Report on the measurements of the refractive index of air,using interference refractometersCitation for published version (APA):Schellekens, P. H. J. (1983). Report on the measurements of the refractive index of air, using interferencerefractometers. (TH Eindhoven. Afd. Werktuigbouwkunde, Vakgroep Produktietechnologie : WPB; Vol.WPB0063). Eindhoven: Technische Hogeschool Eindhoven.

Document status and date:Published: 01/01/1983

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P. Schellekens Metroloqy Labaratory THE

Participating Laboratories:

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REPORT ON THE MEASUREMENTS OF THE REFRACTIVE INDEX OF AIR, USING INTERFERENCE REFRACTOMETERS.

- National Physical Labaratory (NPL), Teddington, United Kingdom. (M. Downs, K.P. Birch).

- Physikalisch Technische Bundesanstalt (PTB), Braunschweig, West-Germany. (G. Wilkening, F. Reinboth).

-Dienst van het IJkwezen, VanSwinden Labaratory (VSL), Delft, Netherlands. (J. Spronck).

-Eindhoven University of Technology (THE), Metroloqy Laboratory, Eindhoven, Netherlands. (P. Schellekens).

This work was organised and partially funded by the Community Bureau of Reference, Commission of the European Communities, Brussels, Belgium.

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CONTENTS:

1 . Introduetion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2. Description of the comparison set-up .......... 5

3. Measurements and results ...................... 19

4. Analysis and conclusions ...................... 35

5. Recommendations and acknowledgements .......... 37

6. Appendices .................................... 38

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Chapter 1.

INTRODUCTION.

For about 15 years laser interferometers have been commercially available and the use of this measuring instrument becomes more and more important, especially in industrial practice. Today most of the metrology laboratorles own one or more of these instruments and they are used for the accurate measurement of length and angle and for calibration of measuring machines. In length measurements the length is calculated from: L = (K * Àv}/N. Here K is the number of counted fringes over L divided by a constant, generally two or four. Ày is the vacuum wavelengthand N the refractive index of the medium, mostly air. As the use of the laser interferometer outside the laboratories, in uncontrolled environments is increasing, the composition of the air plays an important role during measurements.

In a careful analysis Edlén [1] has shown which variables determine the refractive index of air. Recently Jones [2] has revised this work but the results are the same for all practical purposes. Edlén bas given values for the dependenee of N on wavelength, pressure, temperature, humidity, carbon­dioxide and carbon-hydragen contents. For a wavelength of 633 nm the formula of Edlén can be written in the following useful farm:

-4 N-1 = D * 0,104127 * 10 * p- 0,42063 * 10-9 * F

1 + 0,3671 * 10-2* T

with D = 0,27651756 * 10-J* (1+0,54*10-6*(C-300})

P is the pressure in Pa, T the temperature in °C, F the water vapour­pressure in Pa and C the co2-content in ppm. Most commercially available interferometers use the measurement of pressure, temperature and humidity to calculate N, either electronically ar by means of tables prepared for this purpose. The influence of other parameters like variations of co2 content are neglected. Since the accuracy needed is increasing this is nat always permitted and one has to measure the refractive index directly.

Also for the calibration of laser measurement systems a high accuracy of the refractive index value is needed, so in this case it is better to measure N directly and to campare this value with the value used by the interferometer. Ta get a better understanding of the accuracy achievable for the measurement of Nat a level of 1 part in 107, BCR has initiated an international project on comparison of refractometers, constructed in different laboratorles of EC-countries. Partielpants are mentioned on page 1 .

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The project has a dual role: First: a comparison of measured val~es of the refractometers with

calculated values using Edléns formula, Second: a direct comparison of refractometers to get an understanding of

instrumental accuracy. Two meetings of specialists were organised to prepare the experiments, they were held at PTB and Eindhoven University. The experiments were carried out in the Metrology Labaratory of Eindhoven University in June, 1983.

After the comparison each participating laboratory was asked to write a small report on their own measurements and send it to the Eindhoven participant who had to prepare the final report. Due to technica! problems it was impossible for one of the intended participants to take part in the measurements so on the last moment THE and VSL decided to built a second set-up for measuring the refractive index. The laser interferometer to be used in this experiment was kindly lent to us by the metrology lab of Rank Xerox Holland, Venray.

Chapter 2 of this report contains in the first place a description of the measurement facilities available for the comparison and next a short description of each refractometer. In chapter 3 are presented the results of the individual measurements compared to the calculated values according to Edlen. Also the results of direct comparison between NPL and PTB and between NPL and THE are given. After a calculation of systematic and random errors results are discussed in chapter 4 and some suggestions for impravement arepresented. In chapter 5 some recommendations for further research are given. Most of the results are listed in chapter 6.

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Chapter 2.

DESCRIPTION OF THE COMPARISON SET-UP.

During the second specialists meeting held at Eindhoven details of the comparison set-up were discussed. On a stable table a large thermally insulated cabinet should be placed containing the refractometers of the participating laboratories. Facilities for the measurement of temperature,pressure, humidity and co2 content should be present to such a level that the calculation of N from Edlens formula could be carried out with sufficient accuracy. Each participant laboratory should put in a refractometer with, if possible, instruments for measurement of pressure, temperature and humidity.

The following is a detailed description of the facilities used in the set­up.

2.1. Measuring table and insulated cabinet.

From the discusslons it was clear that a surface of 1*2 metre was just sufficient to contain all refractometers without light sourees and vacuum pumps. In the metrology laboratory of THE rather heavy table tops, made of stone at a size of 0,75*1,5 metre, were available soit was decided to use four of these slabs and mount them on a steel frame. Thus a table surface of 1,5*3 metre was available. The insulated cabinet, sizes 2,5*0,75*0,50 metre, was constructed of 50 mm polystyrene covered on both sides by a layer of 5 mm pressed paper. Holes for feed through of cables, tubes and light beams were prepared during building the comparison set-up. Also optica! windows were mounted later, as needed.

