eye damage. At the end of which in the absence of

harmful radiations the unit is switched back into the light state for clear vision. The hands also

remain free at all times and the unit sits permanently in place, protecting the welder at all

times.

2.4.1.1 Glass Laminate

A general construction of a liquid crystal cell is shown in the figure 2.15 below. The

thin layer of liquid crystal material sits alternatively between polarizing sheets (fig 2.16)

which in tend sits between two glass plates that are joined together around the edges with a

strong epoxy. The inner surfaces of the plates are coated with a thin transparent conducting

oxide film in order to enable an electric field to be applied across the active crystal layer. By

overlapping the two glass plates such that a small part of the inner surfaces are exposed along

opposite edges, electrical contacts can be made (see fig 2.15).

Fig 2.15 LC-cell




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Page 31(128)

The figure below shows the layers of the optic glass:

Fig 2.16 Composition of glass laminate (LC-cell) showing the different components

a) LC Cells and Polarisers

As shown on the figure below, depending on the structure of the cell, pure nematic materials

can display induced twisting helixes with both the positive and negative senses of rotation.

However liquid crystal eutectic mixtures are often doped with small quantities of cholesteric

components possessing a natural helical stacking structure with a specific direction of

orientation (fig 2.17). This property defines the spontaneous spiralling direction for the overall

cell and hence prevents the formation of domains or regions of crystal where a reverse twist of

270o occurs instead of the required 90o structure. In the limit of large cell thickness, a helical

structure is capable of rotating the plane of linearly polarised light with nearly 100%

efficiency [8].

The two polarizing sheets are arranged such that they have a angular difference of 90o as

shown on the figure 2.18 b and c below. The sheet on the side of the incident radiation

polarizes the incident light which is then twisted through an angle of 90o by the LC-cell in the

absence of an electric field (fig 2.18 b). This twisted light emerges on the other side of the

glass through the rear polarizing sheet. Notice that there is 100% transmittance of the light that

has been transmitted through the first polarizer and also notice that the arrangement of the

second polarizing sheet corresponds with the path of the twisted light on fig 2.18(b). In the

presence of an applied voltage (fig 2.18 (c)), an external field is created which turn to align the

liquid crystal molecules thereby reducing the twisting effect of the LC cells. This reduction is

in relation to the applied voltage. A minimum twist will occur at a maximum applied voltage

and vice versa. When welding light is detected by the sensors a predefined amount of voltage

LC cells

UV/IR Filter

Polarizers Outer

Protective Plate

Inner Protective Plate




Akoto Chama Leonel

Page 32(128)

is applied to the LC cells to give the selected dark shade. Fig 2.18 (c) shows the case where

the twist effect has been completely removed by the external field.

Note that the inner surfaces of the LC glass plates are usually quoted with a very thin layer of

polyimide which is deposited on top of a transparent conducting oxide layer (the oxide layer

covers the two glass plates during manufacturing). This polyimide layer causes the liquid

crystal cells to adhere permanently and align on the surfaces. Thus the external field does not

very much affect the LC cells as you move closer and closer to the glass surfaces.

Fig 2.17 Helical Stacking structure showing twist angle of 900 of the TN cell

Fig 2.18 (b) Behavior of cell in the absence of applied voltage




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Page 33(128)

Fig 2.18 (c) Behavior of cell when voltage is applied

b) UV/IR Filter

This filter offers permanent protection from ultra violet and Infra Red radiation with a very

high efficiency of almost 100%.

Fig 2.19 UV/IR Filter

The incident IR radiations are permanently reflected as the come into contact with this filter.

Since the filter is permanently in place, the eye is protected at all times. As shown in fig 2.16

it is placed before the first polarizing sheet so that the incident UV/IR radiations are reflected

without any obstruction before the transmitted light is polarized and twisted. Since the other

components are sensitive to heat and also because the liquid crystal molecules are sensitive to

UV light the UV/IR filter is placed in front to prevent any transmission of the UV rays.

Glass substrate

IR light

99.99% reflected/ absorbed

UV light 99.9997%absorbed/reflected by UV/IR

filter and polarising filters




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2.4.1.2 Electronic Circuitry

Fig 2.20 Electronic circuitry connected to the glass laminate

Above is a picture of the electronic circuitry connected to the glass laminate through the wires.

The controlling electronics have the function of detecting whether or not welding is in process

and to apply the appropriate voltages to the liquid crystal cells present in the glass laminate. In

principle the electronics consist of 3 parts; the detectors that take in information from the

environment, the logic circuit that makes decisions depending upon the input information and

the power supply that operates the system and is connected or disconnected from the cell.

The most basic control components of the electronic circuit is the A and NA (negative-A)

terminals connected to the A-cells in the glass laminate. As shown on the square waveform

graph below, in the light state, the voltage drop across the LC cells is zero. When the optical

weld detectors, detect the presence of radiation, information is sent to the logic circuit, which

in turn inputs a very fast and high voltage of about 40V across the glass laminate lasting for a

period of about 4ms.This high voltage serves as the voltage required for a fast switching from

the light state to the dark state. Immediately after the initial peak voltage, the LC cells are

discharged and are then driven with a low DC-voltage that reverses polarity with a periodicity

of 12ms.




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Page 35(128)

After the switch from the light state to the dark state, the voltage amplitude at A now drops to

a lower steady value (in this case we consider 3.5V) as shown on the first graph and an

approximate wave periodicity of 24ms.

Note: that for a darker state after switching has occurred, the steady amplitude voltage value

would be greater and vice versa.

At the same time as shown on the second graph the voltage drop across the NA terminal is 0V

from the light state until after the A-cells have been completely discharged. From this point

onwards (within the dark state) the voltages across the NA-terminal continues with the same

steady amplitude and frequency as that of the A-terminal but completely out of phase and

reversed polarity.

In the absence of radiation the voltage across both terminals fall back to zero and the glass

laminate becomes transparent again. This cycle continues every time in the welding arc is

ignited.

Note

1) Observe that for the first two graphs the voltage is either zero or greater than zero, because

the observation is done independently from a grounded terminal which is common to both the

A and NA terminals

2) The last graph shows a superposition of the voltage drop across the A and NA terminals,

which shows the way the voltage is fed across the LC cells alternatively. Observe that with a

DC-supply, the voltage it made to reverse polarity, thus behaving like an AC source (thanks to

the parallel connection between the A and NA terminals. This intermediate reversing in

polarity is important to prevent any eventual sticking of the LC molecules or ions which may

be present in the cell.

3) The first graph shows a lag in time of about 4ms. This does not mean that the switching

occurs 4ms after the welding arc is ignited, but rather shows an initial time when the welding

arc has not yet been ignited. Within this time the glass laminate is in the light or transparent

state. The actual ignition of the welding arc occurs at 4ms at which time the 40V is fed into

the A-terminal for immediate switching.




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Page 36(128)

Fig 2.21 (a)Above: Voltage drop across A-Terminal; Below: Voltage drop across NA-

Terminal

Fig 2.21 (b) Voltage drops across A and NA terminals plotted on the same axes.

Voltage/Time

0

2

4

6

8

10

0 8 16 24 32 40 48 56 64 72 80 88

T(ms)

Voltage(V

)

NA [V]

Voltage/Time

0

5

10

15

20

25

30

35

40

45

0 8 16 24 32 40 48 56 64 72 80 88T(ms)

Voltage (V

)

A [V]

Light State Dark State

4ms

4ms

Voltage/Time

-10

-5

0

5

10

15

20

25

30

35

40

45

0 8 16 24 32 40 48 56 64 72 80 88

T(ms)

Vo

ltag

e(V

)

A [V]

NA[V]




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2.4.1.3 Switching Time

Making use of the proper definition of the switching time applied to automatic darkening

welding filters[9], the switching time stipulated in eqn. 4 transforms to:

t(ζ=3*ζd)

Ts = (1/ζ1)* ∫ζ(t) dt (8)

t=0

Where ζ d = transmittance at the dark state

ζ l = transmittance in the light state

Normally the application of the above formula could be described according to the picture

below(fig 4.9 applied to a welding filter with different shades):

Page 3

50-300 ms0,1 ms

Fig 2.22 Switching time sequence

As depicted in the picture above the numbers show the different shades of the product. Shade

5-6 are the offset shades i.e. when the product is not in use. When the product is switched on,

the shade moves to the light state (the pictures below each region shows how the welder

perceives his/her object). When the welding light is ignited the product switches to a pre-set

dark state between 9 and 13 within an approximate switching time of 0.1ms. During this time




Akoto Chama Leonel

Page 38(128)

the welder is completely protected from harm. When the welding arc is switched of, the

product then switches back to the light state with a switching time between 50-300ms.

If the filter fails to switch we say that switching failure has occured. Examples of situations

that might result in switching failure include the following:

• Wrong setting of parameters by the user

• Detectors being hidden from the welding arc

• Low battery

• Poor detector functionality

Note: For the purpose of this project 0.5s of switching failure was considered in the

investigation. This was because the blink reflex is often mentioned as 0.25 s, hence 0.5 s gives

some error margin. However, if the welding filter fails to switch several times, a longer time

perhaps should be considered.




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3 Execution

3.1 Comparison of Different Standards

3.1.1 Introduction



radiations were more stringent than they really should have been. These restrictions which

were stipulated in the 1999 Technical Report of the International Electro technical

Commission (IEC) [10] were more restrictive than the most recent investigated permissible

exposure limits of the eyes [5]. As a result of which this comparative study was carried out

between the 1999 Technical Report, 2007 IEC International Standard [11] and the 2006

Directive of The European Parliament and of The Council of 5th April 2006 to show clearly,

the extent to which they differ.

The conclusions drawn from this study were as a result of comparing the MPE limits of the

exposure of the eyes to harmful radiations within the wavelength range from 180nm to

1400nm for both incoherent and coherent sources of radiation irradiating the eyes.

The technique employed was analytic and graphical where the MPE’s from both documents

were either analyzed mathematically or plotted graphically against exposures times between

10-9s to 3x104s for incoherent sources and 10-13 s to 3x104 s for coherent sources, and

analyzed to come out with logical conclusions.

The tool used in this analysis was Microsoft Excel program.

Unless otherwise stated the terms and formulae used in this analysis remain the same as those

used in the 2006 Directive, the 1999 IEC Technical Report and the 2007 IEC International

standard

The main assumption which was made in this study (unless otherwise stated) was that, where

ever possible within each sub interval of comparison, the minimum MPE of the 2006

Directive was compared with the maximum possible MPE of the 1999 Technical report. Also

the size of the object illuminating the eye was considered to be a point source.

Here the analysis shall begin with the incoherent radiation MPE’s followed by the analysis of

the coherent radiation MPE’s.

Note: Since only the incoherent part of the radiations is harmful to the eyes it is expected that

the same conclusion be drawn for the case of coherent radiations.

The comparison will be done using any of the following quantities in different time intervals:

Effective Irradiance, radiant exposure, effective radiant exposure, effective radiance etc.




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3.1.2 Comparison Between the Incoherent MPEs of the 1999 Technical

Report and 2006 Directive

Incoherent radiations are wave packets consisting of radiations with phase differences (out of

phase) and/or with different frequencies. Here the comparison will be done starting from the

smallest wavelength (180nm) progressively to 1400nm. Graphical analysis will only be used

in wavelength ranges which pose remarkable differences in their MPE’s, otherwise simple

logical explanations will be used to illustrate differences and/or similarities.

a) Wavelength Range 180nm to 400nm:

Source

Documen

t

Quantity and

Weighting

Function

Wavelength

(nm)

Exposure

limit value

Units Part of the

body

Hazard

IEC-1999

400nm

Heff=∑H(λ)S(λ)∆λ

180nm

180-400

(UVA,UVB

and UVC)

Heff = 30

Daily value 8

hours

[Jm-2]

Eye cornea

Conjunctiva

Lens

skin

Photokeratitis

conjunctivitis

cataractogenesis

erythema

elastosis

skin cancer

Directive

-2006

Table 1

The quantity and weighting function used in both documents are the same and the MPE is

given in terms of the effective radiance (Heff) spectrally weighted by S (λ) which is

dimensionless and takes into account the wavelength dependence of the health effects of UV

radiation on eye and skin.As shown on table 1, the MPE’s for both documents are the same

with a maximum permissible radiant exposure limit of 30 Jm-2. Hence Heff=30 Jm-2 for the

entire time interval from 10-9s to 3x104s and equal in both documents.

Conclusion; in this wavelength interval both documents specify equal exposure limits.

b) Wavelength Range 315nm to 400nm;

Source

document

Quantity and

Weighting

Function

Wavelengt

h (nm)

Exposure

limit value

Units Part of the

body

Hazard

IEC-1999

400nm

HuvA=∑H(λ)∆λ

315nm

315-400

(UVA)

HUVA = 104

Daily value 8

hours

[Jm-2]

Eye Lens

cataractogenesis

Directive

-2006

Table 2




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Page 41(128)

The quantity and waiting function used in both documents are the same and the MPE is given

in terms of the radiant exposure (HUVA), the time and wavelength integral or sum of the

radiance within the UVA wavelength range 315nm to 400nm.

As shown on table 2, the MPE’s for both documents were the same with a maximum

permissible radiant exposure limit of 40 Jm-2. Hence HUVA=40 Jm-2 for the entire time interval

from 10-9s to 3x104s.

Conclusion; in this wavelength interval both documents specify equal exposure limits.

c) Wavelength Range 300nm to 700nm:

Source

document

Quantity and

Weighting

Function

Wavelength

(nm)

Exposure

limit value

Units Part of

the body

Hazard

IEC-1999

700nm

LB=∑L(λ)B(λ)∆λ

300nm

300-700

Blue light

LB=106 /t

for t≤10000s

LB:

[Wm-2 sr-1]

Eye

retina

photo retinitis LB=100

for t>10000s

Directive-

2006

LB=106 /t

for t≤10000s

LB=100

for t>10000s

Table 3

Note: 1) For source document Directive-2006, the angular subtense (α) made by the object’s

image on the eye has been considered to be α ≥ 11mrad.

2) The range of 300nm to 700nm covers part of the UVB, all UVA and most of visible

radiation; however, the associated hazard is commonly referred to as ‘blue light’ hazard. Blue

light strictly speaking covers only the range of approximately 400nm to 490nm. [5]

The quantity and weighting function used in both documents are the same with the MPE

given in terms of the effective radiance (LB) of blue light, spectrally weighted by B(λ), which

is dimensionless and takes into account the wavelength dependence of the photochemical

injury caused to the eye by blue light radiation. The MPE’s for both documents given in terms

LB were the same with a maximum permissible radiant exposure limit distributed as shown on

table 3:

For exposure times (t) less than 10,000 seconds, LB = 106/t and for times (t) greater than

10,000 seconds the LB = 100.

Conclusion; in this wavelength interval both documents specify equal exposure limits




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d) Wavelength Range 380nm to 1400nm:

Source

document

Quantity and

Weighting Function

Wavelength

(nm)

Exposure limit

value

Units Part of

the body

Hazard

IEC-1999

1400nm

LRTH=∑L(λ)B(λ)∆λ

380nm

380-1400

Visible &

IRA

LR=41,2/(Cα.t0.9)

t≤1,8x10-5 s

LR:

[Wm-2 sr-

1]

Eye

retina

Retinal burn

LR=5.104/ (Cα.t1/4)

1,8x10-5s < t≤10s

LR=2,8.104/Cα

t>10s

Directive-

2006

LR=8,89.108/Cα

t<10µs

LR=5.107/(Cα t0,25)

10µs<t≤10s

LR=2,8.107/Cα

t>10s

Table 4

Where Cα is a correction factor describing the dependence of the MPEs on the source size.

Note: 1) For IEC-1999, Cα is taken to be Cα=1.5 so that the LR expressions would give the

maximal possible curve while for the Directive-2006 Cα=100 for a minimal possible curve (in

conformity with the assumption made in the introduction).

In this range it was observed that the formulae describing the MPEs in both documents were

the same, but they changed with different time intervals as shown on table4. As a result of

which these formulae were plotted in the Excel work sheet, resulting in the graphical

representations below (fig 3.1).

The quantity and weighting function used in both documents are the same and the MPE given

in terms of effective radiance (LR) for thermal injury, spectrally weighted by R(λ), which is

dimensionless and takes into account the wavelength dependence of the thermal injury caused

to the eye by visible light and IRA radiation.

As shown on figure 3.1 below, the MPE as described by the formulae given in the 1999 IEC

Technical Report is indicated with blue curve and that described by the formulae given in the

2006 Directive is indicated with red curve.




Akoto Chama Leonel

Page 43(128)

From observation it can be seen that the Red line offers a higher maximum permissible

exposure limit. That is for corresponding exposure times the red curve offers greater exposure

limits.

As a conclusion, the 2006 Directive offers a much higher MPE limit than the 1999 IEC

Technical report.

Incoherent MPE(380nm-1400nm)

-100000

100000

300000

500000

700000

900000

1100000

1300000

1500000

0 5 10 15 20

Exposure time (t/s)

Re

tin

al T

he

rma

l

Ha

za

rd(L

rth

)

IEC-1999Directive-2006

Fig. 3.1

Note: In evaluating the functions describing the MPE values in both documents, it was

observed that the formulae were inversely proportional to the limiting angular subtense of the

eye (Cα ) . As a result of which to obtain the maximum possible MPE of the 1999 IEC

Technical report the smallest Cα was used which was equal to Cα=1.5 mrad across the

entire time interval. The assumption made in using this value for Cα was that the dependence

of the minimum angular subtense on the exposure duration due to the time dependence of eye

movements is less than 0.7s (time<0.7s).

Likewise to obtain the minimum possible MPE of the 2006 Technical Report the maximum

possible Cα was used, which was equal to Cα=100mrad across the entire time interval.




Akoto Chama Leonel

Page 44(128)

e) Wavelength Range 780nm to 1400nm:

Source

document

Quantity and

Weighting Function

Wavelength

(nm)

Exposure limit

value

Units Part of

the body

Hazard

IEC-1999

1400nm

LRTH=∑L(λ)B(λ)∆λ

780nm

780-1400

IRA

LR=41,2/(Cα.t0.9)

t≤1,8x10-5s

LR:

[Wm-2sr-1]

Eye retina

Retinal burn

LR=5.104/ (Cα.t1/4)

1,8x10-5s < t≤10s

LR=6000/Cα

t>10s

Directive-

2006

LR=8,89.108/Cα

t<10µs

LR=5.107/(Cα t0,25)

10µs<t≤10s

LR=6.106/Cα

t>10s

Table5

Note: See note under table 4.

Similarly with the preceding range, in this range it was observed that the formulae describing

the MPE’s were the same for both documents but they changed with different time intervals

(table5), as a result of which these formulae were plotted in the Excel work sheet, resulting in

the graphical representations below (fig 3.2).

The quantity and weighting function used in both documents are the same and the MPE given

in terms of effective radiance (LR) for thermal injury, spectrally weighted by R(λ), which is

dimensionless and takes into account the wavelength dependence of the thermal injury caused

to the eye by visible light and IRA radiation.

As shown on figure 3.2 below, the MPE as described by the formulae given in the 1999 IEC

Technical Report is indicated by blue curve and that described by the formulae given in the

2006 Directive is indicated by red curve.




Akoto Chama Leonel

Page 45(128)

From observation it can be seen that, the red curve offers a higher maximum permissible

exposure limit.

As a conclusion, the 2006 Directive offers a much higher MPE limit than the 1999 IEC

Technical report.

Incoherent MPE(780nm-1400nm)

-100000

100000

300000

500000

700000

900000

1100000

1300000

1500000

0 5 10 15 20

Exposure time (t/s)

Eff

ec

tiv

e IR

Ra

dia

nc

e (

Lir

)

IEC-1999

Directive-2006

Fig. 3.2

Note: In evaluating the functions describing the MPE values in both documents, it was

observed that the formulae were inversely proportional to the limiting angular subtense of the

eye (Cα). As a result of which to obtain the maximum possible MPE of the 1999 IEC

Technical report the smallest Cα was used which was equal to Cα=1.5mrad across the

entire time interval. The assumption made in using this value for Cα was that the dependence

of the minimum angular subtense on the exposure duration due to the time dependence of eye

movements is less than 0.7s (time<0.7s).

Likewise to obtain the minimum possible MPE of the 2006 Technical Report the maximum

possible Cα was used, which was equal to Cα=100mrad across the entire time interval.

f) Conclusion

From the above analysis it can be concluded that on average and in most of the exposure time

interval compared above the 2006 Directive gives an overall higher MPE scale that the more

stringent 1999 IEC Technical report.




Akoto Chama Leonel

Page 46(128)

The next step now will be to analyze the results of the coherent radiations sources.

3.1.3 Comparison Between the Coherent MPEs of the 2007 IEC

International Standard and the 2006 Directive

Coherent optical radiations are wave packets consisting of radiations in phase. As it was the

case with the non-coherent radiations, here comparison will be done beginning from the

smallest wavelength (180nm) progressively to 1400nm. Graphical analysis will only be used

in wavelength ranges which pose remarkable differences in their MPE’s, otherwise simple

logical explanations will be used to illustrate differences and/or similarities. The comparison

will be done between the 2006 Directive and the IEC 2007 Directive.

a) Wavelength Range 180nm to 303nm:

This wavelength range will be divided in 2 parts. The first part will range from 180nm to 280

and the second part will range from 280nm to 302nm because they constitute UVC and UVB

respectively.

i) 180nm to 280nm (UVC): The MPEs in both reports were calculated in terms of radiant

exposure(H) and the equivalent irradiance(E). For exposure times less than 10-9 s, the

irradiance MPE in both reports was given as E=3x104Wm-2 , while for times greater than 10-9

s, the radiant exposure MPE limit was given as H=30Jm-2. We see here that both reports give

the same MPEs in this range.

Source Document Wavelength (nm) Duration(s)

10-13-10-9 10-9-3x104

IEC-2007 180-280

UVC

E=3x1010[Wm-2] H=30[Jm-2]

Directive-2006

Table 6

ii) 280nm to 302.5nm (UVB):




Akoto Chama Leonel

Page 47(128)

As was the case in the previous wavelength interval, the MPEs in both reports were calculated

in terms of radiant exposure (H) and the equivalent irradiance (E). For exposure times less

than 10-9 s, the irradiance MPE in both reports was given as E=3x104Wm-2, while for times

greater than 10-9 s, the radiant exposure MPE limit was given as H=30Jm-2. We see here that

both reports still give the same MPEs in this range.

Source Document Wavelength (nm) Duration(s)

10-13-10-9 10-9-3x104

IEC-2007 280-302.5

UVB

E=3x1010[Wm-2] H=30[Jm-2]

Directive-2006

Table7

b) Wavelength Range 302.5nm to 315nm:

MPE IEC-2007 table

Wavelength (nm) Exposure time (s)

10-13 – 10-9 10-9 – 10 10 – 3x104

302,5 to 315

E=3x1010

[Wm-2]

Photochemical Hazard

(t>T1) H=C2 [Jm-2]

Thermal Hazard

(t≦T1) H=C1 [Jm-2]

H=C2 [Jm-2]

Table 8

MPE Directive 2006 table

Wavelength (nm) Exposure time (s)

10-13 – 10-9 10-9 – 10 10 – 3x104

303

H=40 [Jm-2]; if t<2,6x10-9 then H=5,6x103t0,25 H=40 [Jm-2]

304 H=60 [Jm-2]; if t<1,3x10-8 then H=5,6x103t0,25 H=60 [Jm-2]




Akoto Chama Leonel

Page 48(128)

305

E=3x1010

[Wm-2]

H=100 [Jm-2]; if t<1,0x10-7 then H=5,6x103t0,25 H=100 [Jm-2]





310 H=103 [Jm-2]; if t<1,0x10-3 then H=5,6x103t0,25 H=1,0x103 [Jm-2]

311 H=1,6x103[Jm-2]; if t<6,7x10-3 then H=5,6x103t0,25 H=1,6x103 [Jm-2]



314 H=6,3x103[Jm-2]; if t<1,6x100 then H=5,6x103t0,25 H=6,3x103 [Jm-2]

Table 9

To show that the MPE limits specified by both documents are equal it suffices to show that

both tables specify equal MPE limits and this will be done by using the first table to derive the

values of the second, using Microsoft excel. Observe that the MPE specified by the second

columns in both documents are equal hence it is left to show the equality in the last 2 columns.