2.2. Facilities for the measurement of temperature, pressure, humidity and carbon-dioxide content at THE.

2.2.1. Pressure measurement. Usually two types of pressure measurement are in use at the metrology lab of THE. One is a metal-barometer - system Paulin - with a resolution of 5 Pa and a systematic error less than 20 Pa. The other instrument is a Fortin­type mercury-barometer with a resolution of 10 Pa and a systematic error less then 20 Pa. The VSL instrument was based on a quartz-pressure sensor (Paro-Scientific) with a resolution of 1 Pa and a systematic error less then 20 Pa. This instrument consists of a calculation unit and display coupled to the sensor by a flexible wire so the sensor can be placed near to the air sample-place. A comparison of values measured by the different instruments available, on 6-6, showed maximum errors of 10 Pa from a mean value so a systematic error less than 10 Pa would be obtained.

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2.2.2. Temperature measurement. For the measurement of temperature bath resistance thermometers and semiconductors devices {PTB) were employed. THE bas 100 Q {Pt-100) resistance thermometers coupled to a measuring set-up (TI) according to Dauphinee [3]. In this bridge the resistance of the thermometer is coupled to a Diesselhorst-comparator by means of electric null-detection. Besides the Dauphinee-set-up, a conventional two-circuit set-up (TII) using a Diesselhorst-comparator used with precision 10 Q (Pt-10) resistance thermometers was present. These thermometers were used as standards for calibration of PT-100 thermometers. Systematic errors of this temperature measurement were less than 10-2K, random errors were a few mK. The systematic errors in Pt-100 measurements are about 10-2K, random errors less than 10-2K, in the semiconductor devices these are less then 4 * 10-2K.

2.2.3. Measurement of humidity. Measurement of this quantity was in principle possible with two types of instruments: a wet and dry bulb psychrometer and a dewpoint measuring instrument (humidity analyzer 911 EG and G). Systematic errors were within 1\ relative humidity or 30 Pa absolute pressure as claimed by the manufacturer. A comparison over several days between the two instruments has shown a discrepancy of absolute pressures within 20 Pa. Random errors were within 10 Pa (0,1 Kin dewpoint reading).

2.2.4. co2 measurement. The co2 content was measured by gaschromatographic techniques and was carried out by the Chemistry Department of Eindhoven University. For this measurement air samples were taken at regular times during the day and at the end of the day these samples were analyzed. A maximum relative systematic error of 6\ was calculated. At a maximum measured co2 content of 950 ppm this corresponded to an absolute error of 75 ppm which was acceptable. Analyses on other contaminants were also carried out by gaschromatographic techniques have shown insignificant values.

2.3. The comparison set-up.

The refractometers were situated parallel to each other and in the centre a sample-place was arranged containing all the inlets of the refractometers. Also the sensors of pressure and temperature measurement and the inlets for humidity and co2-content were connected to this place. By means of this arrangement each individual measurement of N could be recalculated to the conditions measured at the sample-place. Figure 2.3.a gives a schematic diagram of the comparison set-up and in figure 2.3.b the real situation is shown with an opened cabinet. The temperature measurement set-up TI, was used in the refractometers I, II and IV with a total of eight thermometers.

V / / V/ ///////V////////// V//

V ~ ~ ~ . s :,.../-

~ I n m N: ~ / P-10 P-10 P-10 lUC ~

~>--- iel I 11 ~ ~///////////////////////7//

J2:.F

~~ ~~ I j_ --

3000

1''ig.2.3.a.~chemat~c d~agram of comparison set-up._

I IV :refractometers PI ... Prv= pumping systems IF ... IVF:air inletsystem p-10 resistance thermometers IL ... IVL:laser lightsouree

and counting system Tr ... T111 :temperature

measurement system

p

D s

pressure measurement humidity measurement sample-place

0 g .....

I -.]

I

-8-

Fig. 2.3.b Open cabinet with refractometers and laser systems.

The thermometers used in I and II were calibrated against presision PT-10 THE thermometers. Those used in IV were calibrated at NPL. Set-up T

11 is

connected to four Pt-10 precision thermometers Three of these thermometers were located near the refractometers I, II and III while the fottrth measures the temperature of the sampleplace.

2.4. Briefdescription of the refractometers used tn the comparison.

2.4. 1. The NPL refractometer. The refractometer consisted of a double passed Jamin beam-splitter 1 an air sample cell and a single retro-reflector consisting of a lens and mirror combination - Fig. 2.4.a. Bath surfaces of the beam-splitter block are coated with an aluminium film; the rear surface is fully reflecting and the front partially reflecting. The beam-splitter coatings produced equal intertering intensities for s and p polarisations in the refractometer and this results in maximum fringe contrast. This system does nat require the use of a stabilized laser, and its 'common path' optical contiguration is insensitive to variations in path length resulting from mechanical changes.

The input light beam is split into two laterally separated beams at the beamsplitter. One beam passes twice through the outer light path of the

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refractometer cell while the other, reflected from the back surface of the beam-splitter, passes twice through the central campartment of the cell. The two beams are recombined at the beam-splitter and interfere with each other. A À/4 mica phase retardation plate with its axis suitably oriented is located in one of the outer beams; this produces a phase difference of 90° between the two orthogonally polarized components of the interferogram, which are then examined by means of a polarizing beam-splitter and two photo-detectors. A third polarized and photo-detector are used to examine the single beam output from the system which provides a de signal directly proportional to the energy of the beam after transmission through the system.

An 80 mm focal length achromatle doublet was employed for the retro­reflector. The retro-reflector mirror is mounted on a loudspeaker motion and the distance between the mirror/lens combination must be maintained to better than 1 ~m in order to achleve an absolute measurement of accuracy of 1 part in 108 of air refractive index. This was realised by designing a retro-reflector mount compensated for thermal expansion.

The ends of the glass tubes were cement.ed into channels ground into the cell windows, the spacing of the windows being controlled during fabrication using end bars. The inner and outer cell chambers were accessed through single glass tubes from which pvc tubes connected the cell chambers to a control manifold. This consisted of four valves (V1 - V4) which could be used either for admitting air intoor evacuating either cell chamber. A gauge was mounted on the manifold for the measurement of vacuum pressure. Inserted into the refractometer cell outer chamber were two NPL calibrated platinum resistance thermometer bulbs which were 8 mrn long* 1.6 mm in diameter. These were seperated with respect to the cell centre by 150 mm along its length. With the polarised heliurn neon laser souree emitting 633 nm radiation and a sample cell lengthof 31.64 cm one electronic count corresponds to a path length change of À/8 and a refractive index change of 2.5 partsin 107 .

To obtain reliable bi-directional fringe counting, two electrical signals must be generated from the photo detectors in the interferometer, with constant average de levels and sinusoidal components related to the optical path difference and in phase-quadrature. The counter logic is set to trigger each time one of the signals passed through its average values.

Photo detector CD

Polarising beam splitter

Laser beam

Semi-reftecting surface ~

/ Fully reflecting

surface

~.:..Po;:;.lariser

Photo ® detector

detector @ Single beam

output

ln\erferometer beam splitter

enelosure wall

I'A\ @ © Plotinurn resistance 'Cl thermometers

®

+ Vacuum gauge

To Vacuum pump

Fig. 2.4.a. Principles of NPL-refractometer.

Lens

t Phose plate

® ®

End view

I .... 0

I

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In this refractometer, the required electronic counting signals are obtained by subtracting from each of the two sinusoidal path-difference signals the de signa! generated at the non-interterenee output. Using this technique, two sinusoidal signals can be obtained, having an average signa! level of zero volts and in phase-quadrature; any de components unrelated to the optica! path are automatically removed. The two sinusoidal path difference signals were matebed by adjusting the energy balance between the two orthogonally polarised components by rotating the plane of vibration of the incident beam, and the level of the de signa! output was controlled by rotating a polarizer in front of the photo-detector. The two counting signals are used to drive a bi-directional counter that displays a count every time one of the signals crosses the zero voltage level, each count representing an optica! path difference of À/8. The measurement sensitivity this represents in terms of refractive index is depent upon the wavelength of the light souree and the length of the refractometer cell employed.

The two counting signals were then used to drive the x and y inputs of an oscilloscope. When the optica! path length was changed this resulted in a circular lissajous figure being displayed centred about zero volts. Under static conditions the resultant vector maintained a fixed angular orientation relative to zero volts and since one complete vector revolution represented one fringe of path length change, fringe fractions could be easily estimated.

The refractometer system was mounted on a box section aluminium support with the laser souree mounted remotely. The wall of the isothermal enelosure was slotted over the refractometer such that the laser was outside the enclosure. A piece of pvc tube was connected from the centre of the enelosure to valve V1. Attached to the end of the pvc tube was a platinum resistance thermometer {C).

Measurement Procedure. The refractometer system was allowed to stabilise in the isothermal chamber for about 18 hours before any measurements were taken. Both chambers of the refractometer cell were pumped out and left under vacuum.

With the cell under vacuum and the system stabilised the reversible fringe counter was set to zero and the fringe fraction determined from the angular orientation of the voltage vector as displayed on the oscilloscope. Valve V2 was then closed and V1 was openend to leak air into the outer chamber of the cell. When the air in the cell had reached atmospheric pressure the resistance of the platinum resistance thermometers was measured on an bridge T1 . The measurement sequence was A-B-C with a repeat on A to check for drift. Whilst the resistance was being measured the new fringe count, angular orientation of the voltage vector and the barometic pressure were all noted. The atmospheric pressure was determined using an aneroid (NPL) barometer outside the isothermal chamber. The dew point of the air in the

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chamber was measured by continuously cycling this a1r through a humidity sensor. Finally the co2 content was measured as described in 2.2.4.

Valve V1 was then c]osed and V2 opened to re-evacuate t.he outer chamber of the cell and the angular orientation of the voltage vector was remeasured. The measured value of refractive index could therefore be determined from the fringe count and measured fractions. These were then compared with the value determined from t.he Edlen equation.

Accuracy of the measurements. As given in detail in appendix 6.2 there has been calculated a random error of 1.6x10-8 (95% confidence interval} and an unknown systematic error of up to 1.4*10-8 (shown by experience, 95% confidence interval) for the measured values of the refractive index of air. Quadratic addition of these errors gives a total uncertainty of 2.2*10-8 (95% confidence interval). For the calculated value of N1 based on Edlens relations, a total uncertainty of ± 8*10-8 (95% confidence interval) has been determined (Chapter 4).