First we shall start by showing that the upper bound specified for values of t in the second

table is the same as the T1 in table 1:

From IEC-2007 Directive the expression for T1= 100,8(λ – 295)x 10-15s

For each wavelength, this evaluates to:

λ T1

303 2,51189E-09

304 1,58489E-08

305 0,0000001

306 6,30957E-07

307 3,98107E-06

308 2,51189E-05

309 0,000158489

310 0,001

311 0,006309573

312 0,039810717

313 0,251188643




Akoto Chama Leonel

Page 49(128)

314 1,584893192

Table 10

Which evaluates to the boundary values of t as shown on the second table. Looking now at the

expression, from IEC-2007 , C1= 5,6x103t0,25 which is equal to the expression for H in the

second table.

Finally from IEC-2007 the expression for C2=100,2(λ-295). Using excel this evaluates according

to the table below:

λ C2

303 39,81072

304 63,09573

305 100

306 158,4893

307 251,1886

308 398,1072

309 630,9573

310 1000

311 1584,893

312 2511,886

313 3981,072

314 6309,573

Table 11

Observe that these values are either equal to or very close to the values on the second table.

The difference is probably because of precision differences else they should be the same.

It has been shown that both tables are equal since we can derive one from the other, hence

they specify equal MPE limits.

c) Wavelength Range 315nm to 400nm (UVA):

Source

Document

Wavelength

(nm)

Duration(s)

10-13-10-9 10-9-10 10-3x104

IEC-2007 315-400

UVA

E=3x1010[Wm-2] H=5,6x103t0,25

[Jm-2]

H=104[Jm-2]

Directive-2006

Table 12




Akoto Chama Leonel

Page 50(128)

In this range the MPEs for both reports were calculated in terms of the radiant exposure (H)

for times greater than 10-9s and in terms of the irradiance (E) for times less than 10-9s. The

formulae used in these calculations for both report were the same and the distribution of the

MPE for different exposure times was as follows:

E=3x1010Wm-2 for times less than 10-9s and H=5.6x103t0,25 for exposure times between 10-9s

and 10s and for the rest of the exposure time, H=104Jm-2. It can be observed that the MPEs

stipulated by both reports are the same.

d) Wavelength Range 400nm to 700nm (Visible Light and IRA):

In this range the MPEs were compared in terms of radiant exposure (H) for the entire time

interval. Within this interval, the IEC range was subdivided into 4 subintervals (where

variations were observed in the MPE values) given as follows:

i) 400nm to 450nm

ii) 450nm to 500nm

iii) 500nm to 600nm

iv) 600nm to 700nm

i) 400nm to 450nm

Source

Document

Duration(s)

10-13-10-11 10-11-10-9 10-9-

1,8x10-5

1,8x10-5-10 10-102 102-104 104-3x104

IEC-2007 H=1,5x10-4

[Jm-2] H=2,7x104t0,75 [Jm-

2]

H=5x10-3

[Jm-2]

H=18t0,75

[Jm-2]

H=100

[Jm-2]

E=C3 [Wm-2]

Directive-

2006

H=1,5x10-

4CE [Jm-2]

H=2,7x104t0,75CE

[Jm-2]

H=5x10-3

CE[Jm-2]

H=18t0,75CE

[Jm-2]

H=100CB

[Jm-2]

α=110

E=1CB

[Wm-2]

α=1,1t0,5

E=1CB

[Wm-2]

α=110

Table 13




Akoto Chama Leonel

Page 51(128)

Where α= angular subtense of the eye expressed in mrads. To draw any conclusion here, we

need the values for

CB, CE and C3 in this wavelength interval.

From IEC-2007, C3=1,0. From Directive-2006, CB=1,0 and CE=1,0. Hence MPEs from both

documents are equal since their expressions simplify to the same expressions.

ii) 450nm to 500nm:

Source

Document

Duration(s)

10-13-10-11 10-11-10-9 10-9-

1,8x10-5

1,8x10-5-10 10-102 102-104 104-3x104

IEC-2007 H=1,5x10-4

[Jm-2] H=2,7x104t0,75 [Jm-

2]

H=5x10-3

[Jm-2]

H=18t0,75

[Jm-2]

H=100C3

[Jm-2]

E=C3 [Wm-2]

Directive-

2006

H=1,5x10-

4CE [Jm-2]

H=2,7x104t0,75CE

[Jm-2]

H=5x10-3

CE[Jm-2]

H=18t0,75CE

[Jm-2]

H=100CB

[Jm-2]

α=110

E=1CB

[Wm-2]

α=1,1t0,5

E=1CB

[Wm-2]

α=110

Table 14

Where α= angular subtense of the eye expressed in mrads. To draw any conclusion here, we

need the values for

CB, CE and C3 in this wavelength interval.

From IEC-1999, C3=100,02(λ-450) . From Directive-2006, CB=10 0,02 (λ-450) and CE=1,0. Hence

MPEs from both documents are equal since their expressions simplify to the same

expressions.

iii)500nm to 600nm:

Source

Document

Duration(s)

10-13-10-11 10-11-10-9 10-9-

1,8x10-5

1,8x10-5-10 10-102 102-104 104-

3x104




Akoto Chama Leonel

Page 52(128)

IEC-2007 H=1,5x10-4

[Jm-2] H=2,7x104t0,75

[Jm-2]

H=5x10-3

[Jm-2]

H=18t0,75

[Jm-2]

E=10 [Wm-2]

Directive-

2006

Thermal

Retinal

Damage

H=1,5x10-4CE

[Jm-2]

H=2,7x104t0,75CE

[Jm-2]

H=5x10-3

CE[Jm-2]

H=18t0,75CE

[Jm-2]

E=10 [Wm-2]

Photochemical

Retinal

damage

H=100C

B [Jm-2] α=110 or

E=1CB [Wm-

2]

E=1CB

[Wm-

2]

α=1,1t0

E=1CB

[Wm-2]

α=110

Table 15

Here the MPE limit value given for IEC-2007 is equal to the thermal retinal injury MPE given

for Directive-2006. Observe that for the photochemical retinal hazard, the expressions

describing the limiting values for Directive-2006 differ from the constant value as stipulated

in IEC-2007. To understand the difference a mathematical analysis is done as shown below:

The MPE limit of IEC-2007 gives E=10 [Wm-2]

Looking now at the expression given by Directive-2006 we have E=1CB

But CB=10 0,02 (λ – 450 )

Where λ=wavelength. CB is an exponential function of λ. It suffices therefore to take the

lower bound λ=500 and the upper bound λ=600 to get the minimum and maximum CB values

and hence the range of MPE limit values.

For λ=500, CB=10 and hence E=10 [Wm-2]

For λ=600, CB=100 and hence E=1000 [Wm-2]

Hence for this wavelength interval, the minimum MPE limit which corresponds to that obtain

when λ=500 is equal to 10 [Wm-2], which implies that every other MPE limiting value within

this range ≥10 [Wm-2]. Comparing this range with the limiting value E=10 [Wm-2] for the

thermal retinal damage and because the most restrictive of all limiting values applied within

an interval is considered, it is logical to consider the limiting value in this case to be E=10

[Wm-2]. Observe that this conclusion makes the limiting value equal to that specified by IEC-

2007.

Hence a logical conclusion here would be that the limiting values for both documents are

equal.

iv)600nm to 700nm




Akoto Chama Leonel

Page 53(128)

Source

Document

Duration(s)

10-13-10-11 10-11-10-9 10-9-

1,8x10-5

1,8x10-5-10 10-102 102-

104

104-3x104

IEC-2007 H=1,5x10-4

[Jm-2] H=2,7x104t0,75

[Jm-2]

H=5x10-3

[Jm-2]

H=18t0,75

[Jm-2]

E=10 [Wm-2]

Directive-

2006

H=1,5x10-

4CE [Jm-2]

H=2,7x104t0,75CE

[Jm-2]

H=5x10-3

CE[Jm-2]

H=18t0,75CE

[Jm-2]

E=10 [Wm-2]

Table 16

CE=1,0 for point sources. The hazard studied in this wavelength region is the Thermal Retinal

Damage. The observation made here is that expressions describing the MPEs are the same,

hence specifying equal limiting values.

e) Wavelength Range 700nm to 1400nm (Visible Light and IRA):

Due to many variations in the parameters this interval will be divided into 4 subintervals for

comparison.

1)700nm- 1050nm:

Source

Document

Wavele

ngth

(nm)

Duration(s)

10-13-10-11 10-11-10-9 10-9-1,8x10-5 1,8x10-5-10 10 - 3x104

IEC-2007 700-1050

Visible

& IRA

H=1,5x10-4C4

[Jm-2]

H=2,7x104t0,75C4 [Jm-2] H=5x10-3C4

[Jm-2]

H=18t0,75C4

[Jm-2]

E=10C4C7

[Wm-2]

Directive-

2006

H=1,5x10-4CACE

[Jm-2]

H=2,7x104t0,75CACE

[Jm-2]

H=5x10-

3CACE [Jm-2]

H=18t0,75CACE

[Jm-2]

E=10CACC

[Wm-2]

Table 17

In this range the MPE is expressed in terms of the radiant exposure (H) and the irradiance (E).

Here the formulae will be compared to see if the result to the same conclusion.

First we check if for these intervals the following are true:

i) C4= CACE

ii) C4C7=CACC




Akoto Chama Leonel

Page 54(128)

i) C4= CACE:

From IEC-1999, C4=100,002(λ-700)

From 2006-Directive, CA=10 0,002(λ-700) and CE=1,0 (using point sources) This implies that

CA*CC=100,002(λ-700)=C4 Hence (i) is true.

ii) From IEC-2007 C7=1 which implies that C4C7= 100,002(λ-700)

Also from Directive-2006, CC=1,0 which implies that CACC=10 0,002(λ-700)=C4C7

The above derivation clearly shows that these correction factors are the same for both

documents hence all formulae are the same. Here we conclude that both documents specify the

same MPE limits.

2)1050nm-1150nm:

Source

Docume

nt

Wavelen

gth (nm)

Duration(s)

10-13-10-11 10-11-10-9 10-9-5x10-5 5x10-5-10 10 - 3x104

IEC-

2007

1050 - 1150

Visible &

IRA

H=1,5x10-4C7

[Jm-2]

H=2,7x104t0,75C7

[Jm-2]

H=5x10-3C7

[Jm-2]

H=90t0,75C7

[Jm-2]

E=10C4C7

[Wm-2]

Directive

-2006

H=1,5x10-3CCCE

[Jm-2]

H=2,7x103t0,75CCCE

[Jm-2]

H=5x10-2CCCE

[Jm-2]

H=90t0,75CCCE

[Jm-2]

E=10CACC

[Wm-2]

Table 18




i) C7= CcCE

ii) C4C7=CACC

i) C7= CcCE:




Akoto Chama Leonel

Page 55(128)

From IEC-1999, C7=1

From 2006-Directive, Cc=1,0 and CE=1,0 (using point sources) This implies that

CE*Cc=1,0=C7 Hence (i) is true.

ii) From IEC-2007 C4=5 which implies that C4C7= 5

Also from Directive-2006, CA=5,0 which implies that CACC=5=C4C7



same MPE limits.

3)1150nm-1200nm:

Source

Document

Wavelength

(nm)

Duration(s)

10-13-10-11 10-11-10-9 10-9-5x10-5 5x10-5-10 10 - 3x104

IEC-2007 1150 - 1200

Visible &

IRA

H=1,5x10-4C7

[Jm-2]

H=2,7x104t0,75C7

[Jm-2]

H=5x10-

3C7 [Jm-2]

H=90t0,75C7

[Jm-2]

E=10C4C7

[Wm-2]

Directive-

2006

H=1,5x10-

3CCCE [Jm-2]

H=2,7x103t0,75CC

CE [Jm-2]

H=5x10-

2CCCE [Jm-

2]

H=90t0,75CC

CE [Jm-2]

E=10CACC

[Wm-2]

Table 19




i) C7= CcCE

ii) C4C7=CACC

iii) C7= CcCE:




Akoto Chama Leonel

Page 56(128)

From IEC-2007, C7=100,018(λ-1150)

From 2006-Directive, Cc=100,018(λ-1150) and CE=1,0 (using point sources) This implies that

CECc=100,018(λ-1150) =C7 Hence (i) is true.

ii) From IEC-2007 C4=5 which implies that C4C7= 5x100,018(λ-1150)

Also from Directive-2006, CA=5,0 which implies that CACC=5x100,018*(λ-1150)



same MPE limits.

4)1200nm-1400nm:

Source

Document

Wavelengt

h (nm)

Duration(s)

10-13-10-11 10-11-10-9 10-9-5x10-5 5x10-5-10 10 - 3x104

IEC-2007 1200 -

1400

Visible &

IRA

H=1,5x10-4C7

[Jm-2]

H=2,7x104t0,75C7

[Jm-2]

H=5x10-3C7

[Jm-2]

H=90t0,75C7

[Jm-2]

E=10C4C7

[Wm-2]

Directive-

2006

H=1,5x10-3CCCE

[Jm-2]

H=2,7x103t0,75CCCE

[Jm-2]

H=5x10-2CCCE

[Jm-2]

H=90t0,75CCCE

[Jm-2] E=10CACC

[Wm-2]

Table 20




i) C7= CcCE

ii) C4C7=CACC

iii) C7= CcCE:

From IEC-2007, C7=8




Akoto Chama Leonel

Page 57(128)

From 2006-Directive, Cc=8 and CE=1,0 (using point sources) This implies that CECC=8 =C7

Hence (i) is true.

ii) From IEC-2007 C4=5 which implies that C4C7= 5x8=40

Also from Directive-2006, CA=5,0 which implies that CACC=5x8=40=C4C7



same MPE limits.

3.1.4 Conclusion from Complete Analysis

To give a final conclusion to the above analysis of all documents, we see that the 2007 IEC

document and the 2006 Directive specify equal MPE limits for coherent sources while the

2006 Directive specifies a greater MPE limit than that specified by the 1999 IEC Technical

report, hence we shall employ the 2006 Directive for further analysis in this project.




Akoto Chama Leonel

Page 58(128)

3.2) Study of Filter Characteristics

In order to be able to investigate harm that may be caused to the eyes if not properly protected,

it is necessary to understand how the filter works.

Here we shall study the filter characteristics by measuring the transmittance ζ(λ) of two

different shades in the wavelength range 380nm to 780nm.

From these measurements, we shall then obtain the luminous transmittance (T) [12, 13] for

each shade using the formula (9)

780nm 780nm

T= [∑ V(λ).S(λ).ζ(λ) ∆λ / ∑ V(λ).S(λ).∆λ] (9)

380nm 380nm

Where V(λ) = Luminous efficiency function for daylight

ζ(λ) = measured spectral transmittance of the filter

S(λ) = Spectral distribution of radiation of CIE standard illuminant A

After obtaining the luminous transmittance T, we shall then use it to calculate the

corresponding shade number S [7,9] using the formulation(10):

S= 1- (7/3).Log(T) (10)

We are now prepared to understand the level of protection we can obtain from each shade

number.

Question?

What amount of incident luminance can we use the obtained luminous transmittances to

reduce it to a comfortable level?

Answer:




Akoto Chama Leonel

Page 59(128)

If Lw [7,9] is the luminance of the incident spectrum then we require a luminous transmittance

T (according to eqn. 11) to reduce it to a comfortable level.

In other words we can interpret (11) as: a luminous transmittance (T) of the filter will reduce

the incident spectrum to a comfortable level for all incident spectrum with luminance less than

or equal to (730/T)

Lw = 730 / T (cdm-2

) (11)

We are now we equipped to work with sample data:

Consider table 21 (see annex):

The Luminous transmittance obtained from the measured transmittance of both states denoted

T3 and T13 were calculated from table according to (9) and the corresponding shade numbers

S3 and S13 according to (10) to obtained the following:

T3 = 0,113224465 S3 = 3,207473

T13 = 4,79E-06 S13 = 1,34E+01

To know the incident luminance (Lw) for which these transmittances can give a comfortable

level of luminance we use (11).

According to (11) the incident luminance on the filter for which corresponding transmittances

can protect the eyes will be:

T3 = 0,113224465 Lw = 6447,369808 cdm-2

T13 = 4,79E-06 Lw = 1,52E+08 cdm-2

Hence for Lw = 6447,369808, the eye would be comfortable by using T3 = 0,113224465

Similarly for Lw = 1,52E+08, the eye would be comfortable by using T13 = 4,79E-06

This is clearly represented on the table 22 below:

Description Shade Number (S) Transmittance (T) Incident

Luminance(cdm-2

)

Light state

3,207473 0,113224465 6447,369808

Dark state

1,34E+01 4,79E-06 1,52E+08

Table 22




Akoto Chama Leonel

Page 60(128)

The above table could be extended to comprise of all the shades and transmittances as shown

on the table 23 below:

Shade

T

Incident

Luminance(Lw)

1,3 0,745 979,8657718

1,5 0,615 1186,99187

1,7 0,501 1457,085828

2 0,373 1957,104558

2,5 0,228 3201,754386

3 0,139 5251,798561

4 0,0518 14092,66409

5 0,0193 37823,8342

6 0,0072 101388,8889

7 0,0027 270370,3704

8 0,001 7,3E-5

9 0,00037 1,972972973E-6

10 0,000139 5,251798561E-6

11 0,000052 1,403846154E-7

12 0,000019 3,842105263E-7

13 7,2E-06 1,013888889E-8

14 2,7E-06 2,703703704E-8

Table 23 Luminance and corresponding shade

From the above analysis we observe that the level of protection offered by different shades are

different, which leads us to the concept of protection factor[12,13].

3.2.1) Protection Factor:

Filter protection factor is the factor by which a filter attenuates the weighted ocular exposure.

Since the transmittances for different shades are different, this implies that they also have

different extends of protection against harmful radiations, hence different protection factors.

The extent to which a filter can protect the eyes also depends on the strength of the incident

spectrum.




Akoto Chama Leonel

Page 61(128)

Note: For the wavelength range between 380nm to 780nm, studies was made on the spectral

luminance which is not harmful to the eyes, so instead of talking about protection factor in this

range we shall talk about the comfort factor( formula is the same).

Hence the protection factor should be a function of both the incident spectrum and the

transmittance of the shade as well as the comfort factor. The protection factor is defined

according to [12, 13].

By:

780nm 780nm

PFn= [∑ L(λ).V(λ). ∆λ / ∑ L(λ).V(λ).ζn(λ).∆λ] (12)

380nm 380nm

Where PFn = protection factor for shade n

L(λ) = spectral radiance from the source

ζn(λ) = spectral transmittance for shade n

Note: In the wavelength range 380nm t0 780nm, PFn = CFn

From the protection factor PFn we can obtain the figure of merit [12] by:

PFn.Tn = Ω (13)

Where Tn = luminous transmittance for shade n

Ω = constant

To understand clearly the concept of protection factor we shall first of all seek to meaning of

protection factor: If PFn is the protection factor for a particular source and at a state n of the

filter, then the filter will allow 1/PFn of the incident spectrum to pass through it. We shall

consider a spectrum of Irradiance Eλ incident on shade n = 3 ( this sample is taken from the

article)

As an example, let us consider an arbitrary spectrum of constant spectral irradiance Eλ=107

Wm-3 to obtain the corresponding spectral radiance we use the linear relationship:

Lλ = 4.Eλ / π α2

(W sr-1

m-2

m-1

) (14)

Where α is the angular subtends at the eye. For point sources α ≤ 1,7 mrad. In this case we

consider α = 0,03rad, which is typical of welding arcs.




Akoto Chama Leonel

Page 62(128)

Note that it is the angular subtense of 0.03mrad that is used in determining the protection of

the different shades of the filter and shade number.

Substituting the value for Eλ into (14) we obtain Lλ = 1,4154281670E+10 W sr-1 m-2 m-1

Table 24 (see annex) shows the calculation using the distribution of the photopic response of

the eyes:

From which we obtain the CF according to (12) to be CF3= 8,565943295

We now know the comfort factor and the luminous transmittance for the light state(shade 3)

Hence we can obtain the figure of merit Ω from (13).

CF3 = 8,565943295

T3 = 0,113224465

Hence CF3.T3 = Ω = 9,7E-1

Intuitively, if we know the luminous transmittance for all other shades (Table 3) we can use

(13) to obtain their corresponding comfort factors against the light source. As an example, let

us consider the dark state (shade 13) with T13 = 4,79E-06

The corresponding comfort factor is:

CF13 = Ω / T13 = 9,7E-1 / 4,79E-06 = 202505,2

Hence for this particular light source we have obtained the figure of merit and the comfort

factors of light state (shade 3) and the dark state (shade 13).

Up to this point we have studied the characteristics of the filter in the wavelength range from

380nm to 780nm to understand the following:

- Luminous transmittance

- Shade number

- Extent of protection

- Protection factor

- Figure of merit

We shall now focus our attention to the Blue light region (300nm to 700nm) and in the Visible

and IRA region (380nm to 1400nm)

3.2.2) Blue Light Region (300nm to 700nm)




Akoto Chama Leonel

Page 63(128)

In this region we seek to understand the protection that the filter will offer against blue light

injury on the retina of the eye.

The spectral property that we will use in this region is the effective radiance (blue light) :

which is the calculated radiance spectral weighted by B(λ), expressed in watts per square

metre per steradian [ Wm-2sr-1 ].

Again we shall work with the light state and the dark state (shade 3 and 13 respectively) to

understand the level of protection that the filter can offer against this type of injury.

a) Case 1 (Shade 3):

Shade 3 has a T = 0,139 and can comfortably reduce an incident spectral luminance of Lv =

5251,798561 cdm-2. The relationship between the luminance and the spectral radiance is given

[7] by :

780nm

Lv = 683.∑V(λ).L(λ).∆λ

(15)

380nm

If we assume that the source emits at a constant (intensity) hence constant spectral radiance

L(λ), then (15)can be rearranged to give:

780nm

L(λ) = Lv / (683 x ∑V(λ).∆λ ) (16)

380nm

From which we have the L(λ) = 7.1959887E+7 Wm-3sr-1 and correspondingly using (14) we

have

Eλ = 50839,66048Wm-3

This implies that a source with spectral irradiance Eλ = 50839,66048 Wm-3 will be prevented

from damaging the eye by shade 3. The obtained value for L(λ) is now put into the following

equation (17) to obtain the incident effective radiance (LB)[10,12]:

700nm




Akoto Chama Leonel

Page 64(128)

LB = ∑L(λ).B(λ).∆λ (17)

300nm

LB = 4,936574026 Wm-2sr-1 (calculated from table 6.5 (see annex))

An interpretation of this result is as follows: Shade 3 can be used to protect the eyes if the

incident spectrum has an incident effective radiance of LB = 4,936574026 Wm-2sr-1

To know the amount of blue light which is transmitted through the filter, we need to know the

blue light transmittance TB [14]which is given by

700nm 700nm

TB = ∑ ζ(λ).B(λ).∆λ / ∑ B(λ).∆λ (18)

300nm 300nm

To be more specific the blue light transmittance for shade 3 is given by the formula

700nm 700nm

TB3 = ∑ ζ3(λ).B(λ).∆λ / ∑ B(λ).∆λ (19)

300nm 300nm

Where the calculated TB3 = 0,008345

Table 6.6 (see annex) shows the calculation of TB3

With the calculated TB3 = 0,008345 the transmitted LB in our example will be

LBT= TB3.LB = 0,008345x4,936574026 = 0,041196 Wm-2sr-1

Here we have used the formulation that:

ζ = ξ ζ / ξ i (20)

Where ζ = Transmittance

ξ i = Incident quantity

ξ ζ = Transmitted quantity

If we compare this with the maximum LB MPE according to the directive 2006, we will see

that this value is far lower than what can damage the eyes.