2.4.2. PTB-refractometer~ The refractometer consists of a Mach-Zehnder interfetameter with an integrated block with two bores and optical windows which serve as measuring chambers (see Fig. 2.4.b). The lengthof the chambers is 160.044 mm (20°C). The interferometer is driven by a stabilized two-mode HeNe-laser (beat frequency ~ 600 MHz). Changes of the optical lengthof one of the armsof the interferometer produce phase shifts of the beat oscillation. These shifts are measured relative to the phase of a reference path. Complete fringes (= 360° of phase) are counted by a fringe counter, whereas the high­resolving evaluation of the fringe patterns is done by tracing back phase shifts to the rotation of a polarizing filter. Thus, fraction of complete fringes are detected by measuring a rotation angle: 180° of rotatien (ex) = 360° of phase = 1 complete fringe. Fringe fraction and amount of complete fringes are added to calculate the refractive index. The resolution of the interferometer is about i 1*10-9, the uncertainty is about ± 1*10-B in terms of N. The temperature of the air probe in the measuring chamber equals t.he block temperature, as the heat capacity of the probe volume is very small compared to that of the rather solid aluminium block. The block temperature is measured at the surface (03 ). A small difference between probe temperature and block temperature is likely to occur in case the surrounding temperature becomes different from the block temperature. The contribution of the temperature measurement to the uncertainty is i± 4*10- 8 in terms of N for e3-e2 i± 0.5 R.

For the experiments carried out this means an overall uncertainty of the refractometer of ± 5*10-8while for the calculated values, using Edlêns formula, a total uncertainty of i 8 * 10-8 has been determinated (Chapter 4) .

r--·-·

I . I . I nterferometer I I I llnsuloted box

·-·, . I '

I

Photo­diode

PoL fitter (rotary)

Fig. 2.4.b. PTB-refractometer.

I I

9()0

Cf> ffJ !QQ_QJ

Oivider Mixer Fring? counter oo oo ffJ [>

Servo drive Rotation angle

Laser

~---~ V Vacuummeter

Throttle

Vocuum pump

I _,. w I

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Metbod of measurement. The individual measurements had been carried out with both measuring chambers tilled as reference. After pumping down one chamber and allowing a certain time for settling of temperature, bath counters were registrated (complete fringes, fringe-fraction) and the chamber filled again to continue measurements. Thus an interval of about 4 min was reached. The speed of pumping and flooding was about 1 bar/30 sec. The temperature of the block (=

measuring temperature 93) was taken tagether with the counter readings.In addition, air temperatures at several points in the cabinet ( PTB (92 ), common air inlet (91), THE} were taken every 20 min tagether with the pressure. Measurements of the.dew point and of the co2-content were made at several times, spread over the whole day.

Calculation. The readings for complete fringes and for fringe-fractions were taken to calculate the refractive index (N-1} of the air in the measuring chamber at the temperature of 93 . In order to be able to campare the results of all groups these results were transformed to the temperature at the common air inlet {91), or to the air temperature near the PTB refractometer (92 ), respectively with 91, a2 lineary extrapolated with time. As the change of refractive index with time is no linear function no mean values have been calculated.

2.4.3. THE-Refractometer. This system is based on an ordinary double-beam interferometer using a commercially available laser-system (Hewlett-Packard 5526A}. Both beams are passing through 406 mm long cells which can both be evacuated. The measurement-system uses the remote-interferometer and corner-cubes as usual; only an extra beam-bender is used so bath beams are parallel and close together. Normally the counting system counts in~ or, if preferred, ~ units, but bere an extra 10 times extender is used so the least count equals ~· In a cell length of 406 mm this means about 70.000 counts at an air­vacuum change so one count corresponds to a resolving power of 5*10-9 in N. Both cells are made of invar, to decrease temperature sensitivity, and are closed by quartz windows. Temperature is measured on the vacuum-cell and inside the other cell, the measuring or sample-cel!, using Pt-100 thermometers as described before. The pressure in both the cells is checked by a Pirani-gauge befare starting the measurement. As the interferometer is essentially asymmetrie the corner-cubes are mounted in a steel block staggered 50 mm to correct for asymmetry. Temperature of the block is monitored during the measurement to allow correction for thermal expansion.

Tl

VACUUM PUMP

~Fig. 2.4.c. Diagram of THE-refractometer.

D p

o _________ '------~ -L

-0'---------

1111111 0

0

E

I .... U"' I

RI: Remote Interferometer; T1, T2 , T3: Temperature measurement; L: Laser; E: Extender; D: Display; C: Corner-cubes; BB: Beambender; SC/VC: Sample-place/vacuum-cell; fS: Filling Station; P: Pirani gage; AT: Adjustment Table; S: Sample valve; W: Quartz Windows; TI: Temperature measurement system.

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The air sample is taken through a special needie valve so the filling can be controlled perfectly. Figure 2.4.c shows a.schematic diagram of the apparatus. Pressure and humidity values, belonging to the air sample, were determined from the results measured on the sample-place while co2 values were taken from the results of the analysis of air samples.

Measurement procedure. First both cells were evacuated and temperature measurement of T1, T2 and T3 was carried out. Then an air sample was brought into the sample-cel! and after equilibrium the number of counts was taken and again the temperature of T1, T2 and T3 was measured. From the number of counts, corrected for small temp~~ature effects, actual cell length and vacuum-wavelength, the refractive index of air was calculated. Also the Edlén-value was calculated from the measured data of pressure, temperature, humidity and co2 content. The filling of the sample-cel! takes only a few minutes; this is the real measuring time. Re-evacuation of the system takes around ten minutes due to relatively great length of pumping lines between cells and pumping system.

Measurement accuracy. As mentioned before resolving power of the refractometer _is one count corresponding to 5*10-9 in N. Together with other influences a total unknown systematic error has been calculated as 2.5*10-8 (95\ confidence interval) in N. If a result of measurement is recalculated to sample-piace conditlans due to temperature differences this value rises to 5*10-8 in N. Random errors will be within 2*10-8 in N. So a total error of 6*10-8 in N is expected. (95\ confidence interval). A specification of these errors is given in appendix 6.3. Total error in the calculated value from Edléns formula will be less then 8*10-8 in N (95\ confidence interval). These errors are specified in Chapter 4.

2.4.4. VSL-Refractometer. This refractometer is based on the same measurement-system as the THE refractometer but the set-up and filling system are different, in fact this was the prototype THE-refractometer. One beam of the interferometer is passing through open air, the other beam passes the sample-cel! which is made of steel. The sample-cel! is closed by glass-plates extending in the air pathof the interferometer. As with the THE-refractometer the corner-tubes are staggered over 50 mm to correct for asymmetry of the interferometer. The block containing the corner-cubes is made of aluminium.

L 2 / 36* -10* ~DISPLAY I/

h 1/ HP- LASER

u I/ 1 4

9

.,.. _!=N_ ___] ~~ (:::) J- u r: /." ~~

I I PIRANI DIFF. PUMP ROTARY PUMP

Fig. 2.4.b. Diagram of VSL refractometer.

< 3

~ V v6 5./

' /6

\ 1

7 (P,T,H,C02)

..1..8

1. Beamsplitter 2. Beambender 3. Glass windows 4. Sample-cell 5. Aluminium mounting block for corner-cubes 6. Corner-cubes 7. Air inlet 8. Triple-valve for air inlet and pumping

Pr 9. ess ure measurement T 1 Thermometer for sample-cell T2 Thermometer of the aluminium block T 3 Thermometer of the open air path

syst em

I ,_. ....., I

-18-

First the measurement-cell is evacuated and then slowly filled with the air­sample to be measured. The least counts here is also i but a total extension of 360 times is used so one count equals ~· Since the sample-cel! has a length of 278 mm a vacuum to .air change in the cell gives around 170.000 counts. Temperature of sample-cel!, aluminium-block and air path are measured by Pt-100 thermometers so corrections for expansion and air path changes during the measurement can be made using Edlens formula. A Pirani­gauge is used for checking the vacuum after evacuation. Figure 2.4.d gives a schematic diagram of the apparatus. Temperature measurement was carried out by the Dauphine-setup T1 while pressure, humidity and co2 content were measured as described in 2.2.

Measurement procedure. In principle there are two possibilities for the measurement of N. First it is possible to start with the sample-cel! filled with air to be measured and then pumping out slowly until a sufficient vacuum level (< SPa) is reached. Air conditions should be measured befare starting pumping. Second it is possible to start with an evacuated sample-cel! and fill it with air. The second methad has the advantage to be faster so corrections for expansion and changes in the open air pathare smaller. Better agreement with calculated values, was achieved when the second methad was used so it was decided to use this metbod for the measurements. As the temperature of the air sample was measured by a thermometer on the outside of the cell gradients could be present. Differences between measured and calculated values can be partly explained by this effect. On 10-6 the temperature of the inlet-place has been taken for calculation of N and no corrections have been carried out for drifts of the interferometer-system. In this case the real measuring time was only 2 minutes and the results show much better agreement with calculated values.

Accuracy of the measurements. The usabie resolution during the measurement was determined to be 2 counts (~). This gives an uncertainty of 3*10-9 in N. In appendix 6.4 a specification of random and systematic errors has been given. An systematic error of 1.5*10-8 and a random error of 5.0*10-8has been determined (95\ confidence interval). Since the systematic error for the measurement of air temperature will be around 0.04K the total uncertainty increases to 6.6*10-S in N if one uses this temperature for recalculation of measured values of N to inletplace conditions. The uncertainty of results calculated from Edléns formula will be 8*10-8 in N as specified in 4.1 (95% confidence interval).

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Chapter 3.

MEASUREMENTS AND RESULTS.

The measurementprogram can be split up in four parts: 3.1. Adjustments and tests. 3.2. Individual measurements. 3.3. Comparison of individual results by recalculation to sample-piace and

conditions. 3.4. Direct comparison of pairs of refractometers using the same

inlet-system. 3.5. Changes of co2-content during the measuring period.

3.1. Adjustments and tests.

After arrival the refractometers were set-up as described in 2.3. The cabinet was prepared for the measurements and glass windows were fitted to admit the laser-beams into the cabinet. Figure 3.1.a shows the measuring table containing the cabinet and part of the instrumentation. The NPL­temperature-measurements were performed by connecting the NPL-thermometers to the THE-T1 temperature-measurement-system. After the preliminary tests it was decided to use the THE-dewpoint hygrometer for humidity measurements while the co2 correction was to be calculated from the THE measurements of the co2-content. The first co2 measurements gave contents of 970 and 980 ppm against a normal content of 300 ppm [1]. Soit was decided to take air­samples spread over the whole day and to use interpolated values from the co2 analysis in the determination of Edlens-refractivity values. THE and VSL used the Edlens formula as given in the introduction. Comparison of results from this formula with PTB and NPL results of N shows differences smaller than 5*10-9 in N.

3.2. Results of individual measurements.

As mentioned before it was decided to carry out first individual measurements of N and to compare these results with calculated values. Since some of the participants have carried out a great number of measurements complete results are given in appendices. In the following paragraphs the results of each of the refractometers are surveyed by showing up the differences between measured and calculated (Edlén) values, taking the latter ones as a reference. It should be pointed out that, by doing this, systematic and random errors of the calculated values are - at least optically - transfered to the measured values. This procedure was taken only for the sake of simplicity of the graphs.