To obtain the blue light protection factor PFBLPH(see table below), corresponding to this

spectral radiance of source and transmittance of filter we use the following formular:

700nm 700nm




Akoto Chama Leonel

Page 65(128)

PFBLPH= ∑L(λ).B(λ).∆λ / ∑L(λ).B(λ).ζ(λ).∆λ

(21)

300nm 300nm

The calculation of PFBLPH = 119.8385377 using the same L(λ) calculated from the assumed Eλ

above, is shown on Table 6.7 (see annex):

We have now obtained the blue light protection factor and the blue light transmittances,

We will now use them to calculate the Blue light figure of merit which is given by the

formular:

PFn(PLPH). T = Φ (22)

Where Φ = constant

In this case PFn(PLPH). T = 119,8385377x0,008345 = 16,65756 = Φ

b) Case 2 (Shade 13)

A similar analysis made for the dark state (shade 13) will be:

Shade 13 has a T = 7,2E-06 and can comfortably reduce a maximum incident spectral

luminance of Lv = 1,013888889E+8 cdm-2.

Assuming that the source emits at a constant (intensity) hence constant spectral radiance L(λ) and using (15) we obtain the corresponding L(λ) to be

L(λ) = 1,38923E+12 Wm-3sr-1 with a corresponding E(λ) = 9,814878898E+08 Wm-3.

This implies that a source with spectral irradiance Eλ = 9,814878898E+08 Wm-3 will be

prevented from damaging the eye by shade 13.

The incident LB = 9,54E+4 Wm-2sr-1. This calculation is shown on Table 6.8 (see annex):

If we perform a similar calculation as for shade 3 we will obtain a corresponding blue light

transmittance (TB13) for shade 13.

TB13 = 1,16934E-06

Hence the transmitted LB will be LBT = LBxTB13=9,54E+4x1,16934E-06=0,111442 Wm-2sr-1

We now know the luminous transmittance and the figure of merit for this shade( as it is

constant for all shades) hence we can deduce the blue light protection factor for the shade

according to (22) to have




Akoto Chama Leonel

Page 66(128)

PF13(BLPH) = Φ / T = 2313550

In the same light, if the T for any shade is known, the PFn(BLPH) can be deduced.

So far we have been analysing the filter characteristics for α = 0,03rad which is typical of

welding arcs.

Note that more restriction is observed of if α = 1,7mrad

We will now turn our attention to the analysis of the visible light and IRA region (380nm to

1400nm).

3.2.3) Visible Light and IRA (380nm t0 1400nm)

Here we shall do a similar analysis as with the previous section with α = 0,03 rad.

In this region we seek to understand the protection that the filter will offer against visible light

and IRA injury on the retina of the eye (retinal burn).

The spectral property that we will use in this region is the effective radiance (thermal injury) :

which is the calculated radiance spectral weighted by R(λ), expressed in watts per square

metre per steradian [ Wm-2sr-1 ].

Again we shall work with the light state and the dark state (shade 3 and 13 respectively) to

understand the level of protection that the filter can offer against this type of injury.

a) Case 1 (Shade 3):

Shade 3 has a T = 0,139 and can comfortably reduce a incident spectral luminance of Lv =

5251,798561 cdm-2.

If we assume that the source emits at a constant (intensity) hence constant spectral radiance

L(λ) then from (16) L(λ) = 7.1959887E+7 Wm-3sr-1 and correspondingly using (14) we have

Eλ = 50839,66048Wm-3

This implies that a source with maximum spectral irradiance Eλ = 50839,66048 Wm-3 will be


The obtained value for L(λ) is now put into the following equation (23) to obtain the incident

effective radiance (LR):

1400nm

LR = ∑L(λ).R(λ).∆λ (23)

380nm

LR = 75,96 Wm-2sr-1 ( calculated from Table 29 ( see annex))




Akoto Chama Leonel

Page 67(128)

An interpretation of this result is as follows: Shade 3 can be used to protect the eyes if the

incident spectrum has an incident effective radiance of LR = 75,96 Wm-2sr-1

To know the amount of Visible and IRA radiation which is transmitted through the filter, we

need to know the visible and IRA transmittance TV-IRA [14] which is given by

1400nm 1400nm

Tn(V-IRA) = ∑ ζn(λ).R(λ).∆λ / ∑ R(λ).∆λ (24)

380nm 380nm

To be more specific the visible and IRA transmittance for shade 3 is given by the formula

1400nm 1400nm

T3(V-IRA) = ∑ ζ3(λ).R(λ).∆λ / ∑ R(λ).∆λ (25)

380nm 380nm

Where the calculated T3(V-IRA) = 0,027859815

Table 6.10 (see annex) shows the calculation of T3(V-IRA)

With the calculated TV-IRA = 0,027859815 the transmitted LR in our example will be

LRT= T3(V-IRA).LR = 0,027859815 x75,96 = 2,116231Wm-2sr-1

If we compare this with the maximum LR MPE according to the directive 2006, we will see

that this value is far lower than what can damage the eyes.

To obtain the retinal thermal hazard protection factor PFRTH (see table below), corresponding

to this spectral radiance of source and transmittance of filter we use the following formula [12,

13]:

1400nm 1400nm

PFRTH= ∑L(λ).R(λ).∆λ / ∑L(λ).R(λ).ζ(λ).∆λ (26)

380nm 380nm

The calculated PFRTH = 35,89399341 using the same L(λ) calculated from the assumed Eλ

above, we have Table 6.11 (see annex):

We have now obtained the retinal thermal hazard protection factor and the Visible and IRA

transmittance,

We will now calculate the visible and IRA figure of merit which is given by the formular:

PFn(RTH). T = Φ (27)




Akoto Chama Leonel

Page 68(128)

Where Φ = constant

In this case PFn(RTH). T = 35, 89399341 x 0,139 = 4, 989265= Φ

b) Case 2 (Shade 13)

A similar analysis made for the dark state (shade 13) will be:

Shade 13 has a T = 7,2E-06 and can comfortably reduce an incident spectral luminance of

Lv = 1,013888889E+8 cdm-2.

Assuming that the source emits at a constant (intensity) hence constant spectral radiance L(λ) and using (15) we obtain the corresponding L(λ) to be

L(λ) = 1,38923E+12 Wm-3sr-1 with a corresponding E(λ) = 9,814878898E+08 Wm-3.

This implies that a source with spectral irradiance Eλ = 9,814878898E+08 Wm-3 will be


The incident LR = 1,47E+06 Wm-2sr-1. This calculation is shown on Table 6.12 (see annex):

If we perform a similar calculation as for shade 3 we will obtain a corresponding visible and

IRA transmittance (TV-IRA) for shade 13.

T13(V-IRA) = 2,88143E-06

Hence the transmitted LR will be

LRT = LRxT13(V-IRA)= 1,47E+06 +4x2,88143E-06=4,235705827 Wm-2sr-1

We now know the visible and IRA transmittance for this shade and using the figure of merit

for obtained from shade 3 we can deduce the blue light protection factor for this shade

according to (14) to have

PF13(V-IRA) = Φ / T = 692953,5

In the same light, if the T for any state is known, the PFn(RTH) can be deduced.

All above analysis have been done for the filter characteristics for α = 0,03rad which is typical

of welding arcs.

Below is Table 33 showing the different shades, luminous transmittance, corresponding

spectral radiance that could be reduced to a comfortable level, and the corresponding incident

blue light and visible-IRA radiations.

Shade T Incident Luminance L(λ) LB LR

1,3 0,745 979,8657718 13426072,96 0,921052 14,1724




Akoto Chama Leonel

Page 69(128)

1,5 0,615 1186,99187 16264104,64 1,115746 17,16819

1,7 0,501 1457,085828 19964918,87 1,369628 21,07473

2 0,373 1957,104558 26816151,09 1,839635 28,30681

2,5 0,228 3201,754386 43870282,26 3,009578 46,30895

3 0,139 5251,798561 71959887,44 4,936574 75,96

4 0,0518 14092,66409 193096995,3 13,24679 203,8309

5 0,0193 37823,8342 518260329,3 35,55356 547,0694

6 0,0072 101388,8889 1389225605 95,3033 1466,45

7 0,0027 270370,3704 3704601613 254,1421 3910,533

8 0,001 730000 10002424355 686,1838 10558,44

9 0,00037 1972972,973 27033579337 1854,551 28536,32

10 0,000139 5251798,561 71959887444 4936,574 75960

11 0,000052 14038461,54 1,92354E+11 13195,84 203046,9

12 0,000019 38421052,63 5,26443E+11 36114,94 555707,4

13 7,2E-06 101388888,9 1,38923E+12 95303,3 1466450

14 2,7E-06 270370370,4 3,7046E+12 254142,1 3910533

Table 33 Shade transmittance and incident spectral properties

Analysis will then be done on this table using the MPE’s specified by the 2006 Directive to

show the shades which need more protection against the blue light and visible-IRA incident

radiations within an exposure time of 0,5s, which is the main aim of this project.




Akoto Chama Leonel

Page 70(128)

4 Result : Determination of Damage from Intense Light Exposure

In determining the hazard which may be caused to the eyes from exposure to intense light,

instead of using mathematical analysis we shall employ a graphical technique whereby the

incident spectra will be plotted on the same axes as the MPE limits stipulated in the adopted

2006 directive (see section 3.1 of chapter 3). At any given exposure time the MPE limit value

will be divided by the incident spectrum value to give what we shall called the protection ratio

(PR). If the result is greater than or equal to one (≥ 1) then no further protection is needed

otherwise further protection will be needed. This explanation is shown mathematically below:

≥ 1 no further protection needed

PR = MPE Limitt /Incident Spectrumt = <1 further protection needed (28)

In this investigation two types of sources will be considered: point source (α = 0,0017rad) and

welding arc (α = 0,03rad).

Depending on the particular spectral property for investigation, t will be considered for

exposure duration of 0,5s and long exposure times. In the cases of blue light and Visible &

IRA, long exposure times are when t >10000s and t> 10s respectively because after these

times the MPE limit values remain constant.

To understand the reasoning behind this techniques, let us consider the example below:

Consider the incident spectrum of a CIA-E source corresponding to that which can be

protected by shade 3.This is shown graphically below (fig 4.1):

E(λ) / λ(nm)

0

20000

40000

60000

80000

100000

120000

140000

160000

0 200 400 600 800 1000 1200 1400 1600

wavelength λ(nm)

E(λ

)[W

m^

-2 s

r^-1

]

E(λ) / λ(nm)




Akoto Chama Leonel

Page 71(128)

Fig 4.1 E(λ)/ λ(nm)

From this spectrum, the blue light and the Visible & IRA radiations are calculated using

equations 17 and 23 respectively (Lλ is obtained using equation 14). These are then plotted for

different angular subtense (α = 0,03rad and α = 0,0017rad). The ratio of the MPE limit and the

incident spectrum are then obtained according to equation 28.

The graph for α = 0,03rad is shown below (it has been zoomed for clarity so only the part

necessary for investigation is shown)

LB/T Graph

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

2000000

0 2 4 6 8 10

Exposure time (T/s)

LB

[Wm

^-2

sr^

-1]

MPE Limit LB

(α≥11mrad)

Source Blue l ight (LBi)

Fig 4.2 LB/T Graph (zoomed)

LB/T Graph

1

100

10000

1000000

100000000

10000000000

0 5000 10000 15000

Exposure time(t/s)

LB

[W

m^

-2 s

r^-1

]

MPE Limit LB

(α≥11mrad)

Source Blue

light (LBi)

Fig 4.2 LB/T Graph (entire graph shown on a logarithmic scale)




Akoto Chama Leonel

Page 72(128)

The red line ( ILBiI ≈1.6 )shows the source incident LB and the blue line shows the MPE limit

value.

For t = 0,5s equation 28 gives:

PR = MPE Limitt=0.5 /Incident Spectrumt=0.5 = 1250590.654 >> 1

Hence no protection is needed.

For very long exposure time, we consider fig 4.3 below. For this example t > 10000s,

LB/T Graph

0

500

1000

1500

2000

0 2000 4000 6000 8000 10000

Exposure time(t/s)

LB

[W

m^

-2 s

r^-1

]

MPE Limit LB

(α≥11mrad)

Source Blue

light (LBi)

Fig 4.3 LB/T Graph (zoomed)

LB/T Graph

1

100

10000

1000000

100000000

10000000000

0 5000 10000 15000

Exposure time(t/s)

LB

[W

m^

-2 s

r^-1

]

MPE Limit LB

(α≥11mrad)

Source Blue

light (LBi)

Fig 4.3 LB/T Graph (entire graph shown on a logarithmic scale)

Caluclations show that:

PR = MPE Limit t>10000 /Incident Spectrum t>10000 = 62.5295327 > 1




Akoto Chama Leonel

Page 73(128)

Hence no protection is needed.

Note: For the long exposure time, we have considered any value after t = 10000s since from

this point onwards the MPE limit is a constant value

This method was later generalised to the different shades and different assumed spectra using

the different values of the angular subtense (α = 0,03rad and α = 0,0017rad).

Also in following investigations light sources with three different spectral distributions have

been considered. To give a feeling on what is meant by different spectral irradiances the figure

below (fig 4.4) is used to illustrate 3 different spectra all with light intensity for which shade

13 could be used to protect the eyes. Graph 1 (Blue line) is a rough approximation of sub-

figure 6 in figure 3.1 in chapter 3 (whose spectral distribution will be used in the proceding

investigation). Graph 2 (purple line) is the standard CIE-A source and Graph 3 is an arbitrary

constant curve which will also be used in the second investigation. Observe that all three

graphs show different spectral distribution but are all shielded from damaging the eyes by

shade 13.

Spectral Irradiance/Wavelength

0

500000000

1000000000

1500000000

2000000000

2500000000

3000000000

3500000000

4000000000

300 500 700 900 1100 1300 1500

Wavelngth [nm]

Sp

ec

tra

l Ir

rad

ian

ce

[Wm

^-3

]

Graph 1

Graph 2 (CIE-A)

Graph 3

Fig 4.4 Different Spectra which may correspond to different welding arcs.

In the investigation, same spectral irradiance was used and it was assumed that it was

produced initially from a welding arc and later from a point source.




Akoto Chama Leonel

Page 74(128)

The following results were obtained:

a) CIE-A Source without Filter in Place

The first investigation was made of the CIE-A standard source corresponding to the different

shades

E(λ)

Shade

α = 0,03rad

Blue Light Protection Ratio

(300nm – 700nm)

Required Visible & IRA

Protection Ratio (380nm -

1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

CIE-A 1,3 6702806,023 335,1403011 152385,0908 71833,85264

CIE-A 1,5 5533188,865 276,6594432 125794,4038 59299,08641

CIE-A 1,7 4507524,587 225,3762294 102476,4168 48307,06063

CIE-A 2 3355901,539 167,795077 76294,81727 35965,13696

CIE-A 2,5 2051328,555 102,5664277 46635,9741 21984,05155

CIE-A 3 1250590,654 62,5295327 28431,5807 13402,55774

CIE-A 4 466047,4523 23,30237262 10595,36604 4994,622237

CIE-A 5 173643,1627 8,682158137 3947,694299 1860,930679

CIE-A 6 64778,79646 3,238939823 1472,714971 694,2332067

CIE-A 7 24292,04867 1,214602434 552,2681143 260,3374525

CIE-A 8 8997,055064 0,449852753 204,543746 96,42127871

CIE-A 9 3328,910374 0,166445519 75,68118603 35,67587312

CIE-A 10 1250,590654 0,062529533 28,4315807 13,40255774

CIE-A 11 467,8468633 0,023392343 10,63627479 5,013906493

CIE-A 12 170,9440462 0,008547202 3,886331175 1,832004295

CIE-A 13 64,77879646 0,00323894 1,472714971 0,694233207

CIE-A 14 24,29204867 0,001214602 0,552268114 0,260337453




Akoto Chama Leonel

Page 75(128)

Fig. 4.5 PR when using the standard CIE-A source without filter in place for α = 0,03rad

E(λ)

Shade

α = 0,0017rad


(300nm – 700nm)


Protection Ratio (380nm -1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

CIE-A 1,3 948734,0443 47,43670222 8635,155145 4070,584983

CIE-A 1,5 783183,1372 39,15915686 7128,349549 3360,281563

CIE-A 1,7 638007,7264 31,90038632 5806,99695 2737,400103

CIE-A 2 475003,7564 23,75018782 4323,372979 2038,024428

CIE-A 2,5 290350,8216 14,51754108 2642,705199 1245,762921

CIE-A 3 177012,1237 8,850606185 1611,122906 759,478272

CIE-A 4 65965,66912 3,298283456 600,4040759 283,0285934

CIE-A 5 24577,94236 1,228897118 223,7026769 105,4527385

CIE-A 6 9168,973314 0,458448666 83,45384838 39,33988171

CIE-A 7 3438,364993 0,17191825 31,29519314 14,75245564

CIE-A 8 1273,468516 0,063673426 11,59081228 5,46387246

CIE-A 9 471,1833509 0,023559168 4,288600542 2,02163281

CIE-A 10 177,0121237 0,008850606 1,611122906 0,759478272

CIE-A 11 66,22036282 0,003311018 0,602722238 0,284121368

CIE-A 12 24,1959018 0,001209795 0,220225433 0,103813577

CIE-A 13 9,168973314 0,000458449 0,083453848 0,039339882

CIE-A 14 3,438364993 0,000171918 0,031295193 0,014752456

Fig 4.6 PR when using the standard CIE-A source without filter in place for α = 0,0017rad

Note that for all PR < 1, protection against damage is needed. Observation above, we will

need some protection for certain shades.




Akoto Chama Leonel

Page 76(128)

b) Light Source with Constant Spectral Distribution without Filter in Place:

The sources were chosen such that it has the maximum possible incident spectrum that could

be protected by the corresponding shade.

E(λ)

Shade

α = 0,03rad


(300nm – 700nm)



t = 0,5s t>10000s t = 0,5s t>10s

103,98 1,3 2156785,64 107,839282 138761,119 65411,55515

104,064 1,5 1777489,252 88,87446261 114358,327 53908,15576

104,065 1,7 1773401,14 88,67005702 114095,3102 53784,17045

104,29 2 1056347,925 52,81739623 67962,25702 32037,19426

104,493 2,5 661922,2555 33,09611277 42586,09252 20074,95011

104,71 3 401612,2797 20,08061399 25838,52947 12180,20154

105,17 4 139253,777 6,962688849 8959,170328 4223,324721

105,6 5 51737,68393 2,586884197 3328,6474 1569,113918

106 6 20597,14296 1,029857148 1325,158398 624,6755021

106,46 7 7141,788479 0,357089424 459,4812494 216,5980162

106,85 8 2909,423775 0,145471189 187,183599 88,23775999

107,3 9 1032,30251 0,051615126 66,41524718 31,30793868

107,8 10 326,4427166 0,016322136 21,00234524 9,900439508

108,16 11 142,4974141 0,007124871 9,167856213 4,321698591

108,55 12 58,05063616 0,002902532 3,734803811 1,760574773

109 13 20,59714296 0,001029857 1,325158398 0,624675502




Akoto Chama Leonel

Page 77(128)

109,5 14 6,513388505 0,000325669 0,41905188 0,197539739

Fig 4.7 PR when using a constant spectral distribution source for α = 0,03rad

E(λ)

Shade

α = 0,0017rad


(300nm – 700nm)

Visible & IRA Protection Ratio

(380nm -1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

103,98 1,3 305277,5146 15,26387573 7863,130074 3706,654792

104,064 1,5 251590,8354 12,57954177 6480,305197 3054,795493

104,065 1,7 251012,1925 12,55060963 6465,400909 3047,769659

104,29 2 149518,4607 7,475923033 3851,194564 1815,441008

104,493 2,5 93690,34047 4,684517024 2413,21191 1137,580506

104,71 3 56845,3333 2,842266665 1464,183337 690,2114208

105,17 4 19710,37183 0,985518592 507,6863186 239,3217342

105,6 5 7323,097514 0,366154876 188,6233527 88,91645534

106 6 2915,377631 0,145768882 75,09230924 35,39827845

106,46 7 1010,868858 0,050543443 26,0372708 12,27388758

106,85 8 411,808036 0,020590402 10,60707061 5,000139733

107,3 9 146,115005 0,00730575 3,763530673 1,774116525

107,8 10 46,20562161 0,002310281 1,190132897 0,561024905

108,16 11 20,16948537 0,001008474 0,519511852 0,244896254

108,55 12 8,216650553 0,000410833 0,211638883 0,099765904

109 13 2,915377631 0,000145769 0,075092309 0,035398278

109,5 14 0,921923355 4,60962E-05 0,023746273 0,011193919

Fig 4.8 PR when using a constant spectral distribution source for α = 0,0017rad




Akoto Chama Leonel

Page 78(128)

Observe that for this assumed incident spectra (which correspond to the different shades) PR <

1, hence we now seek to see if the filter can protect the eyes from damage using the

transmittance of the light state (shade 3).

c) Light Source with Constant Spectral Distribution with Filter in Place

Since this investigation concerns switching from light to dark state, we will assume that our

filter is in the light state and we shall use the transmittance of the light state to draw our

conclusions below. In the presence of the filter we have the following conclusions on the

table below:

E(λ)

Shade

α = 0,03rad


(300nm – 700nm)



t = 0,5s t>10000s t = 0,5s t>10s

106,46 7 Eye is

protected*

106,85 8 Eye is

protected*

107,3 9 Eye is

protected*

107,8 10 Eye is

protected*

108,16 11 Eye is

protected*

108,55 12 Eye is

protected*

109 13

Eye is

protected*

Eye is

protected*

109,5 14 Eye is

protected*

Eye is

protected*

Eye is

protected*

* = light state transmittance protects the eyes




Akoto Chama Leonel

Page 79(128)

Fig 4.9 Conclusion drawn with filter in the light state for α = 0,03rad

E(λ)

Shade

α = 0,0017rad


(300nm – 700nm)


(380nm -1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

105,17 4 Eye is

protected*

105,6 5 Eye is

protected*

106 6 Eye is

protected*

106,46 7 Eye is

protected*

106,85 8 Eye is

protected*

107,3 9 Eye is

protected*

107,8 10 Further

protection

needed from

t≈3260s

Eye is

protected*

108,16 11 Further

protection

needed from

t≈1425s

Eye is

protected*

Eye is

protected*

108,55 12 Further

protection

needed from

Eye is

protected*

Eye is

protected*




Akoto Chama Leonel

Page 80(128)

t≈575s

109 13

Further

protection

needed from

t≈200s

Eye is

protected*

Eye is

protected*

109,5 14 Eye is

protected*

Further

protection

needed from

t≈55s

Eye is

protected*

Further

protection

needed from

t≈2s


Fig 4.10 Conclusion drawn with filter in the light state for α = 0,0017rad

Observe that, for exposure time of 0.5s (which is the goal of this project) the light state

transmittance offer enough protection. In the same way, different sources with different

properties could be investigated to see if there is no risk of damage in case of a delay in

switching from the light state to the dark state. To this effect we will look at the example of

the welding spectrum below, which is a rough approximation of sub-figure 6 of figure 2.13 in

chapter 2. This spectrum was chosen because of its very intense blue light radiation. After the

approximated distribution of the spectrum was obtained, it was then multiplied by arbitrary

constant factors in order for it to correspond to the intensity of light that could be protected by

the different shades of the welding filter. It was then investigated on two different angular

subtenses (α = 0,03rad and α = 0,0017rad).

The results of this investigation are presented on the tables 4.11 and 4.12 below.

d) Approximation of Real Welding Spectra without Filter In Place

E(λ)

Shade

α = 0,03rad


(300nm – 700nm)


(380nm -1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

3 252939,6151 12,64698075 19103,29973 9005,235424

4 79043,62971 3,952181485 5969,781166 2814,13607

5 35130,50209 1,756525105 2653,236074 1250,727142




Akoto Chama Leonel

Page 81(128)

6 12646,98075 0,632349038 955,1649866 450,2617712

7 4516,778841 0,225838942 341,1303523 160,8077754

8 1580,872594 0,07904363 119,3956233 56,2827214

9 632,3490377 0,031617452 47,75824933 22,51308856

10 252,9396151 0,012646981 19,10329973 9,005235424

11 63,23490377 0,003161745 4,775824933 2,251308856

12 31,61745188 0,001580873 2,387912466 1,125654428

13 12,64698075 0,000632349 0,955164987 0,450261771

14 4,864223367 0,000243211 0,367371149 0,173177604

Fig 4.11 PR for α = 0,0017rad without filter in place

E(λ)

Shade

α = 0,0017rad


(300nm – 700nm)


(380nm -1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

3 35801,78557 1,790089279 1082,520318 510,2966741

4 11188,05799 0,5594029 338,2875994 159,4677106

5 4972,470218 0,248623511 150,3500442 70,87453806

6 1790,089279 0,089504464 54,12601591 25,5148337

7 639,3175995 0,03196588 19,33071997 9,112440608

8 223,7611598 0,011188058 6,765751988 3,189354213

9 89,50446393 0,004475223 2,706300795 1,275741685

10 35,80178557 0,001790089 1,082520318 0,510296674

11 8,950446393 0,000447522 0,27063008 0,127574169

12 4,475223197 0,000223761 0,13531504 0,063787084




Akoto Chama Leonel

Page 82(128)

13 1,790089279 8,95045E-05 0,054126016 0,025514834

14 0,688495876 3,44248E-05 0,020817698 0,009813398

Figure 4.12 PR for α = 0,03rad without filter in place

Observe that certain PRs are less than one which means that, these shades needed further

protection.