-20-

3.2.1. NPL results. The NPL results of individual measurements are listed in appendix 6.1. The differences between measured and calculated (Edlén) values are given in graphic farm in figure 3.2.a. Part of the results on 10-6 were influenced somewhat by the Eindhoven filling system since some of these values are taken from the comparison measurements between NPL and THE. Also a few of the measurements on 9-6 may be influenced by the NPL-PTB comparison (3.3). Since the calculated values have a total uncertainty of 8*10-B in N, as shown in 4.1., nobetter results can be expected.

Figure 3.1.a.

16

12

IA.

~ ..I. t.Z..

if ~ '~ ~ ~ $ ~-t ~ .....-t

0 ~ 11 'po J ~ 13 Po 14f ~ 't ~ 1---U

8

4

0

4

8

12

16 . Fig. 3.2.a. NPL measurements.

A

~ " I. \ " ~ h/

............. , __

~ ~ ~b-. 1'1 17 Po /'[ t'n

""'0 ''

A lJ.

~ / .. 18 po

l).: 7 -6 o: 8 -6 c: 9 -6 <>: 1 0-6

Time

'

I N ..... I

-22-

3.2.2. PTB - Results. Complete PTB-results are listed in appendix 6.2. Results of 7-6 are recalculated to temperature a2 outside the refractometer while the results from 8-6 to 10-6 are recalculated to the temperature of the sample-place. No differences in pressure and humidity between sample-cel! and sample-piace have been supposed.Figure 3.2.b shows graphs of the differences between measured and calculated values. The results of 9-6 and 10-6 show good agreement with calculated values but some of the results of 7-6 and 8-6 differ considerably from the calculated values. The apparatus then was checked and the arrangement of the temperature sensors was altered to remave unwanted thermal effects. After that the temperature of the air probe in the refractometer was measured with a smaller systematic error and from then on the results show a good agreement with Edléns values. From the results of 9-6 and 10-6 it can be concluded that results of the measurements are within ±1*10-7 of the calculated values which is the aim of these camparisen measurements as given in the task description of BCR.

3.2.3. THE - Results. These results are listed in appendix 6.3. Since the complete measuring-procedure, due to the pumping duration, took more time than with the ether refractometers, less results are available. Also the preparatien of the air-sample for co2 analysis and the modification of the filling station, for direct camparisen measurements with NPL, taak some extra time. The THE-results are graphically represented in figure 3.2.c. Here again the differences between measured and calculated values are given. They show a goed reproducibility of the measurements but there is a mean offset of +1,1*10-7 from the calculated values. The analysis given in paragraph 3.4 will explain, at least for a part, this offset.

3.2.4. VSL - Results. After the replacement of the valves preliminary measurements were carried out on 8-6. Results of measurements on 9-6 and 10-6 are given in appendix 6.4. The results of 9~6 show relatively large differences with calculated values which may be explained, at least partly, by a temperature difference between wall and air-sample in the sample-cel!. On 10-6 this problem was evereome by using the temperature measured at the sample-place, considering that the temperature of the air-sample changes only slightly. The results are represented graphically in figure 3.2.d and show better results for the measurements on 10-6. It was concluded that a temperature measurement inside the sample-cell would imprave the results.

32

A~ .. 1)11o8 2 8

l 24

20

16

12

} ~ lol I

1'\ V "r J ~ I '!-I

~ ~ /. ' 8 [)

r 4

0

4

~~ ..J. ~

1~ ~ " l..

V· 11 00~ !)_ 1~ 13 ....,( "---'t ~ -........

< tf"' '-V

8

12

16

Fig. 3.2.b. PTB measuréments.

rV ~ <r>--. p ~ t.

' '" fJ ~ "' I L l LJ K I \

00'- ~ ~ ~o ... ' ~ 16 l t.

r

) h...__r L_.r ...

V /

V

1\ _..(

\ J ~ N (o 18

h ~

c

I V 00

I me

19 oo

0 7-6

0 8-6

Ä 9-6

<>10..6

I I'.) w I

A(n-1)lt108

l 20

18

16

12

8

i. ~ ~ ~

I '\ ~ .....{ ~ !,...~ --r--I"'

~ ;s 1-l

' :~ ~

~ ~ 4

0

1000 1100 1200 1300 1400

Fig. 3.2.c. THE measurements.

( ~ --A 1.,...1

"03 ~ '1!

. ....,.__, ~ (

1500 1600

~ j

-' '-n.., fA~J "\

~

1700 1800

.. Time

19 00

0:7-6 [] : 8-6

6.: 9-6

<> :10-6

I N ~ I

40

1

30

Q.... - V ....

' f\ V 20

\ ~ mi 1\

10

IL..- .. V 110~ 1200 1300 1400

0

Fig. 3.2.d. VSL measurements.

r--~I

\ ~ ,V .....

.

1500 1600

~ ~

1700

11

18 00

T I me

8 : 9-6 BI 1o-6

I N IJt I

-26-

3.3. Comparison of individual resuits by recalculation to sample-piace conditions.

To make a direct comparison of the measured values of N possible, some results are re-calculated to sample-piace conditions. Since on 7-6 no temperatures for the sample-piace were available the temperature condition on the outside of the PTB-refractometer was taken as reference. On the other days information about the inlet conditions was available so the results are then referred to conditions at the sample-place. Since only a limited number of measurements coincide in time only these values are taken for re­calculation. In appendix 6.5 these values are given whiie these are shown graphicaliy in figures 3.3.a to 3.3.d. If different values of pressure and humidity were measured, compared to sample-piace conditions, the measured value of N was aiso corrected for this differences. As explained befare the measured results of PTB at 7-6 and 8-6 are probably influenced by a systematic error in the temperature measurement. After 11.00 h on 10-6 the NPL-refractometer was connected to the THE inletsystem, so the results were altered compared to values measured before 11.00 h.