With the filter now in place and set to the light state (shade 3) the following conclusion were

drawn for the condition PR < 1: These conclusions are shown on figure 4.13 and 4.14

E) Approximation of Real Welding Spectra with Filter in Place.

E(λ)

Shade

α = 0,03rad


(300nm – 700nm)


(380nm -1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

6

Eye is

protected*

7

Eye is

protected*

8

Eye is

protected*

9

Eye is

protected*

10

Eye is

protected*

11

Further

protection

needed from

t≈4500s

12

Further

protection

needed from

t≈2370s




Akoto Chama Leonel

Page 83(128)

13

Further

protection

needed from

t≈1050s

Eye is

protected*

Eye is

protected*

14

Further

protection

needed from

t≈345s

Eye is

protected*

Eye is

protected*

* = light state transmittance protects the eyes: Fig 4.13 Conclusion drawn with filter in the light

state for α = 0,03rad

E(λ)

Shade

α = 0,0017rad


(300nm – 700nm)


(380nm -1400nm)

t = 0,5s t>10000s t = 0,5s t>10s

4

Eye is

protected*

5

Eye is

protected*

6

Eye is

protected*

7

Eye is

protected*

8

Eye is

protected*

9

Further

protection

needed from

t≈6200s

10

Further

protection

needed from

t≈2530s

Eye is

protected*




Akoto Chama Leonel

Page 84(128)

11

Further

protection

needed from

t≈630s

Eye is

protected*

Eye is

protected*

12

Further

protection

needed from

t≈320s

Eye is

protected*

Eye is

protected*

13

Further

protection

needed from

t≈130s

Eye is

protected*

Eye is

protected*

14 Further

protection

needed from

t≈45s

Further

protection

needed from

t≈1050s

Further

protection

needed from

t≈1.2s

Further

protection

needed from

t≈1.2s


Figure 4.14 Conclusion drawn with filter in the light state for α = 0,0017rad




Akoto Chama Leonel

Page 85(128)




Akoto Chama Leonel

Page 86(128)

5 Discussion The work was carried out in the Research and Development (R&D) Department of 3M

Svenska AB branch in Gagnef, Sweden. So many challenges were faced during the evolution

of the project, which led to a deeper research and understand of the problem area to bring forth

solutions to these mile stones. In order for simulation to be successfully done, an excel

worksheet was developed from scratch which served as the main simulation tool (see

accompanying CD on the cover of this project report). Critical thinking was employed, with

best and worse case scenarios investigated.

The fundamental aspects of LC-technology was studied at depth, the optics of the eyes and the

sources and processes producing electromagnetic radiations was also looked into.

A combination of all these made it possible to simulate the product properties according to

the most recent international standards and to draw logical conclusions, thus attaining the

objective of the project.




Akoto Chama Leonel

Page 87(128)

6 Conclusion / Recommendations

a) Conclusion

The objective of this project was to determine the thermal and blue light photochemical

hazard protection needed by automatic welding filters within 0.5 seconds of switching failure.

Before simulating to get our results an introduction was done to understand the technology

behind the filter and how the filter works. Also, since the filter filters waves coming from

welding arcs, an introduction was also made to understand the kind of intense light radiation

from such process. Yet to understand the level of protection the eye needed, we also needed to

have a limit beyond which damage may be caused to the eyes. To this effect, different MPE

standards were compared and that with least restrictive limits was used (2006 Directive)

In order to get a mathematical formulation to quantify our results the concept of the

Protection Ratio was introduced as defined by equation 28 of chapter 4. Finally, simulations

were made on different spectra for the unprotected eye and when using the filter in the light

state (shade 3).

The conclusion was that in the case of 0.5 s of switching failure, blue light attenuation will be

needed for products with the darkest shade 11 or higher. The transmittance requirements can

be taken from the tables of chapter 4 as the protection ratios below 1 (PR<1). In case of a

switching failure the requirement for the darkest shade of a product shall apply also to the

lightest state. The light state of the current product fulfils the requirement and the eye is

protected. Even in the case were the filter failed to switch, the eye would not be damaged

since the light state transmittance could still attenuate the incident light to below the harmful

level.

Today there are products that are shade 3 in the light state and shade 13 in the darkest state.

Since we have the interference filter that block a lot of blue light the products are safe. If it

would be possible to make a product with shade 1.2 in the light state and not necessarily use

an interference filter, then we would not be sure that such a product would be safe without

having a requirement for blue light transmittance. The most important conclusion of this work

is the transmittance requirements needed when the darkest state is above shade 11. For

example consider figure 4.12. If the darkest shade is 13, the VIS/IR-transmittance in the

lightest state (that might theoretically be nearly clear) must not be higher than 0.054 (5.4%) in

case of a switching failure. You then have a light source relating to the shade 13, but the

welding filter is in the light state and you need to be protected until you close your eyes or turn

your head after about 0.5 s. The importance of the values below 1.0 is further pointed out by

the red colour numbers of the boxes. For example figure 4.12.Hence a requirement would be

needed for the light state when the darkest state is above shade 11.

However one can confidently conclude that the eye stands little or no chance of damage within

0.5 s of switching failure with products today.




Akoto Chama Leonel

Page 88(128)

b) Recommendations:

- The protection ratio can be expressed in a standard as the weighted transmittance (TB and TV-

IRA) and the requirement can be taken from the values of chapter 4 where the protection factor

is below 1.

- The emission spectrum from the welding arc in different welding situations varies depending

on the welding method, material, shielding gas and current used. Therefore it would be good

to analyze different welding spectra and do the analysis for each spectrum.

- The blink reflex is often mentioned as 0.25 s hence 0.5 s then gives some error margin.

However, if the welding filter fails to switch several times, a longer time perhaps should be

considered for further investigation.




Akoto Chama Leonel

Page 89(128)

7 References [1] P. Jägemalm, On the Optics and Surface Physics of Liquid Crystal, Göteborg, Sweden

1999 pp. 85

[2] L. M. Mlinov and V. G. Chigrinov, Electrooptic Effects in Liquid Crystal Materials,

New York, Spring-Verlag New York, Inc., 1994

[3] V. G. Chigrinov, Liquid Crystal Devices : Physics and Applications, Boston, Artech

House Optoelectronics Library, 1999, pp 85-102

[4] B. Bahadur, Liquid Crystal Applications and Uses Vol 2

[5] “Minimum health and Safety requirements regarding the exposure of workers to risk

arising from physical agents (artificial optical radiation) (19th individual Directive within the

meaning of Article 16(1) of Directive 89/391/EEC)”, Official Journal of the European Union,

Directive 2006/257ec, pp. L114/38 – Lii1/52, April 2006

[6] Palmebalds, Sandvik Welding Handbook, Goterborg, Sweden AB, 1977

[7] E. Sutter, and A. Schirmacher, “ The Infrared Transmittance of Eye Protection

Filters”, Pysikalisch – Technische Bundesanstalt Braunschweig, 2005

[8] S. Palmer, The Optical Properties of Automatically Darkening Welding Filters on

Liquid Crystal Technology, Uppsala, University of Uppsala, 1998

[9] E. Buhr and E. Sutter, “ Dynamic Filters for Protection Devices”, Physikalisch –

Technische Bundesanstalt, Braunschweig, (West Germany), March 1990

[10] “Compilation of maximum Permissible Exposure to Incoherent Optical Radiation”

IEC tR 60825-9, Geneva, Switzerland, October 1999

[11] “Safety of Laser Products; Part 1 : Equipment Classification and requirement” IEC

60825 – 1, Geneva, Switzerland, March, 2007

[12] D. Mc G Clarkson, “ Determination of eye filter protection factors assocviated with

retinal thermal hazard and blue light photochemical hazard for intense pulse light

source”,Institute of Physics Publishing, UK, January 2006

[13] Eyewear for protection against intense light sources used on humans and animals for

cosmetic and medical application, Part 1, Specification for Products, British Standard, BS

8497 – 1: 2008

[14] Occupational and Educational Personal Eye and Face Protection Devices, American

National Standard, American Society of safety Engineers, ANSI Z87, January 2008 .




Akoto Chama Leonel

Page 90(128)

Appendices

Appendix A (Annex) Calculations

λ(nm) V(λ) SCIE-A(λ) ∆λ ζ3 ζ13 D ∏3 ∏13

380 0 9,8 5E-09 2,54E-06 8,55E-09 0 0 0,00E+00

385 0,0001 10,9 5E-09 -2,4E-07 3,39E-09 5,45E-12 -1,28811E-18 1,85E-20

390 0,0001 12,09 5E-09 -5,8E-06 3,79E-09 6,045E-12 -3,48795E-17 2,29E-20

395 0,0002 13,35 5E-09 -2,4E-06 3,86E-08 1,335E-11 -3,15207E-17 5,15E-19

400 0,0004 14,71 5E-09 7,95E-05 2,89E-07 2,942E-11 2,33973E-15 8,49E-18

405 0,0006 16,15 5E-09 0,000195 7,06E-07 4,845E-11 9,43919E-15 3,42E-17

410 0,0012 17,68 5E-09 0,000475 1,11E-06 1,0608E-10 5,03741E-14 1,18E-16

415 0,0022 19,29 5E-09 0,000701 1,23E-06 2,1219E-10 1,48714E-13 2,61E-16

420 0,004 20,99 5E-09 0,000845 1,18E-06 4,198E-10 3,54545E-13 4,94E-16

425 0,0073 22,79 5E-09 0,001049 1,12E-06 8,31835E-10 8,72577E-13 9,29E-16

430 0,0116 24,67 5E-09 0,001217 1,03E-06 1,43086E-09 1,74172E-12 1,47E-15

435 0,0168 26,64 5E-09 0,001427 9,20E-07 2,23776E-09 3,19417E-12 2,06E-15

440 0,023 28,7 5E-09 0,00176 8,58E-07 3,3005E-09 5,80724E-12 2,83E-15

445 0,0298 30,85 5E-09 0,002133 7,67E-07 4,59665E-09 9,80379E-12 3,53E-15

450 0,038 33,09 5E-09 0,002546 6,93E-07 6,2871E-09 1,60095E-11 4,36E-15

455 0,048 35,41 5E-09 0,003273 6,67E-07 8,4984E-09 2,78146E-11 5,67E-15

460 0,06 37,81 5E-09 0,004134 6,73E-07 1,1343E-08 4,68908E-11 7,63E-15

465 0,0739 40,3 5E-09 0,005351 6,87E-07 1,48909E-08 7,96796E-11 1,02E-14

470 0,091 42,87 5E-09 0,007315 7,50E-07 1,95059E-08 1,4269E-10 1,46E-14

475 0,1126 45,52 5E-09 0,009852 8,55E-07 2,56278E-08 2,52475E-10 2,19E-14

480 0,139 48,24 5E-09 0,013387 1,00E-06 3,35268E-08 4,48828E-10 3,36E-14

485 0,1693 51,04 5E-09 0,019245 1,28E-06 4,32054E-08 8,31501E-10 5,52E-14

490 0,208 53,91 5E-09 0,027964 1,72E-06 5,60664E-08 1,56786E-09 9,64E-14

495 0,2586 56,85 5E-09 0,040507 2,63E-06 7,35071E-08 2,97752E-09 1,93E-13

500 0,323 59,86 5E-09 0,05928 3,97E-06 9,66739E-08 5,73087E-09 3,84E-13

505 0,4073 62,93 5E-09 0,087976 6,11E-06 1,28157E-07 1,12747E-08 7,83E-13

510 0,503 66,06 5E-09 0,12158 1,00E-05 1,66141E-07 2,01994E-08 1,66E-12

515 0,6082 69,25 5E-09 0,147754 1,22E-05 2,10589E-07 3,11153E-08 2,58E-12

520 0,71 72,5 5E-09 0,163568 1,31E-05 2,57375E-07 4,20983E-08 3,37E-12

525 0,7932 75,79 5E-09 0,17287 1,24E-05 3,00583E-07 5,19618E-08 3,72E-12

530 0,862 79,13 5E-09 0,170758 1,12E-05 3,4105E-07 5,82369E-08 3,83E-12




Akoto Chama Leonel

Page 91(128)

535 0,9149 82,52 5E-09 0,160155 9,35E-06 3,77488E-07 6,04567E-08 3,53E-12

540 0,954 85,95 5E-09 0,149557 7,37E-06 4,09982E-07 6,13154E-08 3,02E-12

545 0,9803 89,41 5E-09 0,14706 6,16E-06 4,38243E-07 6,4448E-08 2,70E-12

550 0,995 92,91 5E-09 0,146509 5,55E-06 4,62227E-07 6,77206E-08 2,57E-12

555 1 96,44 5E-09 0,145312 5,22E-06 4,822E-07 7,00696E-08 2,52E-12

560 0,995 100 5E-09 0,140117 4,85E-06 4,975E-07 6,97082E-08 2,41E-12

565 0,9786 103,58 5E-09 0,136125 4,29E-06 5,06817E-07 6,89903E-08 2,17E-12

570 0,952 107,18 5E-09 0,133278 3,84E-06 5,10177E-07 6,79955E-08 1,96E-12

575 0,9154 110,8 5E-09 0,128646 3,72E-06 5,07132E-07 6,52402E-08 1,88E-12

580 0,87 114,44 5E-09 0,121628 3,53E-06 4,97814E-07 6,05481E-08 1,76E-12

585 0,8163 118,08 5E-09 0,111346 3,29E-06 4,81944E-07 5,36625E-08 1,59E-12

590 0,757 121,73 5E-09 0,102724 2,94E-06 4,60748E-07 4,73297E-08 1,35E-12

595 0,6949 125,39 5E-09 0,097063 2,76E-06 4,35668E-07 4,22872E-08 1,20E-12

600 0,631 129,04 5E-09 0,092695 2,64E-06 4,07121E-07 3,7738E-08 1,08E-12

605 0,5668 132,7 5E-09 0,089898 2,55E-06 3,76072E-07 3,3808E-08 9,58E-13

610 0,503 136,35 5E-09 0,086728 2,71E-06 3,4292E-07 2,97408E-08 9,28E-13

615 0,4412 139,99 5E-09 0,082917 2,70E-06 3,08818E-07 2,56062E-08 8,35E-13

620 0,381 143,62 5E-09 0,078648 2,65E-06 2,73596E-07 2,15177E-08 7,24E-13

625 0,321 147,24 5E-09 0,071321 2,40E-06 2,3632E-07 1,68545E-08 5,68E-13

630 0,265 150,84 5E-09 0,059863 2,09E-06 1,99863E-07 1,19644E-08 4,18E-13

635 0,217 154,42 5E-09 0,046208 1,73E-06 1,67546E-07 7,74193E-09 2,90E-13

640 0,175 157,98 5E-09 0,0329 1,33E-06 1,38233E-07 4,54789E-09 1,84E-13

645 0,1382 161,52 5E-09 0,022313 9,84E-07 1,1161E-07 2,4904E-09 1,10E-13

650 0,107 165,03 5E-09 0,015031 7,03E-07 8,82911E-08 1,32706E-09 6,20E-14

655 0,0816 168,51 5E-09 0,010203 5,03E-07 6,87521E-08 7,01462E-10 3,46E-14

660 0,061 171,96 5E-09 0,006982 3,78E-07 5,24478E-08 3,66205E-10 1,98E-14

665 0,0446 175,38 5E-09 0,004926 2,88E-07 3,91097E-08 1,92653E-10 1,12E-14

670 0,032 178,77 5E-09 0,003475 2,21E-07 2,86032E-08 9,93947E-11 6,32E-15

675 0,0232 182,12 5E-09 0,002434 1,74E-07 2,11259E-08 5,14161E-11 3,67E-15

680 0,017 185,43 5E-09 0,00183 1,60E-07 1,57616E-08 2,88486E-11 2,53E-15

685 0,0119 188,7 5E-09 0,001356 1,38E-07 1,12277E-08 1,52296E-11 1,55E-15

690 0,0082 191,93 5E-09 0,001043 1,18E-07 7,86913E-09 8,21086E-12 9,26E-16

695 0,0057 195,12 5E-09 0,000804 1,25E-07 5,56092E-09 4,47336E-12 6,93E-16

700 0,0041 198,26 5E-09 0,000622 1,11E-07 4,06433E-09 2,52934E-12 4,49E-16

705 0,0029 201,36 5E-09 0,000463 1,37E-07 2,91972E-09 1,35255E-12 4,00E-16

710 0,0021 204,41 5E-09 0,000377 1,57E-07 2,14631E-09 8,08532E-13 3,37E-16

715 0,0015 207,41 5E-09 0,00031 1,90E-07 1,55558E-09 4,82058E-13 2,95E-16

720 0,001 210,36 5E-09 0,000253 2,53E-07 1,0518E-09 2,6647E-13 2,66E-16




Akoto Chama Leonel

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725 0,0007 213,27 5E-09 0,000206 3,33E-07 7,46445E-10 1,53539E-13 2,49E-16

730 0,0005 216,12 5E-09 0,000183 4,62E-07 5,403E-10 9,87457E-14 2,50E-16

735 0,0004 218,92 5E-09 0,000158 6,52E-07 4,3784E-10 6,90948E-14 2,86E-16

740 0,0002 221,67 5E-09 0,000127 8,25E-07 2,2167E-10 2,80602E-14 1,83E-16

745 0,0002 224,36 5E-09 9,26E-05 1,24E-06 2,2436E-10 2,07804E-14 2,78E-16

750 0,0001 227 5E-09 0,000105 1,74E-06 1,135E-10 1,19456E-14 1,98E-16

755 0,0001 229,59 5E-09 7,69E-05 2,27E-06 1,14795E-10 8,82919E-15 2,60E-16

760 0,0001 232,12 5E-09 5,34E-05 2,97E-06 1,1606E-10 6,19851E-15 3,45E-16

765 0 234,57 5E-09 5,71E-05 3,81E-06 0 0 0,00E+00

770 0 237,01 5E-09 3,81E-05 4,89E-06 0 0 0,00E+00

775 0 239,35 5E-09 3,96E-05 5,85E-06 0 0 0,00E+00

780 0 241,68 5E-09 3,17E-05 6,97E-06 0 0 0,00E+00

∑D=1,08E-5 ∑∏3=1,22E-06 ∑∏13=5,17E-11

Table 21 Calculation of luminous transmittance

Where ζ3 = The measured transmittance of the light state

ζ13 = The measured transmittance of the dark state

D = V(λ).S(λ).∆λ

∏3 = V(λ).S(λ). ζ3.∆λ

∏13 = V(λ).S(λ). ζ13.∆λ

Λ(nm) L(λ) L(λ).V(λ).∆λ L(λ).V(λ).ζ3(λ).∆λ

380 14154281670 0 0

385 14154281670 0,007077141 -1,67268E-09

390 14154281670 0,007077141 -4,0835E-08

395 14154281670 0,014154282 -3,34197E-08

400 14154281670 0,028308563 2,25134E-06

405 14154281670 0,042462845 8,27275E-06

410 14154281670 0,08492569 4,03286E-05

415 14154281670 0,155697098 0,000109121

420 14154281670 0,283085633 0,000239082

425 14154281670 0,516631281 0,000541935

430 14154281670 0,820948337 0,000999303

435 14154281670 1,18895966 0,001697114

440 14154281670 1,627742392 0,002864017

445 14154281670 2,108987969 0,004498076

450 14154281670 2,689313517 0,006848095




Akoto Chama Leonel

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455 14154281670 3,397027601 0,011118213

460 14154281670 4,246284501 0,017553708

465 14154281670 5,230007077 0,027985296

470 14154281670 6,44019816 0,047111625

475 14154281670 7,96886058 0,0785062

480 14154281670 9,837225761 0,131692419

485 14154281670 11,98159943 0,230589586

490 14154281670 14,72045294 0,411648003

495 14154281670 18,3014862 0,741329936

500 14154281670 22,8591649 1,355102135

505 14154281670 28,82519462 2,535918802

510 14154281670 35,5980184 4,328002999

515 14154281670 43,04317056 6,359788584

520 14154281670 50,24769993 8,218920133

525 14154281670 56,1358811 9,704214951

530 14154281670 61,004954 10,41705946

535 14154281670 64,7487615 10,36987005

540 14154281670 67,51592357 10,0974477

545 14154281670 69,37721161 10,20261495

550 14154281670 70,41755131 10,31682644

555 14154281670 70,77140835 10,28395475

560 14154281670 70,41755131 9,86669648

565 14154281670 69,25690021 9,427579159

570 14154281670 67,37438075 8,979543142

575 14154281670 64,7841472 8,334193716

580 14154281670 61,57112527 7,488766263

585 14154281670 57,77070064 6,432534876

590 14154281670 53,57395612 5,503309558

595 14154281670 49,17905166 4,773461494

600 14154281670 44,65675867 4,139447073

605 14154281670 40,11323425 3,606087856

610 14154281670 35,5980184 3,087348442

615 14154281670 31,22434536 2,589024021

620 14154281670 26,96390658 2,120644333

625 14154281670 22,71762208 1,620234016

630 14154281670 18,75442321 1,122698986

635 14154281670 15,35739561 0,709632342

640 14154281670 12,38499646 0,407469789




Akoto Chama Leonel

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645 14154281670 9,780608634 0,218237886

650 14154281670 7,572540694 0,113819346

655 14154281670 5,774946921 0,058920522

660 14154281670 4,317055909 0,030142849

665 14154281670 3,156404812 0,015548296

670 14154281670 2,264685067 0,007869668

675 14154281670 1,641896674 0,003996032

680 14154281670 1,203113942 0,002202074

685 14154281670 0,842179759 0,00114236

690 14154281670 0,580325548 0,000605527

695 14154281670 0,403397028 0,000324504

700 14154281670 0,290162774 0,000180576

705 14154281670 0,205237084 9,50756E-05

710 14154281670 0,148619958 5,59864E-05

715 14154281670 0,106157113 3,28971E-05

720 14154281670 0,070771408 1,79297E-05

725 14154281670 0,049539986 1,01901E-05

730 14154281670 0,035385704 6,46712E-06

735 14154281670 0,028308563 4,46732E-06

740 14154281670 0,014154282 1,79173E-06

745 14154281670 0,014154282 1,31098E-06

750 14154281670 0,007077141 7,44852E-07

755 14154281670 0,007077141 5,44322E-07

760 14154281670 0,007077141 3,77974E-07

765 14154281670 0 0

770 14154281670 0 0

775 14154281670 0 0

780 14154281670 0 0

∑( )=1512,46 ∑( )=176,57

Table 24 Calculation of Comfort Factor

λ(nm) L(λ) B(λ) ∆λ L(λ).B(λ).∆λ

300 71959887 0,01 5E-09 0,003597994

305 71959887 0,01 5E-09 0,003597994

310 71959887 0,01 5E-09 0,003597994

315 71959887 0,01 5E-09 0,003597994




Akoto Chama Leonel

Page 95(128)

320 71959887 0,01 5E-09 0,003597994

325 71959887 0,01 5E-09 0,003597994

330 71959887 0,01 5E-09 0,003597994

335 71959887 0,01 5E-09 0,003597994

340 71959887 0,01 5E-09 0,003597994

345 71959887 0,01 5E-09 0,003597994

350 71959887 0,01 5E-09 0,003597994

355 71959887 0,01 5E-09 0,003597994

360 71959887 0,01 5E-09 0,003597994

365 71959887 0,01 5E-09 0,003597994

370 71959887 0,01 5E-09 0,003597994

375 71959887 0,01 5E-09 0,003597994

380 71959887 0,01 5E-09 0,003597994

385 71959887 0,013 5E-09 0,004677393

390 71959887 0,025 5E-09 0,008994986

395 71959887 0,05 5E-09 0,017989972

400 71959887 0,1 5E-09 0,035979944

405 71959887 0,2 5E-09 0,071959887

410 71959887 0,4 5E-09 0,143919775

415 71959887 0,8 5E-09 0,28783955

420 71959887 0,9 5E-09 0,323819493

425 71959887 0,95 5E-09 0,341809465

430 71959887 0,98 5E-09 0,352603448

435 71959887 1 5E-09 0,359799437

440 71959887 1 5E-09 0,359799437

445 71959887 0,97 5E-09 0,349005454

450 71959887 0,94 5E-09 0,338211471

455 71959887 0,9 5E-09 0,323819493

460 71959887 0,8 5E-09 0,28783955

465 71959887 0,7 5E-09 0,251859606

470 71959887 0,62 5E-09 0,223075651

475 71959887 0,55 5E-09 0,19788969

480 71959887 0,45 5E-09 0,161909747

485 71959887 0,32 5E-09 0,11513582

490 71959887 0,22 5E-09 0,079155876

495 71959887 0,16 5E-09 0,05756791

500 71959887 0,1 5E-09 0,035979944

505 71959887 0,079433 5E-09 0,028579885




Akoto Chama Leonel

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510 71959887 0,063096 5E-09 0,02270181

515 71959887 0,050119 5E-09 0,018032688

520 71959887 0,039811 5E-09 0,014323874

525 71959887 0,031623 5E-09 0,011377857

530 71959887 0,025119 5E-09 0,009037753

535 71959887 0,019953 5E-09 0,007178943

540 71959887 0,015849 5E-09 0,005702437

545 71959887 0,012589 5E-09 0,004529607

550 71959887 0,01 5E-09 0,003597994

555 71959887 0,007943 5E-09 0,002857989

560 71959887 0,00631 5E-09 0,002270181

565 71959887 0,005012 5E-09 0,001803269

570 71959887 0,003981 5E-09 0,001432387

575 71959887 0,003162 5E-09 0,001137786

580 71959887 0,002512 5E-09 0,000903775

585 71959887 0,001995 5E-09 0,000717894

590 71959887 0,001585 5E-09 0,000570244

595 71959887 0,001259 5E-09 0,000452961

600 71959887 0,001 5E-09 0,000359799

605 71959887 0,001 5E-09 0,000359799

610 71959887 0,001 5E-09 0,000359799

615 71959887 0,001 5E-09 0,000359799

620 71959887 0,001 5E-09 0,000359799

625 71959887 0,001 5E-09 0,000359799

630 71959887 0,001 5E-09 0,000359799

635 71959887 0,001 5E-09 0,000359799

640 71959887 0,001 5E-09 0,000359799

645 71959887 0,001 5E-09 0,000359799

650 71959887 0,001 5E-09 0,000359799

655 71959887 0,001 5E-09 0,000359799

660 71959887 0,001 5E-09 0,000359799

665 71959887 0,001 5E-09 0,000359799

670 71959887 0,001 5E-09 0,000359799

675 71959887 0,001 5E-09 0,000359799

680 71959887 0,001 5E-09 0,000359799

685 71959887 0,001 5E-09 0,000359799

690 71959887 0,001 5E-09 0,000359799

695 71959887 0,001 5E-09 0,000359799




Akoto Chama Leonel

Page 97(128)

700 71959887 0,001 5E-09 0,000359799

∑( ) =4,94

Table 25 Calculation of LB

λ(nm) ζ3 B(λ) ∆λ B(λ).∆λ ζ3(λ).B(λ).∆λ

300 5,69E-06 0,01 5E-09 5E-11 2,84497E-16

305 4,02E-06 0,01 5E-09 5E-11 2,00794E-16

310 1,88E-06 0,01 5E-09 5E-11 9,39061E-17

315 1,07E-05 0,01 5E-09 5E-11 5,33604E-16

320 3,56E-06 0,01 5E-09 5E-11 1,77895E-16

325 -3,2E-06 0,01 5E-09 5E-11 -1,60496E-16

330 -6,7E-07 0,01 5E-09 5E-11 -3,32579E-17

335 -1,7E-07 0,01 5E-09 5E-11 -8,5698E-18

340 2,09E-05 0,01 5E-09 5E-11 1,04373E-15

345 4,26E-08 0,01 5E-09 5E-11 2,13229E-18

350 -1,8E-06 0,01 5E-09 5E-11 -8,93657E-17

355 4,15E-06 0,01 5E-09 5E-11 2,07578E-16

360 3,64E-06 0,01 5E-09 5E-11 1,82168E-16

365 -2,9E-06 0,01 5E-09 5E-11 -1,47321E-16

370 1,54E-05 0,01 5E-09 5E-11 7,68111E-16

375 -6,9E-06 0,01 5E-09 5E-11 -3,42965E-16

380 2,54E-06 0,01 5E-09 5E-11 1,27203E-16

385 -2,4E-07 0,013 5E-09 6,5E-11 -1,53627E-17

390 -5,8E-06 0,025 5E-09 1,25E-10 -7,21248E-16

395 -2,4E-06 0,05 5E-09 2,5E-10 -5,90276E-16

400 7,95E-05 0,1 5E-09 5E-10 3,97642E-14

405 0,000195 0,2 5E-09 0,000000001 1,94823E-13

410 0,000475 0,4 5E-09 0,000000002 9,49738E-13

415 0,000701 0,8 5E-09 0,000000004 2,80341E-12

420 0,000845 0,9 5E-09 4,5E-09 3,8005E-12

425 0,001049 0,95 5E-09 4,75E-09 4,98265E-12

430 0,001217 0,98 5E-09 4,9E-09 5,96455E-12

435 0,001427 1 5E-09 0,000000005 7,13697E-12

440 0,00176 1 5E-09 0,000000005 8,79751E-12

445 0,002133 0,97 5E-09 4,85E-09 1,03441E-11

450 0,002546 0,94 5E-09 4,7E-09 1,19681E-11




Akoto Chama Leonel

Page 98(128)

455 0,003273 0,9 5E-09 4,5E-09 1,47282E-11

460 0,004134 0,8 5E-09 0,000000004 1,65356E-11

465 0,005351 0,7 5E-09 3,5E-09 1,87282E-11

470 0,007315 0,62 5E-09 3,1E-09 2,26773E-11

475 0,009852 0,55 5E-09 2,75E-09 2,7092E-11

480 0,013387 0,45 5E-09 2,25E-09 3,01211E-11

485 0,019245 0,32 5E-09 1,6E-09 3,07925E-11

490 0,027964 0,22 5E-09 1,1E-09 3,07608E-11

495 0,040507 0,16 5E-09 8E-10 3,24052E-11

500 0,05928 0,1 5E-09 5E-10 2,96402E-11

505 0,087976 0,079433 5E-09 3,97164E-10 3,49408E-11

510 0,12158 0,063096 5E-09 3,15479E-10 3,83559E-11

515 0,147754 0,050119 5E-09 2,50594E-10 3,70261E-11

520 0,163568 0,039811 5E-09 1,99054E-10 3,25588E-11

525 0,17287 0,031623 5E-09 1,58114E-10 2,73332E-11

530 0,170758 0,025119 5E-09 1,25594E-10 2,14462E-11

535 0,160155 0,019953 5E-09 9,97631E-11 1,59776E-11

540 0,149557 0,015849 5E-09 7,92447E-11 1,18516E-11

545 0,14706 0,012589 5E-09 6,29463E-11 9,25688E-12

550 0,146509 0,01 5E-09 5E-11 7,32547E-12

555 0,145312 0,007943 5E-09 3,97164E-11 5,77128E-12

560 0,140117 0,00631 5E-09 3,15479E-11 4,42039E-12

565 0,136125 0,005012 5E-09 2,50594E-11 3,4112E-12

570 0,133278 0,003981 5E-09 1,99054E-11 2,65295E-12

575 0,128646 0,003162 5E-09 1,58114E-11 2,03407E-12

580 0,121628 0,002512 5E-09 1,25594E-11 1,52758E-12

585 0,111346 0,001995 5E-09 9,97631E-12 1,11082E-12

590 0,102724 0,001585 5E-09 7,92447E-12 8,1403E-13

595 0,097063 0,001259 5E-09 6,29463E-12 6,10975E-13

600 0,092695 0,001 5E-09 5E-12 4,63474E-13

605 0,089898 0,001 5E-09 5E-12 4,49489E-13

610 0,086728 0,001 5E-09 5E-12 4,3364E-13

615 0,082917 0,001 5E-09 5E-12 4,14584E-13

620 0,078648 0,001 5E-09 5E-12 3,93238E-13

625 0,071321 0,001 5E-09 5E-12 3,56603E-13

630 0,059863 0,001 5E-09 5E-12 2,99316E-13

635 0,046208 0,001 5E-09 5E-12 2,31039E-13

640 0,0329 0,001 5E-09 5E-12 1,64501E-13




Akoto Chama Leonel

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645 0,022313 0,001 5E-09 5E-12 1,11567E-13

650 0,015031 0,001 5E-09 5E-12 7,51527E-14

655 0,010203 0,001 5E-09 5E-12 5,10139E-14

660 0,006982 0,001 5E-09 5E-12 3,49113E-14

665 0,004926 0,001 5E-09 5E-12 2,46298E-14

670 0,003475 0,001 5E-09 5E-12 1,73748E-14

675 0,002434 0,001 5E-09 5E-12 1,2169E-14

680 0,00183 0,001 5E-09 5E-12 9,15156E-15

685 0,001356 0,001 5E-09 5E-12 6,78216E-15

690 0,001043 0,001 5E-09 5E-12 5,21713E-15

695 0,000804 0,001 5E-09 5E-12 4,02214E-15

700 0,000622 0,001 5E-09 5E-12 3,11163E-15

∑( )=6,86E-08 ∑( )=5,73E-10

Table 26 Calculation of TB3

λ(nm) L(λ) B(λ) ζ3 ∆λ L(λ).B(λ).∆λ L(λ).B(λ).ζ(λ).∆λ

300 71959887 0,01 5,69E-06 5E-09 0,003598 2,04723E-08

305 71959887 0,01 4,02E-06 5E-09 0,003598 1,44491E-08

310 71959887 0,01 1,88E-06 5E-09 0,003598 6,75747E-09

315 71959887 0,01 1,07E-05 5E-09 0,003598 3,83981E-08

320 71959887 0,01 3,56E-06 5E-09 0,003598 1,28013E-08

325 71959887 0,01 -3,2E-06 5E-09 0,003598 -1,1549E-08

330 71959887 0,01 -6,7E-07 5E-09 0,003598 -2,3932E-09

335 71959887 0,01 -1,7E-07 5E-09 0,003598 -6,1668E-10

340 71959887 0,01 2,09E-05 5E-09 0,003598 7,51064E-08

345 71959887 0,01 4,26E-08 5E-09 0,003598 1,53439E-10

350 71959887 0,01 -1,8E-06 5E-09 0,003598 -6,4307E-09

355 71959887 0,01 4,15E-06 5E-09 0,003598 1,49373E-08

360 71959887 0,01 3,64E-06 5E-09 0,003598 1,31088E-08

365 71959887 0,01 -2,9E-06 5E-09 0,003598 -1,0601E-08

370 71959887 0,01 1,54E-05 5E-09 0,003598 5,52732E-08

375 71959887 0,01 -6,9E-06 5E-09 0,003598 -2,468E-08

380 71959887 0,01 2,54E-06 5E-09 0,003598 9,1535E-09

385 71959887 0,013 -2,4E-07 5E-09 0,004677 -1,1055E-09

390 71959887 0,025 -5,8E-06 5E-09 0,008995 -5,1901E-08

395 71959887 0,05 -2,4E-06 5E-09 0,01799 -4,2476E-08




Akoto Chama Leonel

Page 100(128)

400 71959887 0,1 7,95E-05 5E-09 0,03598 2,86143E-06

405 71959887 0,2 0,000195 5E-09 0,07196 1,40195E-05

410 71959887 0,4 0,000475 5E-09 0,14392 6,8343E-05

415 71959887 0,8 0,000701 5E-09 0,28784 0,000201733

420 71959887 0,9 0,000845 5E-09 0,323819 0,000273484

425 71959887 0,95 0,001049 5E-09 0,341809 0,000358551

430 71959887 0,98 0,001217 5E-09 0,352603 0,000429208

435 71959887 1 0,001427 5E-09 0,359799 0,000513576

440 71959887 1 0,00176 5E-09 0,359799 0,000633068

445 71959887 0,97 0,002133 5E-09 0,349005 0,000744363

450 71959887 0,94 0,002546 5E-09 0,338211 0,000861225

455 71959887 0,9 0,003273 5E-09 0,323819 0,001059837

460 71959887 0,8 0,004134 5E-09 0,28784 0,001189899

465 71959887 0,7 0,005351 5E-09 0,25186 0,001347678

470 71959887 0,62 0,007315 5E-09 0,223076 0,001631853

475 71959887 0,55 0,009852 5E-09 0,19789 0,001949534

480 71959887 0,45 0,013387 5E-09 0,16191 0,00216751

485 71959887 0,32 0,019245 5E-09 0,115136 0,002215824

490 71959887 0,22 0,027964 5E-09 0,079156 0,002213543

495 71959887 0,16 0,040507 5E-09 0,057568 0,002331877

500 71959887 0,1 0,05928 5E-09 0,03598 0,002132908

505 71959887 0,079433 0,087976 5E-09 0,02858 0,002514337

510 71959887 0,063096 0,12158 5E-09 0,022702 0,002760083

515 71959887 0,050119 0,147754 5E-09 0,018033 0,002664397

520 71959887 0,039811 0,163568 5E-09 0,014324 0,002342929

525 71959887 0,031623 0,17287 5E-09 0,011378 0,001966891

530 71959887 0,025119 0,170758 5E-09 0,009038 0,001543265

535 71959887 0,019953 0,160155 5E-09 0,007179 0,001149747

540 71959887 0,015849 0,149557 5E-09 0,005702 0,000852837

545 71959887 0,012589 0,14706 5E-09 0,00453 0,000666124

550 71959887 0,01 0,146509 5E-09 0,003598 0,00052714

555 71959887 0,007943 0,145312 5E-09 0,002858 0,000415301

560 71959887 0,00631 0,140117 5E-09 0,00227 0,000318091

565 71959887 0,005012 0,136125 5E-09 0,001803 0,00024547

570 71959887 0,003981 0,133278 5E-09 0,001432 0,000190906

575 71959887 0,003162 0,128646 5E-09 0,001138 0,000146371

580 71959887 0,002512 0,121628 5E-09 0,000904 0,000109924

585 71959887 0,001995 0,111346 5E-09 0,000718 7,99346E-05




Akoto Chama Leonel

Page 101(128)

590 71959887 0,001585 0,102724 5E-09 0,00057 5,85775E-05

595 71959887 0,001259 0,097063 5E-09 0,000453 4,39657E-05

600 71959887 0,001 0,092695 5E-09 0,00036 3,33515E-05

605 71959887 0,001 0,089898 5E-09 0,00036 3,23451E-05

610 71959887 0,001 0,086728 5E-09 0,00036 3,12047E-05

615 71959887 0,001 0,082917 5E-09 0,00036 2,98334E-05

620 71959887 0,001 0,078648 5E-09 0,00036 2,82973E-05

625 71959887 0,001 0,071321 5E-09 0,00036 2,56611E-05

630 71959887 0,001 0,059863 5E-09 0,00036 2,15387E-05

635 71959887 0,001 0,046208 5E-09 0,00036 1,66256E-05

640 71959887 0,001 0,0329 5E-09 0,00036 1,18375E-05

645 71959887 0,001 0,022313 5E-09 0,00036 8,02832E-06

650 71959887 0,001 0,015031 5E-09 0,00036 5,40798E-06

655 71959887 0,001 0,010203 5E-09 0,00036 3,67096E-06

660 71959887 0,001 0,006982 5E-09 0,00036 2,51222E-06

665 71959887 0,001 0,004926 5E-09 0,00036 1,77235E-06

670 71959887 0,001 0,003475 5E-09 0,00036 1,25029E-06

675 71959887 0,001 0,002434 5E-09 0,00036 8,75676E-07

680 71959887 0,001 0,00183 5E-09 0,00036 6,58545E-07

685 71959887 0,001 0,001356 5E-09 0,00036 4,88044E-07

690 71959887 0,001 0,001043 5E-09 0,00036 3,75424E-07

695 71959887 0,001 0,000804 5E-09 0,00036 2,89433E-07

700 71959887 0,001 0,000622 5E-09 0,00036 2,23913E-07

∑( ) =4,94 ∑( ) =4,12E-2

Table 27 Calculation of PFBLPH

λ(nm) L(λ) B(λ) ∆λ L(λ).B(λ).∆λ

300 1,39E+12 0,01 5E-09 69,46128024

305 1,39E+12 0,01 5E-09 69,46128024

310 1,39E+12 0,01 5E-09 69,46128024

315 1,39E+12 0,01 5E-09 69,46128024

320 1,39E+12 0,01 5E-09 69,46128024

325 1,39E+12 0,01 5E-09 69,46128024

330 1,39E+12 0,01 5E-09 69,46128024

335 1,39E+12 0,01 5E-09 69,46128024

340 1,39E+12 0,01 5E-09 69,46128024




Akoto Chama Leonel

Page 102(128)

345 1,39E+12 0,01 5E-09 69,46128024

350 1,39E+12 0,01 5E-09 69,46128024

355 1,39E+12 0,01 5E-09 69,46128024

360 1,39E+12 0,01 5E-09 69,46128024

365 1,39E+12 0,01 5E-09 69,46128024

370 1,39E+12 0,01 5E-09 69,46128024

375 1,39E+12 0,01 5E-09 69,46128024

380 1,39E+12 0,01 5E-09 69,46128024

385 1,39E+12 0,013 5E-09 90,29966431

390 1,39E+12 0,025 5E-09 173,6532006

395 1,39E+12 0,05 5E-09 347,3064012

400 1,39E+12 0,1 5E-09 694,6128024

405 1,39E+12 0,2 5E-09 1389,225605

410 1,39E+12 0,4 5E-09 2778,45121

415 1,39E+12 0,8 5E-09 5556,902419

420 1,39E+12 0,9 5E-09 6251,515222

425 1,39E+12 0,95 5E-09 6598,821623

430 1,39E+12 0,98 5E-09 6807,205464

435 1,39E+12 1 5E-09 6946,128024

440 1,39E+12 1 5E-09 6946,128024

445 1,39E+12 0,97 5E-09 6737,744183

450 1,39E+12 0,94 5E-09 6529,360343

455 1,39E+12 0,9 5E-09 6251,515222

460 1,39E+12 0,8 5E-09 5556,902419

465 1,39E+12 0,7 5E-09 4862,289617

470 1,39E+12 0,62 5E-09 4306,599375

475 1,39E+12 0,55 5E-09 3820,370413

480 1,39E+12 0,45 5E-09 3125,757611

485 1,39E+12 0,32 5E-09 2222,760968

490 1,39E+12 0,22 5E-09 1528,148165

495 1,39E+12 0,16 5E-09 1111,380484

500 1,39E+12 0,1 5E-09 694,6128024

505 1,39E+12 0,079433 5E-09 551,7505612

510 1,39E+12 0,063096 5E-09 438,2710493

515 1,39E+12 0,050119 5E-09 348,1310689

520 1,39E+12 0,039811 5E-09 276,5303374

525 1,39E+12 0,031623 5E-09 219,6558548

530 1,39E+12 0,025119 5E-09 174,4788474




Akoto Chama Leonel

Page 103(128)

535 1,39E+12 0,019953 5E-09 138,5934748

540 1,39E+12 0,015849 5E-09 110,0887102

545 1,39E+12 0,012589 5E-09 87,44657083

550 1,39E+12 0,01 5E-09 69,46128024

555 1,39E+12 0,007943 5E-09 55,17505612

560 1,39E+12 0,00631 5E-09 43,82710493

565 1,39E+12 0,005012 5E-09 34,81310689

570 1,39E+12 0,003981 5E-09 27,65303374

575 1,39E+12 0,003162 5E-09 21,96558548

580 1,39E+12 0,002512 5E-09 17,44788474

585 1,39E+12 0,001995 5E-09 13,85934748

590 1,39E+12 0,001585 5E-09 11,00887102

595 1,39E+12 0,001259 5E-09 8,744657083

600 1,39E+12 0,001 5E-09 6,946128024

605 1,39E+12 0,001 5E-09 6,946128024

610 1,39E+12 0,001 5E-09 6,946128024

615 1,39E+12 0,001 5E-09 6,946128024

620 1,39E+12 0,001 5E-09 6,946128024

625 1,39E+12 0,001 5E-09 6,946128024

630 1,39E+12 0,001 5E-09 6,946128024

635 1,39E+12 0,001 5E-09 6,946128024

640 1,39E+12 0,001 5E-09 6,946128024

645 1,39E+12 0,001 5E-09 6,946128024

650 1,39E+12 0,001 5E-09 6,946128024

655 1,39E+12 0,001 5E-09 6,946128024

660 1,39E+12 0,001 5E-09 6,946128024

665 1,39E+12 0,001 5E-09 6,946128024

670 1,39E+12 0,001 5E-09 6,946128024

675 1,39E+12 0,001 5E-09 6,946128024

680 1,39E+12 0,001 5E-09 6,946128024

685 1,39E+12 0,001 5E-09 6,946128024

690 1,39E+12 0,001 5E-09 6,946128024

695 1,39E+12 0,001 5E-09 6,946128024

700 1,39E+12 0,001 5E-09 6,946128024

∑( ) =9,54E+4

Table 28 Calculation of LB




Akoto Chama Leonel

Page 104(128)

λ(nm) L(λ) R(λ) ∆λ L(λ).R(λ).∆λ

380 71959887 0,1 5E-09 0,035979944

385 71959887 0,13 5E-09 0,046773927

390 71959887 0,25 5E-09 0,089949859

395 71959887 0,5 5E-09 0,179899718

400 71959887 1 5E-09 0,359799435

405 71959887 2 5E-09 0,71959887

410 71959887 4 5E-09 1,43919774

415 71959887 8 5E-09 2,87839548

420 71959887 9 5E-09 3,238194915

425 71959887 9,5 5E-09 3,418094633

430 71959887 9,8 5E-09 3,526034463

435 71959887 10 5E-09 3,59799435

440 71959887 10 5E-09 3,59799435

445 71959887 9,7 5E-09 3,49005452

450 71959887 9,4 5E-09 3,382114689

455 71959887 9 5E-09 3,238194915

460 71959887 8 5E-09 2,87839548

465 71959887 7 5E-09 2,518596045

470 71959887 6,2 5E-09 2,230756497

475 71959887 5,5 5E-09 1,978896893

480 71959887 4,5 5E-09 1,619097458

485 71959887 3,2 5E-09 1,151358192

490 71959887 2,2 5E-09 0,791558757

495 71959887 1,6 5E-09 0,575679096

500 71959887 1 5E-09 0,359799435

505 71959887 1 5E-09 0,359799435

510 71959887 1 5E-09 0,359799435

515 71959887 1 5E-09 0,359799435

520 71959887 1 5E-09 0,359799435

525 71959887 1 5E-09 0,359799435

530 71959887 1 5E-09 0,359799435

535 71959887 1 5E-09 0,359799435

540 71959887 1 5E-09 0,359799435

545 71959887 1 5E-09 0,359799435

550 71959887 1 5E-09 0,359799435

555 71959887 1 5E-09 0,359799435

560 71959887 1 5E-09 0,359799435




Akoto Chama Leonel

Page 105(128)