The results show no large differences when compared to the individual measurements but there seems to be a smal! tendency to higher values of refractive index compared to the calcuiated (Edlên) values as seen from the graphs.

380

370 ~~ (N-1) ,1(108

I 360

350

340

')q ·~ ~~

) ~

330 " 320 ~

'\. A

310 "\ ffi 27300 \ ~

290

1f400 1 sOO 1 eOO 1700\ ~1 8~

1 gOO

280

--...,_

'{ 270 ~

' -- --

Fig. 3.3.a. Results on 6-7 near the PTB-refractometer.

Cl: NPL 0: PTB 6.: THE x: Edlén

2 ooo

7 10-

Time

I ('.,)

-...I I

390 (N-1~108

l 380

370

360

350

340

330

320

310

27300

290

280

270

200

250

240

230

$: [B: &: x:

10

Fig. 3.3.b. 19830608 Results at sample-place conditions.

PTB NPL THE Edlén

I N Q) I

360 &

(N-1} *108 355 • • l 350

345

340

i

m ~

L:~

A

335 1\ .....a

~~

330 l ~ kei

325 ~ ~

" 27320 ~

315 '\ 15 .. 11 1 2 1 3 ~ 1 6

310 \ 305 \ 300

\ ~ A

295 f 1\ !V ....,

\ 4~ 290 Î\

285 \ 280 )e

Fig. 3.3.c. 19830609 Results at sample-place conditions.

$: G): &: <5>: x:

10-7

Time -17

~

PTB NPL THE VSL Edlén

I

"" IJ) I

365 (N-Y*1os

t 360

355

350

345

340

27335

330

325

320

315

310

-30-

Cl.

~ 6 \

0 \ 0

\ ...,.A IA

\ ~ tl \ ~0~ :

1000 1100 \i> 30 J

~ i\ ~

\~~ !

I \ (~~

Fig. 3.3.d. 19830610 Results at sample­place conditions. NPL-THE same air inlet after 11.00 h.

o: 0: 6. ~·

x

10-7

PTB

NPL

THE VSL

Edlén

Time

-31-

3.4: Direct comparison of NPL-PTB and NPL-THE refractometers.

For a more direct comparison between the refractometers it was decided to couple two refractometers to one inlet-system. In this way the same air-sample was sent to both refractometers so the performance of the refractometers could be measured, undisturbed by possible differences in the inlet-systems. The results were corrected for any temperature gradients. On 9-6 the measurements between NPL and PTB were carried out. In this case the PTB system was connected to the NPL filling system. In figure 3.4.a the results of the intercomparison are tabulated while they are graphically represented in figure 3.4.b.

Time (N-1 )x108 {N-1 )x108 (N-1)x108 ANx10 8

Edlén NPL PTB (NPL-PTB)

11.20 27345.3 27346.3 27346.5 -0.2 12~00 27337.1 27335.0 27334.0 1.0 14.00 27319.6 27318.8 27318.5 0.3 15.00 27300.6 27297.5 27293.7 3.8 -15.30 27294.1 27293.8 27292.0 1.8

Fig. 3.4.a Results of direct comparison PTB-NPL.

-32-

(N-1) H108

345 ~ 0 . NP . L 0 . PT .

1 340 ~·

:

\ I )( . . B

én Edl

335 ~

330 I ~~~ "'

""' 10-?

" 325

""' 1

.......

27320 "" 315 11 00 1200 1 300 ~ ~0 1500 •1 6oo

310 \ 305 1\ 300 \ 295

[ ~ 290

0 f ~

Fig. 3.4.b Direct comparison NPL-PTB.

The direct comparison between NPL and THE refractometers was carried out on 10-6. The NPL-inlet-system in this case was coupled to the THE filling system. For this experiment an extra outlet-valve was mounted on the THE­filling-system so the NPL inlet-system could be connected to this valve. Results of the experiments are tabulated in figure 3.4.c and shown graphically in figure 3.4.d. The intercomparisen shows a good agreement between NPL and THE results, the THE results being consistently slightly higher (àN<5*10-8). In addition both the NPL and THE results show an offset of+ 7.6*10-8 when compared to the calculated values. Since earlier measurements of NPL show good agreement with calculated values this difference can be attributed to some property of the THE inlet-system. Analysis of Edléns formula show that a lower humidity value of the air in the sample-cel! would cause the measured difference.

Time

-33-

Time (N-1)x108 (N-1)x1o8 (N-1)x108 ANx108

Edlén NPL THE NPL-THE

11.10 27332.4 27341.2 27346.0 -4.8 11.35 27325.9 27332.5 27336.1 -3.6 11.55 27319.8 27327.5 27331.1 -3.6 12.30 27310.2 27317.5 27320.4 -2.9

Fig. 3.4.c Results of direct comparison NPL-THE.

1 340

335

330

0

(\. 1Ö

7

" tJ L_

325 "' ~ [

" 27320

""' 315

1 00 11 30 1~ ~ 1~ ~ 13

310 "' 305 "' 300

Fig. 3.4.d Direct comparison NPL-THE. (Off-sets discussed insection 3.4).

C::,. 0 x

bo

. . . .

. .

T

THE

NPL

Edlén

I me

-34-

3.5. Changes of co2-content durinq the measurinq period.

As explained before each day the co2-content of the air was measured several times. The results show rouqhly the same behaviour each day as may be seen in fiqure 3.5.a. There is a considerable increase of co2-content over the day; which can be related to the number of people {7-8) taking part in the experiments in a 300 m3 volume room which was air controlled by a closed circuit. The influence of the co2-content increase can be calculated from the formula given in paragraph 1. This gives in increase in N of 1.4 parts in 108 for a 100 ppm increase in co2-content.