565 71959887 1 5E-09 0,359799435

570 71959887 1 5E-09 0,359799435

575 71959887 1 5E-09 0,359799435

580 71959887 1 5E-09 0,359799435

585 71959887 1 5E-09 0,359799435

590 71959887 1 5E-09 0,359799435

595 71959887 1 5E-09 0,359799435

600 71959887 1 5E-09 0,359799435

605 71959887 1 5E-09 0,359799435

610 71959887 1 5E-09 0,359799435

615 71959887 1 5E-09 0,359799435

620 71959887 1 5E-09 0,359799435

625 71959887 1 5E-09 0,359799435

630 71959887 1 5E-09 0,359799435

635 71959887 1 5E-09 0,359799435

640 71959887 1 5E-09 0,359799435

645 71959887 1 5E-09 0,359799435

650 71959887 1 5E-09 0,359799435

655 71959887 1 5E-09 0,359799435

660 71959887 1 5E-09 0,359799435

665 71959887 1 5E-09 0,359799435

670 71959887 1 5E-09 0,359799435

675 71959887 1 5E-09 0,359799435

680 71959887 1 5E-09 0,359799435

685 71959887 1 5E-09 0,359799435

690 71959887 1 5E-09 0,359799435

695 71959887 1 5E-09 0,359799435

700 71959887 1 5E-09 0,359799435

705 71959887 0,977237 5E-09 0,3516094

710 71959887 0,954993 5E-09 0,343605793

715 71959887 0,933254 5E-09 0,33578437

720 71959887 0,912011 5E-09 0,328140985

725 71959887 0,891251 5E-09 0,320671584

730 71959887 0,870964 5E-09 0,313372208

735 71959887 0,851138 5E-09 0,306238985

740 71959887 0,831764 5E-09 0,299268135

745 71959887 0,812831 5E-09 0,29245596

750 71959887 0,794328 5E-09 0,28579885




Akoto Chama Leonel

Page 106(128)

755 71959887 0,776247 5E-09 0,279293274

760 71959887 0,758578 5E-09 0,272935783

765 71959887 0,74131 5E-09 0,266723006

770 71959887 0,724436 5E-09 0,260651649

775 71959887 0,707946 5E-09 0,254718493

780 71959887 0,691831 5E-09 0,248920392

790 71959887 0,660693 1E-08 0,475434259

800 71959887 0,630957 1E-08 0,454036192

810 71959887 0,60256 1E-08 0,433601197

820 71959887 0,57544 1E-08 0,414085929

830 71959887 0,549541 1E-08 0,395448992

840 71959887 0,524807 1E-08 0,377650855

850 71959887 0,501187 1E-08 0,360653767

860 71959887 0,47863 1E-08 0,344421674

870 71959887 0,457088 1E-08 0,328920145

880 71959887 0,436516 1E-08 0,3141163

890 71959887 0,416869 1E-08 0,299978737

900 71959887 0,398107 1E-08 0,28647747

910 71959887 0,380189 1E-08 0,27358386

920 71959887 0,363078 1E-08 0,261270558

930 71959887 0,346737 1E-08 0,249511446

940 71959887 0,331131 1E-08 0,238281581

950 71959887 0,316228 1E-08 0,227557143

960 71959887 0,301995 1E-08 0,217315385

970 71959887 0,288403 1E-08 0,207534581

980 71959887 0,275423 1E-08 0,198193986

990 71959887 0,263027 1E-08 0,189273787

1000 71959887 0,251189 1E-08 0,180755064

1010 71959887 0,239883 1E-08 0,172619746

1020 71959887 0,229087 1E-08 0,164850577

1030 71959887 0,218776 1E-08 0,157431079

1040 71959887 0,20893 1E-08 0,150345513

1050 71959887 0,199526 1E-08 0,143578851

1060 71959887 0,2 1E-08 0,143919774

1070 71959887 0,2 1E-08 0,143919774

1080 71959887 0,2 1E-08 0,143919774

1090 71959887 0,2 1E-08 0,143919774

1100 71959887 0,2 1E-08 0,143919774




Akoto Chama Leonel

Page 107(128)

1110 71959887 0,2 1E-08 0,143919774

1120 71959887 0,2 1E-08 0,143919774

1130 71959887 0,2 1E-08 0,143919774

1140 71959887 0,2 1E-08 0,143919774

1150 71959887 0,2 1E-08 0,143919774

1160 71959887 0,126191 1E-08 0,090807238

1170 71959887 0,079621 1E-08 0,057295494

1180 71959887 0,050238 1E-08 0,036151013

1190 71959887 0,031698 1E-08 0,022809747

1200 71959887 0,02 1E-08 0,014391977

1210 71959887 0,02 1E-08 0,014391977

1220 71959887 0,02 1E-08 0,014391977

1230 71959887 0,02 1E-08 0,014391977

1240 71959887 0,02 1E-08 0,014391977

1250 71959887 0,02 1E-08 0,014391977

1260 71959887 0,02 1E-08 0,014391977

1270 71959887 0,02 1E-08 0,014391977

1280 71959887 0,02 1E-08 0,014391977

1290 71959887 0,02 1E-08 0,014391977

1300 71959887 0,02 1E-08 0,014391977

1310 71959887 0,02 1E-08 0,014391977

1320 71959887 0,02 1E-08 0,014391977

1330 71959887 0,02 1E-08 0,014391977

1340 71959887 0,02 1E-08 0,014391977

1350 71959887 0,02 1E-08 0,014391977

1360 71959887 0,02 1E-08 0,014391977

1370 71959887 0,02 1E-08 0,014391977

1380 71959887 0,02 1E-08 0,014391977

1390 71959887 0,02 1E-08 0,014391977

1400 71959887 0,02 1E-08 0,014391977

∑( )=75,96

Table 29 Calculation of LR

λ(nm) ζ3 R(λ) ∆λ R(λ).∆λ ζ3(λ).R(λ).∆λ

380 3,9E-08 0,1 5E-09 5E-10 1,95249E-17

385 4,33E-08 0,13 5E-09 6,5E-10 2,81555E-17




Akoto Chama Leonel

Page 108(128)

390 3,27E-07 0,25 5E-09 1,25E-09 4,08882E-16

395 8,95E-06 0,5 5E-09 2,5E-09 2,23874E-14

400 7,17E-05 1 5E-09 0,000000005 3,5867E-13

405 0,000206 2 5E-09 0,00000001 2,05515E-12

410 0,000416 4 5E-09 0,00000002 8,31356E-12

415 0,000573 8 5E-09 0,00000004 2,294E-11

420 0,000728 9 5E-09 0,000000045 3,27511E-11

425 0,000912 9,5 5E-09 4,75E-08 4,33213E-11

430 0,00099 9,8 5E-09 0,000000049 4,84885E-11

435 0,001257 10 5E-09 0,00000005 6,28477E-11

440 0,001502 10 5E-09 0,00000005 7,50917E-11

445 0,001723 9,7 5E-09 4,85E-08 8,35698E-11

450 0,002212 9,4 5E-09 0,000000047 1,03986E-10

455 0,002803 9 5E-09 0,000000045 1,26156E-10

460 0,003452 8 5E-09 0,00000004 1,38096E-10

465 0,004582 7 5E-09 0,000000035 1,60358E-10

470 0,006205 6,2 5E-09 0,000000031 1,92368E-10

475 0,008121 5,5 5E-09 2,75E-08 2,23336E-10

480 0,01132 4,5 5E-09 2,25E-08 2,54691E-10

485 0,016289 3,2 5E-09 0,000000016 2,60622E-10

490 0,02348 2,2 5E-09 0,000000011 2,58281E-10

495 0,033501 1,6 5E-09 0,000000008 2,6801E-10

500 0,051426 1 5E-09 0,000000005 2,57131E-10

505 0,076005 1 5E-09 0,000000005 3,80023E-10

510 0,104725 1 5E-09 0,000000005 5,23627E-10

515 0,129771 1 5E-09 0,000000005 6,48854E-10

520 0,149814 1 5E-09 0,000000005 7,4907E-10

525 0,160977 1 5E-09 0,000000005 8,04886E-10

530 0,15762 1 5E-09 0,000000005 7,881E-10

535 0,15762 1 5E-09 0,000000005 7,881E-10

540 0,15762 1 5E-09 0,000000005 7,881E-10

545 0,15762 1 5E-09 0,000000005 7,881E-10

550 0,15762 1 5E-09 0,000000005 7,881E-10

555 0,15762 1 5E-09 0,000000005 7,881E-10

560 0,15762 1 5E-09 0,000000005 7,881E-10

565 0,15762 1 5E-09 0,000000005 7,881E-10

570 0,15762 1 5E-09 0,000000005 7,881E-10

575 0,15762 1 5E-09 0,000000005 7,881E-10




Akoto Chama Leonel

Page 109(128)

580 0,15762 1 5E-09 0,000000005 7,881E-10

585 0,15762 1 5E-09 0,000000005 7,881E-10

590 0,15762 1 5E-09 0,000000005 7,881E-10

595 0,15762 1 5E-09 0,000000005 7,881E-10

600 0,15762 1 5E-09 0,000000005 7,881E-10

605 0,15762 1 5E-09 0,000000005 7,881E-10

610 0,15762 1 5E-09 0,000000005 7,881E-10

615 0,15762 1 5E-09 0,000000005 7,881E-10

620 0,15762 1 5E-09 0,000000005 7,881E-10

625 0,15762 1 5E-09 0,000000005 7,881E-10

630 0,15762 1 5E-09 0,000000005 7,881E-10

635 0,15762 1 5E-09 0,000000005 7,881E-10

640 0,15762 1 5E-09 0,000000005 7,881E-10

645 0,15762 1 5E-09 0,000000005 7,881E-10

650 0,15762 1 5E-09 0,000000005 7,881E-10

655 0,15762 1 5E-09 0,000000005 7,881E-10

660 0,15762 1 5E-09 0,000000005 7,881E-10

665 0,15762 1 5E-09 0,000000005 7,881E-10

670 0,15762 1 5E-09 0,000000005 7,881E-10

675 0,15762 1 5E-09 0,000000005 7,881E-10

680 0,001579 1 5E-09 0,000000005 7,89401E-12

685 0,001204 1 5E-09 0,000000005 6,01951E-12

690 0,000904 1 5E-09 0,000000005 4,52177E-12

695 0,000695 1 5E-09 0,000000005 3,47287E-12

700 0,000545 1 5E-09 0,000000005 2,72437E-12

705 0,000426 0,977237 5E-09 4,88619E-09 2,07957E-12

710 0,000337 0,954993 5E-09 4,77496E-09 1,61009E-12

715 0,000271 0,933254 5E-09 4,66627E-09 1,26246E-12

720 0,000221 0,912011 5E-09 4,56005E-09 1,00824E-12

725 0,000183 0,891251 5E-09 4,45625E-09 8,1469E-13

730 0,000149 0,870964 5E-09 4,35482E-09 6,47446E-13

735 0,000125 0,851138 5E-09 4,25569E-09 5,32421E-13

740 0,000105 0,831764 5E-09 4,15882E-09 4,3683E-13

745 8,77E-05 0,812831 5E-09 4,06415E-09 3,56488E-13

750 7,43E-05 0,794328 5E-09 3,97164E-09 2,95228E-13

755 6,38E-05 0,776247 5E-09 3,88124E-09 2,47779E-13

760 5,58E-05 0,758578 5E-09 3,79289E-09 2,11496E-13

765 4,81E-05 0,74131 5E-09 3,70655E-09 1,78215E-13




Akoto Chama Leonel

Page 110(128)

770 4,26E-05 0,724436 5E-09 3,62218E-09 1,54417E-13

775 3,81E-05 0,707946 5E-09 3,53973E-09 1,3473E-13

780 3,43E-05 0,691831 5E-09 3,45915E-09 1,18604E-13

790 2,83E-05 0,660693 1E-08 6,60693E-09 1,86858E-13

800 2,6E-05 0,630957 1E-08 6,30957E-09 1,63956E-13

810 2,9E-05 0,60256 1E-08 6,0256E-09 1,74648E-13

820 2,51E-05 0,57544 1E-08 5,7544E-09 1,44406E-13

830 2,34E-05 0,549541 1E-08 5,49541E-09 1,28546E-13

840 1,89E-05 0,524807 1E-08 5,24807E-09 9,92078E-14

850 1,82E-05 0,501187 1E-08 5,01187E-09 9,11082E-14

860 1,59E-05 0,47863 1E-08 4,7863E-09 7,59617E-14

870 1,39E-05 0,457088 1E-08 4,57088E-09 6,33991E-14

880 1,3E-05 0,436516 1E-08 4,36516E-09 5,65625E-14

890 1,18E-05 0,416869 1E-08 4,16869E-09 4,91348E-14

900 1,07E-05 0,398107 1E-08 3,98107E-09 4,26363E-14

910 8,75E-06 0,380189 1E-08 3,80189E-09 3,32607E-14

920 7,43E-06 0,363078 1E-08 3,63078E-09 2,69592E-14

930 6,63E-06 0,346737 1E-08 3,46737E-09 2,29738E-14

940 6,84E-06 0,331131 1E-08 3,31131E-09 2,26632E-14

950 5,11E-06 0,316228 1E-08 3,16228E-09 1,6158E-14

960 5,29E-06 0,301995 1E-08 3,01995E-09 1,59672E-14

970 4,72E-06 0,288403 1E-08 2,88403E-09 1,361E-14

980 3,82E-06 0,275423 1E-08 2,75423E-09 1,05252E-14

990 3,41E-06 0,263027 1E-08 2,63027E-09 8,96986E-15

1000 3,42E-06 0,251189 1E-08 2,51189E-09 8,5984E-15

1010 2,83E-06 0,239883 1E-08 2,39883E-09 6,77921E-15

1020 2,39E-06 0,229087 1E-08 2,29087E-09 5,4663E-15

1030 2,59E-06 0,218776 1E-08 2,18776E-09 5,66721E-15

1040 2,06E-06 0,20893 1E-08 2,0893E-09 4,29702E-15

1050 2,22E-06 0,199526 1E-08 1,99526E-09 4,42601E-15

1060 1,75E-06 0,2 1E-08 0,000000002 3,49108E-15

1070 1,82E-06 0,2 1E-08 0,000000002 3,64476E-15

1080 1,69E-06 0,2 1E-08 0,000000002 3,37485E-15

1090 1,27E-06 0,2 1E-08 0,000000002 2,53532E-15

1100 1,25E-06 0,2 1E-08 0,000000002 2,5093E-15

1110 1,21E-06 0,2 1E-08 0,000000002 2,41765E-15

1120 1,39E-06 0,2 1E-08 0,000000002 2,78536E-15

1130 8,89E-07 0,2 1E-08 0,000000002 1,77881E-15




Akoto Chama Leonel

Page 111(128)

1140 1,05E-06 0,2 1E-08 0,000000002 2,09077E-15

1150 7,3E-07 0,2 1E-08 0,000000002 1,45932E-15

1160 1,01E-06 0,126191 1E-08 1,26191E-09 1,27309E-15

1170 6,02E-07 0,079621 1E-08 7,96214E-10 4,79001E-16

1180 7,76E-07 0,050238 1E-08 5,02377E-10 3,89978E-16

1190 5,2E-07 0,031698 1E-08 3,16979E-10 1,6486E-16

1200 5,17E-07 0,02 1E-08 2E-10 1,03488E-16

1210 5,16E-07 0,02 1E-08 2E-10 1,03207E-16

1220 7,22E-07 0,02 1E-08 2E-10 1,44387E-16

1230 6,31E-07 0,02 1E-08 2E-10 1,26178E-16

1240 4,5E-07 0,02 1E-08 2E-10 8,99625E-17

1250 2,37E-07 0,02 1E-08 2E-10 4,7482E-17

1260 3,83E-07 0,02 1E-08 2E-10 7,66636E-17

1270 1,61E-07 0,02 1E-08 2E-10 3,2133E-17

1280 1,62E-07 0,02 1E-08 2E-10 3,24651E-17

1290 4,28E-07 0,02 1E-08 2E-10 8,56225E-17

1300 3,2E-07 0,02 1E-08 2E-10 6,40488E-17

1310 3,73E-07 0,02 1E-08 2E-10 7,46377E-17

1320 3,24E-07 0,02 1E-08 2E-10 6,47175E-17

1330 4,46E-07 0,02 1E-08 2E-10 8,92223E-17

1340 4,47E-07 0,02 1E-08 2E-10 8,94558E-17

1350 3,42E-07 0,02 1E-08 2E-10 6,83302E-17

1360 3,83E-07 0,02 1E-08 2E-10 7,6695E-17

1370 4,37E-08 0,02 1E-08 2E-10 8,73399E-18

1380 2,95E-07 0,02 1E-08 2E-10 5,90617E-17

1390 3,64E-08 0,02 1E-08 2E-10 7,27251E-18

1400 2,22E-07 0,02 1E-08 2E-10 4,44486E-17

∑( ) =1,06E-6 ∑( ) =2,94E-8

Table 30 Calculation of T3(V-IRA

λ(nm) L(λ) R(λ) ∆λ ζ3 L(λ).R(λ).∆λ L(λ).R(λ).ζ3(λ).∆λ

380 71959887 0,1 5E-09 3,9E-08 0,0359799 1,40501E-09

385 71959887 0,13 5E-09 4,33E-08 0,0467739 2,02607E-09

390 71959887 0,25 5E-09 3,27E-07 0,0899499 2,94231E-08

395 71959887 0,5 5E-09 8,95E-06 0,1798997 1,611E-06

400 71959887 1 5E-09 7,17E-05 0,3597994 2,58098E-05




Akoto Chama Leonel

Page 112(128)

405 71959887 2 5E-09 0,000206 0,7195989 0,000147888

410 71959887 4 5E-09 0,000416 1,4391977 0,000598243

415 71959887 8 5E-09 0,000573 2,8783955 0,001650758

420 71959887 9 5E-09 0,000728 3,2381949 0,002356767

425 71959887 9,5 5E-09 0,000912 3,4180946 0,003117393

430 71959887 9,8 5E-09 0,00099 3,5260345 0,003489224

435 71959887 10 5E-09 0,001257 3,5979944 0,00452251

440 71959887 10 5E-09 0,001502 3,5979944 0,005403591

445 71959887 9,7 5E-09 0,001723 3,4900545 0,006013672

450 71959887 9,4 5E-09 0,002212 3,3821147 0,007482802

455 71959887 9 5E-09 0,002803 3,2381949 0,009078165

460 71959887 8 5E-09 0,003452 2,8783955 0,009937398

465 71959887 7 5E-09 0,004582 2,518596 0,011539327

470 71959887 6,2 5E-09 0,006205 2,2307565 0,013842787

475 71959887 5,5 5E-09 0,008121 1,9788969 0,016071268

480 71959887 4,5 5E-09 0,01132 1,6190975 0,01832754

485 71959887 3,2 5E-09 0,016289 1,1513582 0,018754347

490 71959887 2,2 5E-09 0,02348 0,7915588 0,01858586

495 71959887 1,6 5E-09 0,033501 0,5756791 0,019285953

500 71959887 1 5E-09 0,051426 0,3597994 0,018503108

505 71959887 1 5E-09 0,076005 0,3597994 0,027346393

510 71959887 1 5E-09 0,104725 0,3597994 0,037680128

515 71959887 1 5E-09 0,129771 0,3597994 0,046691446

520 71959887 1 5E-09 0,149814 0,3597994 0,053903018

525 71959887 1 5E-09 0,160977 0,3597994 0,057919498

530 71959887 1 5E-09 0,15762 0,3597994 0,056711584

535 71959887 1 5E-09 0,15762 0,3597994 0,056711584

540 71959887 1 5E-09 0,15762 0,3597994 0,056711584

545 71959887 1 5E-09 0,15762 0,3597994 0,056711584

550 71959887 1 5E-09 0,15762 0,3597994 0,056711584

555 71959887 1 5E-09 0,15762 0,3597994 0,056711584

560 71959887 1 5E-09 0,15762 0,3597994 0,056711584

565 71959887 1 5E-09 0,15762 0,3597994 0,056711584

570 71959887 1 5E-09 0,15762 0,3597994 0,056711584

575 71959887 1 5E-09 0,15762 0,3597994 0,056711584

580 71959887 1 5E-09 0,15762 0,3597994 0,056711584

585 71959887 1 5E-09 0,15762 0,3597994 0,056711584

590 71959887 1 5E-09 0,15762 0,3597994 0,056711584




Akoto Chama Leonel

Page 113(128)

595 71959887 1 5E-09 0,15762 0,3597994 0,056711584

600 71959887 1 5E-09 0,15762 0,3597994 0,056711584

605 71959887 1 5E-09 0,15762 0,3597994 0,056711584

610 71959887 1 5E-09 0,15762 0,3597994 0,056711584

615 71959887 1 5E-09 0,15762 0,3597994 0,056711584

620 71959887 1 5E-09 0,15762 0,3597994 0,056711584

625 71959887 1 5E-09 0,15762 0,3597994 0,056711584

630 71959887 1 5E-09 0,15762 0,3597994 0,056711584

635 71959887 1 5E-09 0,15762 0,3597994 0,056711584

640 71959887 1 5E-09 0,15762 0,3597994 0,056711584

645 71959887 1 5E-09 0,15762 0,3597994 0,056711584

650 71959887 1 5E-09 0,15762 0,3597994 0,056711584

655 71959887 1 5E-09 0,15762 0,3597994 0,056711584

660 71959887 1 5E-09 0,15762 0,3597994 0,056711584

665 71959887 1 5E-09 0,15762 0,3597994 0,056711584

670 71959887 1 5E-09 0,15762 0,3597994 0,056711584

675 71959887 1 5E-09 0,15762 0,3597994 0,056711584

680 71959887 1 5E-09 0,001579 0,3597994 0,000568052

685 71959887 1 5E-09 0,001204 0,3597994 0,000433163

690 71959887 1 5E-09 0,000904 0,3597994 0,000325386

695 71959887 1 5E-09 0,000695 0,3597994 0,000249907

700 71959887 1 5E-09 0,000545 0,3597994 0,000196045

705 71959887 0,977237 5E-09 0,000426 0,3516094 0,000149645

710 71959887 0,954993 5E-09 0,000337 0,3436058 0,000115862

715 71959887 0,933254 5E-09 0,000271 0,3357844 9,08467E-05

720 71959887 0,912011 5E-09 0,000221 0,328141 7,25526E-05

725 71959887 0,891251 5E-09 0,000183 0,3206716 5,8625E-05

730 71959887 0,870964 5E-09 0,000149 0,3133722 4,65901E-05

735 71959887 0,851138 5E-09 0,000125 0,306239 3,8313E-05

740 71959887 0,831764 5E-09 0,000105 0,2992681 3,14343E-05

745 71959887 0,812831 5E-09 8,77E-05 0,292456 2,56528E-05

750 71959887 0,794328 5E-09 7,43E-05 0,2857989 2,12446E-05

755 71959887 0,776247 5E-09 6,38E-05 0,2792933 1,78301E-05

760 71959887 0,758578 5E-09 5,58E-05 0,2729358 1,52192E-05

765 71959887 0,74131 5E-09 4,81E-05 0,266723 1,28243E-05

770 71959887 0,724436 5E-09 4,26E-05 0,2606516 1,11119E-05

775 71959887 0,707946 5E-09 3,81E-05 0,2547185 9,69517E-06

780 71959887 0,691831 5E-09 3,43E-05 0,2489204 8,5347E-06




Akoto Chama Leonel

Page 114(128)

790 71959887 0,660693 1E-08 2,83E-05 0,4754343 1,34463E-05

800 71959887 0,630957 1E-08 2,6E-05 0,4540362 1,17982E-05

810 71959887 0,60256 1E-08 2,9E-05 0,4336012 1,25677E-05

820 71959887 0,57544 1E-08 2,51E-05 0,4140859 1,03914E-05

830 71959887 0,549541 1E-08 2,34E-05 0,395449 9,25018E-06

840 71959887 0,524807 1E-08 1,89E-05 0,3776509 7,13898E-06

850 71959887 0,501187 1E-08 1,82E-05 0,3606538 6,55613E-06

860 71959887 0,47863 1E-08 1,59E-05 0,3444217 5,4662E-06

870 71959887 0,457088 1E-08 1,39E-05 0,3289201 4,56219E-06

880 71959887 0,436516 1E-08 1,3E-05 0,3141163 4,07023E-06

890 71959887 0,416869 1E-08 1,18E-05 0,2999787 3,53574E-06

900 71959887 0,398107 1E-08 1,07E-05 0,2864775 3,06811E-06

910 71959887 0,380189 1E-08 8,75E-06 0,2735839 2,39344E-06

920 71959887 0,363078 1E-08 7,43E-06 0,2612706 1,93998E-06

930 71959887 0,346737 1E-08 6,63E-06 0,2495114 1,65319E-06

940 71959887 0,331131 1E-08 6,84E-06 0,2382816 1,63084E-06

950 71959887 0,316228 1E-08 5,11E-06 0,2275571 1,16273E-06

960 71959887 0,301995 1E-08 5,29E-06 0,2173154 1,149E-06

970 71959887 0,288403 1E-08 4,72E-06 0,2075346 9,79376E-07

980 71959887 0,275423 1E-08 3,82E-06 0,198194 7,57393E-07

990 71959887 0,263027 1E-08 3,41E-06 0,1892738 6,4547E-07

1000 71959887 0,251189 1E-08 3,42E-06 0,1807551 6,1874E-07

1010 71959887 0,239883 1E-08 2,83E-06 0,1726197 4,87831E-07

1020 71959887 0,229087 1E-08 2,39E-06 0,1648506 3,93354E-07

1030 71959887 0,218776 1E-08 2,59E-06 0,1574311 4,07812E-07

1040 71959887 0,20893 1E-08 2,06E-06 0,1503455 3,09213E-07

1050 71959887 0,199526 1E-08 2,22E-06 0,1435789 3,18495E-07

1060 71959887 0,2 1E-08 1,75E-06 0,1439198 2,51218E-07

1070 71959887 0,2 1E-08 1,82E-06 0,1439198 2,62276E-07

1080 71959887 0,2 1E-08 1,69E-06 0,1439198 2,42854E-07

1090 71959887 0,2 1E-08 1,27E-06 0,1439198 1,82441E-07

1100 71959887 0,2 1E-08 1,25E-06 0,1439198 1,80569E-07

1110 71959887 0,2 1E-08 1,21E-06 0,1439198 1,73974E-07

1120 71959887 0,2 1E-08 1,39E-06 0,1439198 2,00434E-07

1130 71959887 0,2 1E-08 8,89E-07 0,1439198 1,28003E-07

1140 71959887 0,2 1E-08 1,05E-06 0,1439198 1,50452E-07

1150 71959887 0,2 1E-08 7,3E-07 0,1439198 1,05013E-07

1160 71959887 0,126191 1E-08 1,01E-06 0,0908072 9,16117E-08




Akoto Chama Leonel

Page 115(128)

1170 71959887 0,079621 1E-08 6,02E-07 0,0572955 3,44689E-08

1180 71959887 0,050238 1E-08 7,76E-07 0,036151 2,80628E-08

1190 71959887 0,031698 1E-08 5,2E-07 0,0228097 1,18633E-08

1200 71959887 0,02 1E-08 5,17E-07 0,014392 7,44696E-09

1210 71959887 0,02 1E-08 5,16E-07 0,014392 7,42675E-09

1220 71959887 0,02 1E-08 7,22E-07 0,014392 1,039E-08

1230 71959887 0,02 1E-08 6,31E-07 0,014392 9,07978E-09

1240 71959887 0,02 1E-08 4,5E-07 0,014392 6,47369E-09

1250 71959887 0,02 1E-08 2,37E-07 0,014392 3,4168E-09

1260 71959887 0,02 1E-08 3,83E-07 0,014392 5,5167E-09

1270 71959887 0,02 1E-08 1,61E-07 0,014392 2,31229E-09

1280 71959887 0,02 1E-08 1,62E-07 0,014392 2,33619E-09

1290 71959887 0,02 1E-08 4,28E-07 0,014392 6,16138E-09

1300 71959887 0,02 1E-08 3,2E-07 0,014392 4,60895E-09

1310 71959887 0,02 1E-08 3,73E-07 0,014392 5,37092E-09

1320 71959887 0,02 1E-08 3,24E-07 0,014392 4,65706E-09

1330 71959887 0,02 1E-08 4,46E-07 0,014392 6,42043E-09

1340 71959887 0,02 1E-08 4,47E-07 0,014392 6,43723E-09

1350 71959887 0,02 1E-08 3,42E-07 0,014392 4,91703E-09

1360 71959887 0,02 1E-08 3,83E-07 0,014392 5,51897E-09

1370 71959887 0,02 1E-08 4,37E-08 0,014392 6,28497E-10

1380 71959887 0,02 1E-08 2,95E-07 0,014392 4,25007E-09

1390 71959887 0,02 1E-08 3,64E-08 0,014392 5,23329E-10

1400 71959887 0,02 1E-08 2,22E-07 0,014392 3,19852E-09

∑( )=75,96 ∑( )=2,12

Table 31 Calculation of PFRTH

λ(nm) L(λ) R(λ) ∆λ L(λ).R(λ).∆λ

380 1,39E+12 0,1 5E-09 6,95E+02

385 1,39E+12 0,13 5E-09 9,03E+02

390 1,39E+12 0,25 5E-09 1,74E+03

395 1,39E+12 0,5 5E-09 3,47E+03

400 1,39E+12 1 5E-09 6,95E+03

405 1,39E+12 2 5E-09 1,39E+04

410 1,39E+12 4 5E-09 2,78E+04

415 1,39E+12 8 5E-09 5,56E+04

420 1,39E+12 9 5E-09 6,25E+04




Akoto Chama Leonel

Page 116(128)

425 1,39E+12 9,5 5E-09 6,60E+04

430 1,39E+12 9,8 5E-09 6,81E+04

435 1,39E+12 10 5E-09 6,95E+04

440 1,39E+12 10 5E-09 6,95E+04

445 1,39E+12 9,7 5E-09 6,74E+04

450 1,39E+12 9,4 5E-09 6,53E+04

455 1,39E+12 9 5E-09 6,25E+04

460 1,39E+12 8 5E-09 5,56E+04

465 1,39E+12 7 5E-09 4,86E+04

470 1,39E+12 6,2 5E-09 4,31E+04

475 1,39E+12 5,5 5E-09 3,82E+04

480 1,39E+12 4,5 5E-09 3,13E+04

485 1,39E+12 3,2 5E-09 2,22E+04

490 1,39E+12 2,2 5E-09 1,53E+04

495 1,39E+12 1,6 5E-09 1,11E+04

500 1,39E+12 1 5E-09 6,95E+03

505 1,39E+12 1 5E-09 6,95E+03

510 1,39E+12 1 5E-09 6,95E+03

515 1,39E+12 1 5E-09 6,95E+03

520 1,39E+12 1 5E-09 6,95E+03

525 1,39E+12 1 5E-09 6,95E+03

530 1,39E+12 1 5E-09 6,95E+03

535 1,39E+12 1 5E-09 6,95E+03

540 1,39E+12 1 5E-09 6,95E+03

545 1,39E+12 1 5E-09 6,95E+03

550 1,39E+12 1 5E-09 6,95E+03

555 1,39E+12 1 5E-09 6,95E+03

560 1,39E+12 1 5E-09 6,95E+03

565 1,39E+12 1 5E-09 6,95E+03

570 1,39E+12 1 5E-09 6,95E+03

575 1,39E+12 1 5E-09 6,95E+03

580 1,39E+12 1 5E-09 6,95E+03

585 1,39E+12 1 5E-09 6,95E+03

590 1,39E+12 1 5E-09 6,95E+03

595 1,39E+12 1 5E-09 6,95E+03

600 1,39E+12 1 5E-09 6,95E+03

605 1,39E+12 1 5E-09 6,95E+03

610 1,39E+12 1 5E-09 6,95E+03




Akoto Chama Leonel

Page 117(128)

615 1,39E+12 1 5E-09 6,95E+03

620 1,39E+12 1 5E-09 6,95E+03

625 1,39E+12 1 5E-09 6,95E+03

630 1,39E+12 1 5E-09 6,95E+03

635 1,39E+12 1 5E-09 6,95E+03

640 1,39E+12 1 5E-09 6,95E+03

645 1,39E+12 1 5E-09 6,95E+03

650 1,39E+12 1 5E-09 6,95E+03

655 1,39E+12 1 5E-09 6,95E+03

660 1,39E+12 1 5E-09 6,95E+03

665 1,39E+12 1 5E-09 6,95E+03

670 1,39E+12 1 5E-09 6,95E+03

675 1,39E+12 1 5E-09 6,95E+03

680 1,39E+12 1 5E-09 6,95E+03

685 1,39E+12 1 5E-09 6,95E+03

690 1,39E+12 1 5E-09 6,95E+03

695 1,39E+12 1 5E-09 6,95E+03

700 1,39E+12 1 5E-09 6,95E+03

705 1,39E+12 0,977237 5E-09 6,79E+03

710 1,39E+12 0,954993 5E-09 6,63E+03

715 1,39E+12 0,933254 5E-09 6,48E+03

720 1,39E+12 0,912011 5E-09 6,33E+03

725 1,39E+12 0,891251 5E-09 6,19E+03

730 1,39E+12 0,870964 5E-09 6,05E+03

735 1,39E+12 0,851138 5E-09 5,91E+03

740 1,39E+12 0,831764 5E-09 5,78E+03

745 1,39E+12 0,812831 5E-09 5,65E+03

750 1,39E+12 0,794328 5E-09 5,52E+03

755 1,39E+12 0,776247 5E-09 5,39E+03

760 1,39E+12 0,758578 5E-09 5,27E+03

765 1,39E+12 0,74131 5E-09 5,15E+03

770 1,39E+12 0,724436 5E-09 5,03E+03

775 1,39E+12 0,707946 5E-09 4,92E+03

780 1,39E+12 0,691831 5E-09 4,81E+03

790 1,39E+12 0,660693 1E-08 9,18E+03

800 1,39E+12 0,630957 1E-08 8,77E+03

810 1,39E+12 0,60256 1E-08 8,37E+03

820 1,39E+12 0,57544 1E-08 7,99E+03




Akoto Chama Leonel

Page 118(128)

830 1,39E+12 0,549541 1E-08 7,63E+03

840 1,39E+12 0,524807 1E-08 7,29E+03

850 1,39E+12 0,501187 1E-08 6,96E+03

860 1,39E+12 0,47863 1E-08 6,65E+03

870 1,39E+12 0,457088 1E-08 6,35E+03

880 1,39E+12 0,436516 1E-08 6,06E+03

890 1,39E+12 0,416869 1E-08 5,79E+03

900 1,39E+12 0,398107 1E-08 5,53E+03

910 1,39E+12 0,380189 1E-08 5,28E+03

920 1,39E+12 0,363078 1E-08 5,04E+03

930 1,39E+12 0,346737 1E-08 4,82E+03

940 1,39E+12 0,331131 1E-08 4,60E+03

950 1,39E+12 0,316228 1E-08 4,39E+03

960 1,39E+12 0,301995 1E-08 4,20E+03

970 1,39E+12 0,288403 1E-08 4,01E+03

980 1,39E+12 0,275423 1E-08 3,83E+03

990 1,39E+12 0,263027 1E-08 3,65E+03

1000 1,39E+12 0,251189 1E-08 3,49E+03

1010 1,39E+12 0,239883 1E-08 3,33E+03

1020 1,39E+12 0,229087 1E-08 3,18E+03

1030 1,39E+12 0,218776 1E-08 3,04E+03

1040 1,39E+12 0,20893 1E-08 2,90E+03

1050 1,39E+12 0,199526 1E-08 2,77E+03

1060 1,39E+12 0,2 1E-08 2,78E+03

1070 1,39E+12 0,2 1E-08 2,78E+03

1080 1,39E+12 0,2 1E-08 2,78E+03

1090 1,39E+12 0,2 1E-08 2,78E+03

1100 1,39E+12 0,2 1E-08 2,78E+03

1110 1,39E+12 0,2 1E-08 2,78E+03

1120 1,39E+12 0,2 1E-08 2,78E+03

1130 1,39E+12 0,2 1E-08 2,78E+03

1140 1,39E+12 0,2 1E-08 2,78E+03

1150 1,39E+12 0,2 1E-08 2,78E+03

1160 1,39E+12 0,126191 1E-08 1,75E+03

1170 1,39E+12 0,079621 1E-08 1,11E+03

1180 1,39E+12 0,050238 1E-08 6,98E+02

1190 1,39E+12 0,031698 1E-08 4,40E+02

1200 1,39E+12 0,02 1E-08 2,78E+02




Akoto Chama Leonel

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1210 1,39E+12 0,02 1E-08 2,78E+02

1220 1,39E+12 0,02 1E-08 2,78E+02

1230 1,39E+12 0,02 1E-08 2,78E+02

1240 1,39E+12 0,02 1E-08 2,78E+02

1250 1,39E+12 0,02 1E-08 2,78E+02

1260 1,39E+12 0,02 1E-08 2,78E+02

1270 1,39E+12 0,02 1E-08 2,78E+02

1280 1,39E+12 0,02 1E-08 2,78E+02

1290 1,39E+12 0,02 1E-08 2,78E+02

1300 1,39E+12 0,02 1E-08 2,78E+02

1310 1,39E+12 0,02 1E-08 2,78E+02

1320 1,39E+12 0,02 1E-08 2,78E+02

1330 1,39E+12 0,02 1E-08 2,78E+02

1340 1,39E+12 0,02 1E-08 2,78E+02

1350 1,39E+12 0,02 1E-08 2,78E+02

1360 1,39E+12 0,02 1E-08 2,78E+02

1370 1,39E+12 0,02 1E-08 2,78E+02

1380 1,39E+12 0,02 1E-08 2,78E+02

1390 1,39E+12 0,02 1E-08 2,78E+02

1400 1,39E+12 0,02 1E-08 2,78E+02

∑( )=1,47E+6

Table 32 Calculation of LR




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Page 120(128)

Appendix A Data Sheet

The tables below show the spectral irradiance date En(λ) which was used in determining the

shades and their characteristics. Where n = shade number and λ = wavelngth in nano metres

λ(nm) E1,3(λ) E1,5(λ) E1,7(λ) E2(λ) E2,5(λ) E3(λ) E4(λ) E5(λ)

300 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

305 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

310 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

315 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

320 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

325 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

330 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

335 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

340 26,96165 32,66086 40,09267 53,85102 88,09837 144,5067 387,7689 1040,748

345 138,1902 167,4011 205,4924 276,0099 451,5425 740,6597 1987,485 5334,285

350 249,4187 302,1414 370,8922 498,1688 814,9867 1336,813 3587,2 9627,822

355 360,6473 436,8817 536,2919 720,3277 1178,431 1932,966 5186,916 13921,36

360 471,8758 571,622 701,6916 942,4866 1541,875 2529,119 6786,631 18214,9

365 583,1044 706,3622 867,0914 1164,646 1905,319 3125,272 8386,347 22508,43

370 694,3329 841,1025 1032,491 1386,804 2268,763 3721,425 9986,063 26801,97

375 805,5615 975,8428 1197,891 1608,963 2632,208 4317,578 11585,78 31095,51

380 920,6417 1115,249 1369,018 1838,815 3008,237 4934,375 13240,89 35537,72

385 1023,979 1240,43 1522,683 2045,213 3345,896 5488,233 14727,11 39526,65

390 1135,771 1375,853 1688,921 2268,498 3711,182 6087,407 16334,93 43841,95

395 1254,139 1519,242 1864,938 2504,917 4097,956 6721,827 18037,33 48411,08

400 1381,902 1674,011 2054,924 2760,099 4515,425 7406,597 19874,85 53342,85

405 1517,18 1837,885 2256,086 3030,292 4957,452 8131,648 21820,45 58564,72

410 1660,913 2012 2469,82 3317,373 5427,105 8902,015 23887,65 64112,96

415 1812,161 2195,22 2694,731 3619,464 5921,316 9712,662 26062,93 69951,3

420 1971,864 2388,681 2932,213 3938,442 6443,153 10568,62 28359,82 76116

425 2140,962 2593,523 3183,666 4276,184 6995,686 11474,94 30791,82 82643,34

430 2317,575 2807,468 3446,294 4628,936 7572,777 12421,53 33331,91 89460,78

435 2502,642 3031,656 3721,494 4998,575 8177,494 13413,44 35993,6 96604,59

440 2696,165 3266,086 4009,267 5385,102 8809,837 14450,67 38776,89 104074,8

445 2898,143 3510,758 4309,613 5788,515 9469,808 15533,21 41681,78 111871,3

450 3108,575 3765,672 4622,532 6208,816 10157,4 16661,07 44708,27 119994,2

455 3326,523 4029,69 4946,626 6644,127 10869,56 17829,2 47842,85 128407,2

460 3551,986 4302,812 5281,895 7094,449 11606,27 19037,62 51085,51 137110,3

465 3785,904 4586,177 5629,738 7561,658 12370,61 20291,36 54449,78 146139,8

470 4027,338 4878,645 5988,756 8043,878 13159,5 21585,37 57922,14 155459,4

475 4276,287 5180,217 6358,949 8541,109 13972,95 22919,67 61502,58 165069,1

480 4531,812 5489,756 6738,922 9051,474 14807,89 24289,21 65177,6 174932,6




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485 4794,852 5808,398 7130,07 9576,85 15667,39 25699,03 68960,71 185086,3

490 5064,469 6135,007 7530,997 10115,36 16548,37 27144,1 72838,4 195493,7

495 5340,661 6469,582 7941,702 10667 17450,85 28624,41 76810,67 206155,1

500 5623,43 6812,122 8362,186 11231,78 18374,8 30139,97 80877,51 217070,2

505 5911,835 7161,491 8791,052 11807,82 19317,18 31685,73 85025,43 228203

510 6205,877 7517,688 9228,3 12395,12 20277,97 33261,71 89254,4 239553,3

515 6505,555 7880,713 9673,929 12993,67 21257,19 34867,9 93564,45 251121,2

520 6810,87 8250,566 10127,94 13603,48 22254,82 36504,3 97955,56 262906,6

525 7119,942 8624,971 10587,54 14220,8 23264,72 38160,84 102400,7 274837,2

530 7433,712 9005,066 11054,12 14847,49 24289,98 39842,56 106913,4 286949

535 7752,179 9390,851 11527,69 15483,57 25330,58 41549,45 111493,7 299242,1

540 8074,404 9781,188 12006,85 16127,16 26383,47 43276,48 116128 311680,3

545 8399,446 10174,94 12490,19 16776,37 27445,56 45018,62 120802,8 324227,3

550 8728,247 10573,24 12979,13 17433,09 28519,93 46780,89 125531,7 336919,4

555 9059,866 10974,96 13472,26 18095,44 29603,51 48558,27 130301,2 349720,2

560 9394,303 11380,09 13969,57 18763,42 30696,3 50350,76 135111,1 362629,8

565 9730,619 11787,5 14469,68 19435,15 31795,23 52153,32 139948,1 375612

570 10068,81 12197,18 14972,59 20110,63 32900,29 53965,95 144812,1 388666,7

575 10408,89 12609,14 15478,29 20789,87 34011,5 55788,64 149703,1 401793,9

580 10750,84 13023,38 15986,78 21472,86 35128,84 57621,41 154621,2 414993,6

585 11092,79 13437,61 16495,27 22155,85 36246,19 59454,18 159539,2 428193,3

590 11435,69 13852,98 17005,16 22840,71 37366,6 61291,98 164470,8 441429,3

595 11779,52 14269,5 17516,45 23527,45 38490,09 63134,82 169415,8 454701,6

600 12122,41 14684,87 18026,34 24212,32 39610,5 64972,62 174347,4 467937,5

605 12466,24 15101,38 18537,62 24899,06 40733,99 66815,46 179292,5 481209,8

610 12809,13 15516,75 19047,51 25583,92 41854,4 68653,26 184224 494445,8

615 13151,08 15930,99 19556 26266,91 42971,75 70486,03 189142,1 507645,5

620 13492,1 16344,09 20063,1 26948,02 44086,02 72313,76 194046,6 520809

625 13832,17 16756,05 20568,8 27627,26 45197,23 74136,46 198937,6 533936,2

630 14170,37 17165,73 21071,7 28302,74 46302,3 75949,09 203801,6 546990,8

635 14506,68 17573,14 21571,81 28974,47 47401,22 77751,65 208638,6 559973

640 14841,12 17978,27 22069,13 29642,45 48494,01 79544,13 213448,5 572882,6

645 15173,68 18381,12 22563,65 30306,68 49580,66 81326,55 218231,5 585719,7

650 15503,42 18780,56 23053,99 30965,27 50658,1 83093,86 222973,9 598448

655 15830,34 19176,59 23540,13 31618,24 51726,33 84846,07 227675,7 611067,5

660 16154,44 19569,2 24022,08 32265,58 52785,35 86583,17 232337,1 623578,3

665 16475,73 19958,4 24499,84 32907,29 53835,17 88305,17 236957,9 635980,2

670 16794,2 20344,19 24973,4 33543,37 54875,77 90012,06 241538,1 648273,4

675 17108,9 20725,42 25441,39 34171,94 55904,1 91698,81 246064,4 660421,5

680 17419,86 21102,1 25903,78 34793,01 56920,14 93365,42 250536,5 672424,5

685 17727,05 21474,23 26360,58 35406,57 57923,91 95011,89 254954,7 684282,5

690 18030,49 21841,81 26811,8 36012,63 58915,4 96638,22 259318,8 695995,4

695 18330,16 22204,83 27257,43 36611,19 59894,62 98244,41 263628,8 707563,3

700 18625,15 22562,17 27696,07 37200,36 60858,48 99825,42 267871,3 718949,9




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705 18916,37 22914,95 28129,13 37782,02 61810,06 101386,3 272059,7 730191,4

710 19202,9 23262,04 28555,2 38354,31 62746,3 102922 276180,6 741251,6

715 19484,72 23603,45 28974,29 38917,21 63667,19 104432,5 280234 752130,5

720 19761,86 23939,16 29386,39 39470,73 64572,73 105917,9 284219,7 762828,1

725 20035,23 24270,32 29792,91 40016,75 65465,99 107383,1 288151,5 773380,7

730 20302,97 24594,65 30191,04 40551,5 66340,84 108818,1 292002,1 783715,6

735 20566,01 24913,29 30582,19 41076,88 67200,33 110227,9 295785,3 793869,2

740 20824,35 25226,25 30966,35 41592,87 68044,48 111612,5 299500,8 803841,6

745 21077,06 25532,37 31342,13 42097,61 68870,21 112967 303135,3 813596,3

750 21325,07 25832,81 31710,93 42592,96 69680,6 114296,2 306702,2 823169,7

755 21568,38 26127,55 32072,74 43078,94 70475,63 115600,3 310201,6 832561,8

760 21806,06 26415,47 32426,17 43553,65 71252,25 116874,2 313619,9 841736,4

765 22036,22 26694,28 32768,43 44013,36 72004,31 118107,8 316930,1 850620,8

770 22265,44 26971,95 33109,28 44471,18 72753,29 119336,3 320226,9 859469

775 22485,26 27238,25 33436,17 44910,25 73471,59 120514,5 323388,5 867954,5

780 22704,15 27503,4 33761,66 45347,43 74186,81 121687,7 326536,5 876403,8

790 23121,26 28008,68 34381,91 46180,53 75549,73 123923,3 332535,5 892504,6

800 23563,73 28544,68 35039,88 47064,29 76995,52 126294,8 338899,2 909584,4

810 23890,65 28940,71 35526,02 47717,25 78063,75 128047 343601,1 922203,9

820 24243,88 29368,6 36051,28 48422,76 79217,94 129940,2 348681,3 935838,8

830 24575,5 29770,32 36544,4 49085,11 80301,51 131717,6 353450,7 948639,7

840 24886,45 30147 37006,79 49706,18 81317,56 133384,2 357922,9 960642,7

850 25175,79 30497,51 37437,06 50284,09 82263,01 134935 362084,3 971811,7

860 25445,41 30824,11 37837,98 50822,6 83143,99 136380,1 365962 982219,2

870 25694,36 31125,69 38208,18 51319,83 83957,44 137714,4 369542,4 991828,9

880 25923,58 31403,36 38549,04 51777,66 84706,43 138942,9 372839,1 1000677

890 26133,07 31657,14 38860,56 52196,08 85390,96 140065,7 375852,1 1008764

900 26323,78 31888,15 39144,14 52576,98 86014,1 141087,9 378594,9 1016125

910 26495,69 32096,41 39399,78 52920,35 86575,84 142009,3 381067,4 1022761

920 26649,76 32283,04 39628,88 53228,07 87079,26 142835 383283,2 1028708

930 26785,04 32446,91 39830,05 53498,26 87521,28 143560,1 385228,8 1033930

940 26904,34 32591,44 40007,46 53736,56 87911,13 144199,5 386944,7 1038536

950 27005,8 32714,35 40158,33 53939,2 88242,65 144743,3 388403,9 1042452

960 27092,23 32819,04 40286,85 54111,83 88525,05 145206,6 389646,9 1045788

970 27162,69 32904,39 40391,62 54252,55 88755,27 145584,2 390660,3 1048508

980 27217,18 32970,4 40472,65 54361,38 88933,31 145876,2 391443,9 1050611

990 27257,57 33019,33 40532,71 54442,06 89065,31 146092,7 392024,9 1052170

1000 27283,87 33051,2 40571,83 54494,6 89151,26 146233,7 392403,2 1053186

1010 27297,03 33067,13 40591,39 54520,87 89194,23 146304,2 392592,4 1053694

1020 27297,03 33067,13 40591,39 54520,87 89194,23 146304,2 392592,4 1053694

1030 27283,87 33051,2 40571,83 54494,6 89151,26 146233,7 392403,2 1053186

1040 27259,45 33021,61 40535,51 54445,82 89071,45 146102,8 392051,9 1052243

1050 27222,81 32977,23 40481,03 54372,64 88951,73 145906,4 391525 1050829

1060 27175,84 32920,33 40411,18 54278,82 88798,25 145654,7 390849,4 1049016




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1070 27117,6 32849,77 40324,57 54162,49 88607,93 145342,5 390011,7 1046767

1080 27049,96 32767,83 40223,99 54027,39 88386,92 144980 389038,9 1044156

1090 26972,92 32674,52 40109,44 53873,53 88135,21 144567,1 387931 1041183

1100 26886,5 32569,82 39980,92 53700,91 87852,8 144103,9 386688 1037847

1110 26790,67 32453,74 39838,43 53509,52 87539,7 143590,3 385309,9 1034148

1120 26687,34 32328,56 39684,76 53303,13 87202,04 143036,4 383823,7 1030159

1130 26576,48 32194,28 39519,92 53081,72 86839,83 142442,3 382229,3 1025880

1140 26458,12 32050,89 39343,9 52845,3 86453,05 141807,9 380526,9 1021311

1150 26332,23 31898,39 39156,71 52593,87 86041,72 141133,2 378716,5 1016451

1160 26199,77 31737,94 38959,74 52329,3 85608,9 140423,2 376811,4 1011338

1170 26061,68 31570,65 38754,39 52053,48 85157,67 139683,1 374825,3 1006008

1180 25917,94 31396,53 38540,65 51766,4 84688,02 138912,7 372758,1 1000459

1190 25767,63 31214,45 38317,14 51466,19 84196,87 138107,1 370596,3 994657,4

1200 25612,63 31026,68 38086,64 51156,59 83690,39 137276,3 368366,9 988674

1210 25452,92 30833,22 37849,16 50837,61 83168,55 136420,4 366070,1 982509,3

1220 25289,46 30635,2 37606,09 50511,13 82634,43 135544,3 363719,1 976199,5

1230 25120,37 30430,36 37354,64 50173,39 82081,9 134637,9 361287,1 969672,2

1240 24948,45 30222,11 37098,99 49830,02 81520,16 133716,5 358814,6 963036,1

1250 24772,78 30009,3 36837,76 49479,14 80946,14 132775 356288 956254,9

1260 24593,35 29791,94 36570,94 49120,76 80359,84 131813,3 353707,4 949328,7

1270 24409,22 29568,89 36297,14 48753 79758,19 130826,4 351059,2 942221,1

1280 24226,03 29346,98 36024,73 48387,11 79159,61 129844,5 348424,5 935149,8

1290 24038,14 29119,38 35745,34 48011,84 78545,69 128837,5 345722,3 927897,2

1300 23848,38 28889,5 35463,16 47632,82 77925,62 127820,4 342993,1 920572,1

1310 23655,79 28656,21 35176,78 47248,17 77296,35 126788,3 340223,3 913138,2

1320 23461,33 28420,64 34887,61 46859,77 76660,93 125746 337426,5 905631,8

1330 23265,93 28183,93 34597,04 46469,49 76022,45 124698,7 334616,2 898089,1

1340 23068,65 27944,95 34303,68 46075,46 75377,83 123641,3 331778,9 890473,8

1350 22870,43 27704,83 34008,92 45679,55 74730,14 122578,9 328928 882822,3

1360 22670,33 27462,44 33711,37 45279,89 74076,31 121506,5 326050,1 875098,3

1370 22469,29 27218,9 33412,42 44878,35 73419,4 120429 323158,8 867338

1380 22268,26 26975,37 33113,47 44476,81 72762,5 119351,4 320267,4 859577,8

1390 22065,34 26729,56 32811,73 44071,52 72099,46 118263,9 317349 851745

1400 21862,42 26483,75 32509,99 43666,23 71436,42 117176,3 314430,6 843912,2

λ(nm) E6(λ) E7(λ) E8(λ) E9(λ) E10(λ) E11(λ) E12(λ) E13(λ) E14(λ)

300 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

305 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

310 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

315 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

320 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

325 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

330 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418




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335 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

340 2789,782 7439,418 20086,43 54287,65 144506,7 386277,5 1057180 2789782 7439418

345 14298,85 38130,26 102951,7 278247,8 740659,7 1979840 5418510 14298847 38130259

350 25807,91 68821,1 185817 502208 1336813 3573403 9779840 25807912 68821099

355 37316,98 99511,94 268682,2 726168,2 1932966 5166966 14141170 37316977 99511940

360 48826,04 130202,8 351547,5 950128,4 2529119 6760529 18502500 48826043 1,3E+08

365 60335,11 160893,6 434412,8 1174089 3125272 8354092 22863830 60335108 1,61E+08

370 71844,17 191584,5 517278 1398049 3721425 9947655 27225160 71844173 1,92E+08

375 83353,24 222275,3 600143,3 1622009 4317578 11541218 31586490 83353238 2,22E+08

380 95260,84 254028,9 685878,1 1853725 4934375 13189963 36098846 95260844 2,54E+08

385 105953,4 282542,4 762864,4 2061796 5488233 14670469 40150757 1,06E+08 2,83E+08

390 117520,8 313388,7 846149,6 2286891 6087407 16272107 44534189 1,18E+08 3,13E+08

395 129768,6 346049,6 934333,9 2525227 6721827 17967960 49175469 1,3E+08 3,46E+08

400 142988,5 381302,6 1029517 2782478 7406597 19798404 54185105 1,43E+08 3,81E+08

405 156986 418629,3 1130299 3054862 8131648 21736521 59489425 1,57E+08 4,19E+08

410 171858,3 458288,9 1237380 3344270 8902015 23795770 65125265 1,72E+08 4,58E+08

415 187508,3 500022,2 1350060 3648811 9712662 25962692 71055790 1,88E+08 5E+08

420 204033,2 544088,5 1469039 3970375 10568625 28250747 77317834 2,04E+08 5,44E+08

425 221530,1 590746,8 1595016 4310855 11474939 30673393 83948235 2,22E+08 5,91E+08

430 239804,6 639478,9 1726593 4666468 12421533 33203713 90873319 2,4E+08 6,39E+08

435 258954 690543,9 1864469 5039104 13413443 35855165 98129924 2,59E+08 6,91E+08

440 278978,2 743941,8 2008643 5428765 14450669 38627749 1,06E+08 2,79E+08 7,44E+08

445 299877,2 799672,7 2159116 5835449 15533210 41521465 1,14E+08 3E+08 8E+08

450 321651,2 857736,4 2315888 6259158 16661067 44536314 1,22E+08 3,22E+08 8,58E+08

455 344202,7 917873,9 2478259 6697999 17829205 47658836 1,3E+08 3,44E+08 9,18E+08

460 367531,9 980085 2646230 7151972 19037623 50889031 1,39E+08 3,68E+08 9,8E+08

465 391735,9 1044629 2820499 7622969 20291357 54240358 1,48E+08 3,92E+08 1,04E+09

470 416717,6 1111247 3000367 8109099 21585371 57699358 1,58E+08 4,17E+08 1,11E+09

475 442476,9 1179938 3185834 8610361 22919667 61266032 1,68E+08 4,42E+08 1,18E+09

480 468916,6 1250444 3376200 9124864 24289207 64926920 1,78E+08 4,69E+08 1,25E+09

485 496134 1323024 3572165 9654500 25699029 68695481 1,88E+08 4,96E+08 1,32E+09

490 524031,8 1397418 3773029 10197376 27144096 72558255 1,99E+08 5,24E+08 1,4E+09

495 552610,1 1473627 3978793 10753494 28624408 76515244 2,09E+08 5,53E+08 1,47E+09

500 581868,8 1551650 4189455 11322852 30139966 80566447 2,2E+08 5,82E+08 1,55E+09

505 611710,7 1631229 4404317 11903560 31685734 84698405 2,32E+08 6,12E+08 1,63E+09

510 642135,8 1712362 4623378 12495617 33261713 88911118 2,43E+08 6,42E+08 1,71E+09

515 673144,2 1795051 4846638 13099023 34867902 93204585 2,55E+08 6,73E+08 1,8E+09

520 704735,8 1879296 5074098 13713778 36504302 97578808 2,67E+08 7,05E+08 1,88E+09

525 736716,3 1964577 5304357 14336100 38160842 1,02E+08 2,79E+08 7,37E+08 1,96E+09

530 769182,7 2051154 5538116 14967880 39842558 1,07E+08 2,91E+08 7,69E+08 2,05E+09

535 802135,2 2139027 5775373 15609117 41549448 1,11E+08 3,04E+08 8,02E+08 2,14E+09

540 835476,5 2227937 6015431 16257921 43276480 1,16E+08 3,17E+08 8,35E+08 2,23E+09

545 869109,4 2317625 6257588 16912399 45018616 1,2E+08 3,29E+08 8,69E+08 2,32E+09

550 903131,1 2408350 6502544 17574443 46780893 1,25E+08 3,42E+08 9,03E+08 2,41E+09




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555 937444,5 2499852 6749600 18242163 48558274 1,3E+08 3,55E+08 9,37E+08 2,5E+09

560 972049,4 2592132 6998756 18915556 50350762 1,35E+08 3,68E+08 9,72E+08 2,59E+09

565 1006849 2684930 7249311 19592733 52153319 1,39E+08 3,82E+08 1,01E+09 2,68E+09

570 1041843 2778247 7501267 20273693 53965946 1,44E+08 3,95E+08 1,04E+09 2,78E+09

575 1077031 2872082 7754621 20958436 55788644 1,49E+08 4,08E+08 1,08E+09 2,87E+09

580 1112413 2966436 8009376 21646963 57621412 1,54E+08 4,22E+08 1,11E+09 2,97E+09

585 1147796 3060789 8264131 22335489 59454179 1,59E+08 4,35E+08 1,15E+09 3,06E+09

590 1183276 3155402 8519586 23025907 61291982 1,64E+08 4,48E+08 1,18E+09 3,16E+09

595 1218853 3250274 8775740 23718216 63134820 1,69E+08 4,62E+08 1,22E+09 3,25E+09

600 1254333 3344887 9031195 24408634 64972623 1,74E+08 4,75E+08 1,25E+09 3,34E+09

605 1289910 3439759 9287349 25100943 66815461 1,79E+08 4,89E+08 1,29E+09 3,44E+09

610 1325389 3534372 9542804 25791361 68653263 1,84E+08 5,02E+08 1,33E+09 3,53E+09

615 1360772 3628725 9797558 26479887 70486031 1,88E+08 5,16E+08 1,36E+09 3,63E+09

620 1396057 3722820 10051613 27166522 72313764 1,93E+08 5,29E+08 1,4E+09 3,72E+09

625 1431246 3816655 10304968 27851265 74136461 1,98E+08 5,42E+08 1,43E+09 3,82E+09

630 1466239 3909972 10556923 28532225 75949089 2,03E+08 5,56E+08 1,47E+09 3,91E+09

635 1501039 4002770 10807479 29209402 77751646 2,08E+08 5,69E+08 1,5E+09 4E+09

640 1535644 4095050 11056634 29882796 79544133 2,13E+08 5,82E+08 1,54E+09 4,1E+09

645 1570054 4186811 11304390 30552407 81326550 2,17E+08 5,95E+08 1,57E+09 4,19E+09

650 1604173 4277795 11550047 31216343 83093862 2,22E+08 6,08E+08 1,6E+09 4,28E+09

655 1638000 4368001 11793603 31874604 84846068 2,27E+08 6,21E+08 1,64E+09 4,37E+09

660 1671536 4457430 12035061 32527191 86583170 2,31E+08 6,33E+08 1,67E+09 4,46E+09

665 1704780 4546081 12274418 33174103 88305166 2,36E+08 6,46E+08 1,7E+09 4,55E+09

670 1737733 4633954 12511676 33815340 90012056 2,41E+08 6,59E+08 1,74E+09 4,63E+09

675 1770296 4720790 12746134 34449011 91698807 2,45E+08 6,71E+08 1,77E+09 4,72E+09

680 1802471 4806590 12977793 35075116 93365417 2,5E+08 6,83E+08 1,8E+09 4,81E+09

685 1834257 4891353 13206652 35693655 95011887 2,54E+08 6,95E+08 1,83E+09 4,89E+09

690 1865654 4975079 13432712 36304627 96638217 2,58E+08 7,07E+08 1,87E+09 4,98E+09

695 1896663 5057768 13655972 36908034 98244406 2,63E+08 7,19E+08 1,9E+09 5,06E+09

700 1927185 5139161 13875733 37501982 99825420 2,67E+08 7,3E+08 1,93E+09 5,14E+09

705 1957319 5219517 14092695 38088364 1,01E+08 2,71E+08 7,42E+08 1,96E+09 5,22E+09

710 1986966 5298577 14306157 38665289 1,03E+08 2,75E+08 7,53E+08 1,99E+09 5,3E+09

715 2016128 5376341 14516120 39232755 1,04E+08 2,79E+08 7,64E+08 2,02E+09 5,38E+09

720 2044803 5452808 14722583 39790764 1,06E+08 2,83E+08 7,75E+08 2,04E+09 5,45E+09

725 2073090 5528239 14926247 40341207 1,07E+08 2,87E+08 7,86E+08 2,07E+09 5,53E+09

730 2100793 5602115 15125711 40880300 1,09E+08 2,91E+08 7,96E+08 2,1E+09 5,6E+09

735 2128011 5674695 15321676 41409936 1,1E+08 2,95E+08 8,06E+08 2,13E+09 5,67E+09

740 2154742 5745979 15514142 41930114 1,12E+08 2,98E+08 8,17E+08 2,15E+09 5,75E+09

745 2180890 5815707 15702409 42438942 1,13E+08 3,02E+08 8,26E+08 2,18E+09 5,82E+09

750 2206552 5884139 15887176 42938313 1,14E+08 3,06E+08 8,36E+08 2,21E+09 5,88E+09

755 2231728 5951275 16068444 43428226 1,16E+08 3,09E+08 8,46E+08 2,23E+09 5,95E+09

760 2256321 6016856 16245512 43906789 1,17E+08 3,12E+08 8,55E+08 2,26E+09 6,02E+09

765 2280136 6080364 16416982 44370221 1,18E+08 3,16E+08 8,64E+08 2,28E+09 6,08E+09

770 2303854 6143612 16587751 44831760 1,19E+08 3,19E+08 8,73E+08 2,3E+09 6,14E+09




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775 2326600 6204267 16751522 45274384 1,21E+08 3,22E+08 8,82E+08 2,33E+09 6,2E+09

780 2349249 6264664 16914593 45715117 1,22E+08 3,25E+08 8,9E+08 2,35E+09 6,26E+09

790 2392408 6379755 17225338 46554967 1,24E+08 3,31E+08 9,07E+08 2,39E+09 6,38E+09

800 2438192 6501844 17554979 47445890 1,26E+08 3,38E+08 9,24E+08 2,44E+09 6,5E+09

810 2472019 6592050 17798536 48104151 1,28E+08 3,42E+08 9,37E+08 2,47E+09 6,59E+09

820 2508568 6689515 18061689 48815376 1,3E+08 3,47E+08 9,51E+08 2,51E+09 6,69E+09

830 2542881 6781017 18308745 49483095 1,32E+08 3,52E+08 9,64E+08 2,54E+09 6,78E+09

840 2575056 6866816 18540404 50109200 1,33E+08 3,57E+08 9,76E+08 2,58E+09 6,87E+09

850 2604995 6946654 18755966 50691799 1,35E+08 3,61E+08 9,87E+08 2,6E+09 6,95E+09

860 2632893 7021048 18956830 51234676 1,36E+08 3,65E+08 9,98E+08 2,63E+09 7,02E+09

870 2658652 7089740 19142297 51735938 1,38E+08 3,68E+08 1,01E+09 2,66E+09 7,09E+09

880 2682370 7152988 19313067 52197478 1,39E+08 3,71E+08 1,02E+09 2,68E+09 7,15E+09

890 2704047 7210792 19469139 52619295 1,4E+08 3,74E+08 1,02E+09 2,7E+09 7,21E+09

900 2723780 7263413 19611214 53003280 1,41E+08 3,77E+08 1,03E+09 2,72E+09 7,26E+09

910 2741568 7310849 19739291 53349435 1,42E+08 3,8E+08 1,04E+09 2,74E+09 7,31E+09

920 2757510 7353359 19854071 53659650 1,43E+08 3,82E+08 1,04E+09 2,76E+09 7,35E+09

930 2771507 7390686 19954853 53932034 1,44E+08 3,84E+08 1,05E+09 2,77E+09 7,39E+09

940 2783852 7423606 20043737 54172262 1,44E+08 3,85E+08 1,05E+09 2,78E+09 7,42E+09

950 2794350 7451601 20119323 54376550 1,45E+08 3,87E+08 1,06E+09 2,79E+09 7,45E+09

960 2803293 7475449 20183712 54550573 1,45E+08 3,88E+08 1,06E+09 2,8E+09 7,48E+09

970 2810584 7494890 20236203 54692440 1,46E+08 3,89E+08 1,07E+09 2,81E+09 7,49E+09

980 2816222 7509924 20276795 54802150 1,46E+08 3,9E+08 1,07E+09 2,82E+09 7,51E+09

990 2820401 7521070 20306890 54883487 1,46E+08 3,91E+08 1,07E+09 2,82E+09 7,52E+09

1000 2823123 7528328 20326487 54936450 1,46E+08 3,91E+08 1,07E+09 2,82E+09 7,53E+09

1010 2824484 7531957 20336285 54962932 1,46E+08 3,91E+08 1,07E+09 2,82E+09 7,53E+09

1020 2824484 7531957 20336285 54962932 1,46E+08 3,91E+08 1,07E+09 2,82E+09 7,53E+09

1030 2823123 7528328 20326487 54936450 1,46E+08 3,91E+08 1,07E+09 2,82E+09 7,53E+09

1040 2820596 7521589 20308290 54887270 1,46E+08 3,91E+08 1,07E+09 2,82E+09 7,52E+09

1050 2816805 7511480 20280995 54813499 1,46E+08 3,9E+08 1,07E+09 2,82E+09 7,51E+09

1060 2811945 7498519 20246001 54718921 1,46E+08 3,89E+08 1,07E+09 2,81E+09 7,5E+09

1070 2805918 7482448 20202609 54601645 1,45E+08 3,89E+08 1,06E+09 2,81E+09 7,48E+09

1080 2798919 7463784 20152218 54465453 1,45E+08 3,88E+08 1,06E+09 2,8E+09 7,46E+09

1090 2790948 7442529 20094828 54310345 1,45E+08 3,86E+08 1,06E+09 2,79E+09 7,44E+09

1100 2782005 7418681 20030439 54136322 1,44E+08 3,85E+08 1,05E+09 2,78E+09 7,42E+09

1110 2772091 7392241 19959052 53943384 1,44E+08 3,84E+08 1,05E+09 2,77E+09 7,39E+09

1120 2761398 7363728 19882066 53735313 1,43E+08 3,82E+08 1,05E+09 2,76E+09 7,36E+09

1130 2749928 7333141 19799480 53512109 1,42E+08 3,81E+08 1,04E+09 2,75E+09 7,33E+09

1140 2737680 7300480 19711296 53273773 1,42E+08 3,79E+08 1,04E+09 2,74E+09 7,3E+09

1150 2724655 7265745 19617513 53020304 1,41E+08 3,77E+08 1,03E+09 2,72E+09 7,27E+09

1160 2710949 7229196 19518830 52753595 1,4E+08 3,75E+08 1,03E+09 2,71E+09 7,23E+09

1170 2696660 7191092 19415948 52475536 1,4E+08 3,73E+08 1,02E+09 2,7E+09 7,19E+09

1180 2681787 7151432 19308868 52186128 1,39E+08 3,71E+08 1,02E+09 2,68E+09 7,15E+09

1190 2666234 7109958 19196887 51883480 1,38E+08 3,69E+08 1,01E+09 2,67E+09 7,11E+09

1200 2650196 7067188 19081408 51571373 1,37E+08 3,67E+08 1E+09 2,65E+09 7,07E+09




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1210 2633671 7023122 18962429 51249808 1,36E+08 3,65E+08 9,98E+08 2,63E+09 7,02E+09

1220 2616757 6978019 18840651 50920678 1,36E+08 3,62E+08 9,92E+08 2,62E+09 6,98E+09

1230 2599260 6931360 18714673 50580198 1,35E+08 3,6E+08 9,85E+08 2,6E+09 6,93E+09

1240 2581472 6883924 18586596 50234043 1,34E+08 3,57E+08 9,78E+08 2,58E+09 6,88E+09

1250 2563294 6835452 18455719 49880322 1,33E+08 3,55E+08 9,71E+08 2,56E+09 6,84E+09

1260 2544728 6785942 18322043 49519035 1,32E+08 3,52E+08 9,64E+08 2,54E+09 6,79E+09

1270 2525676 6735136 18184867 49148290 1,31E+08 3,5E+08 9,57E+08 2,53E+09 6,74E+09

1280 2506721 6684589 18048392 48779437 1,3E+08 3,47E+08 9,5E+08 2,51E+09 6,68E+09

1290 2487280 6632747 17908416 48401126 1,29E+08 3,44E+08 9,43E+08 2,49E+09 6,63E+09

1300 2467645 6580386 17767042 48019031 1,28E+08 3,42E+08 9,35E+08 2,47E+09 6,58E+09

1310 2447718 6527247 17623567 47631262 1,27E+08 3,39E+08 9,28E+08 2,45E+09 6,53E+09

1320 2427596 6473590 17478693 47239710 1,26E+08 3,36E+08 9,2E+08 2,43E+09 6,47E+09

1330 2407378 6419674 17333119 46846267 1,25E+08 3,33E+08 9,12E+08 2,41E+09 6,42E+09

1340 2386965 6365239 17186145 46449040 1,24E+08 3,31E+08 9,05E+08 2,39E+09 6,37E+09

1350 2366454 6310545 17038471 46049922 1,23E+08 3,28E+08 8,97E+08 2,37E+09 6,31E+09

1360 2345750 6255332 16889398 45647021 1,22E+08 3,25E+08 8,89E+08 2,35E+09 6,26E+09

1370 2324948 6199861 16739624 45242228 1,2E+08 3,22E+08 8,81E+08 2,32E+09 6,2E+09

1380 2304146 6144389 16589851 44837435 1,19E+08 3,19E+08 8,73E+08 2,3E+09 6,14E+09

1390 2283150 6088399 16438678 44428859 1,18E+08 3,16E+08 8,65E+08 2,28E+09 6,09E+09

1400 2262153 6032409 16287505 44020283 1,17E+08 3,13E+08 8,57E+08 2,26E+09 6,03E+09




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determination of retinal thermal hazard and blue light photochemical hazard protection

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