800 .I.

~ ~ t:::=-J ~ v

/ ~ ~I-' ~ ~

.Jd-~ ~~ / 0 . 19830607 . ~ / 6 . 08 .

0 : 09

L '/ <> : 10

600

_, ',

&_ ~ 500

. ~ V' 5!l

) (A 400

300 900 1000 1100 1200 1300 1400 1500 1a00 1~ 1800

Time

Fig. 3.5.a. co2-content in cabinet during experiments.

-35-

Chapter 4.

UNCERTAINTY ANALYSIS AND CONCLUSIONS.

In the preceding chapters experiments and measurements are described as they have been carried out in June 1983. Now an analysis of uncertainty of the calculated values of N will be given as well as a survey of the uncertainty of the results of each refractometer. Details about random and systematic uncertainty are represented in the appendices. Some conclusions about the measurements and results are given in the second part of this chapter.

4.1. Uncertainty of calculated values of refractive index of air.

In chapter 1. the formula has been given for the calculation of N from measured values of P, T, H and co2-content. From literature, [1] and [2], a maximum systematic uncertainty of ~ 5*10-8 is given for the calculated value of N without taken in account any uncertainty in P, T, H and co2-content. Uncertainties in P, T, H and co2 cause additional uncertainty in the calculated value of N. This influence can be calculated by partial differentlation of N = F(P,T,H,co2} and gives the following relations:

dN/dP = 2.67 * 10-9 ,dP in Pa dN/dT = -9.20 * 10-7 ,dT in I{

dN/dF = -4.21 * 10-10 ,dF in Pa dN/dC = 1. 45 * 10-10 ,de in ppm

Systematic uncertainty in pressure-measurement will be within 20 Pa while random uncertainty is estimated as less then 10 Pa. Total uncertainty in N due tothese uncertainties will be ± 6*10-8 . Systematic part in temperature­measurement will be 10-2K maximum while the random part is estimated as 10-2K. So the uncertainty in N due to temperature uncertainty will be ±1.3*10-8 . Systematic uncertainty in the measurement of absolute humidity has been estimated earlier as ±30 Pa while the random uncertainty as calculated, is small compared to this value. From this an uncertainty in N of ±1.3*10-8 can be calculated. For the co2-content only an overall relative uncertainty of ~6\ was available which results in 57 ppm for the maximum measured co2-content. This uncertainty causes an uncertainty in N of ±0.8*10-8. Quadratic addition of partlal uncertainties described here give a total uncertainty in N of ~8*10-8 . All uncertainties given correspond to 95\ confidence interval (2o). Uncertainties of the measured values were calculated by the partielpants and depend, of course, on the refractometer principle used. The partleipants have calculated their total uncertalnty in the measured values of N as:

-36-

NPL: ~ 2.2 * 10-8

PTB: ~ 1.0 * 10-8

THE: ~ 4.0 * 10-8

VSL: ~ 6.0 * 10-8

These are instrumental uncertainties and additional uncertainties will occur when the differential temperature measurement is used.The magnitude of these errors will be at least 3*10-8 and will be dependent upon the measurement situation. The uncertainties of THE and VSL are somewhat higher than the values calculated by PTB and NPL because their results had to be corrected for the expansion of the interferometer-path. This correction was calculated from the measured temperatures.

4.2. Conclusions.

The intercomparisen has provided the information required for the development of instruments for use in industrial applications were a length accuracy of 1 * 10-7 is required.

From the results presented here it may be concluded that most measured values covered the aim of the project being a maximum uncertainty of 1 * 10-7 in the measurement of the refractive index of air.

The direct comparison of PTB, NPL and THE refractometers showed an agreement of better than 5 * 10-8 and thus significantly better than the aim of the project.

In addition the comparison of measured and calculated values proved that the model uncertainty of Edléns formula is better than 5 * 10-8 provided that the correction is carried out for co2-content.

The measurements in some cases indicated some imperfections of the set-up which required modification. Special attention has to be paid to the measurement of temperature which is the most limiting factor with respect to the deviations of a comparison (see chap. 4.1 for the dN/dT value). Impraper temperature measurements caused most of the troubles during our measurement.

It is worth noting that during the experiments the atmosphere was not contaminated to any extend. However the co 2-production of around eight people caused an increase of up to three times the normal content (3 in 104). In industrial environments much larger disturbance of co2-content tagether with organic vapours might be expected and large errors are possible if these factors are neglected as in the usual procedure in commercially availably laser interferometers. It might be concluded that to achieve an absolute accuracy of 1 * 10-7 it is essential to measure the refractive index directly with a refractometer, these measurements having no dependenee on variations of the constituentsof the air.

-37-

Chapter 5.

RECOMMENDATIONS AND ACKNOWLEDGEMENTS.

The value of the direct comparison of different refractometers was underlined by the results in this report which made the isolation of a number of minor instrumentation differences between individual instruments possible, and higher accuracies to be achieved in the measurements by the examination of an indentical sample of the surrounding air.

A second intercomparison between these instruments, when they have been improved, in 1985 would culminate this essential standardisation work. If by these experiments a good agreement can be reached, information about the accuracy of Edlens formula can be obtained giving more information about possible systematic effects.

We like to thank the Community Bureau of Reference (BCR) of the European Commission for the organisation, the financlal support and the stimulating enthusiasm contributed to this intercomparison exercise which was done within the Applied Metrology Programmof BCR under the supervision of Dr. K. Hoffmann. Last but not least we like to thank Prof.Drs. J. Koning of the Metrology Labaratory of Eindhoven University for his hospitality and support before and during the experiments and for reading the draft report.

REFERENCES.

[1] Bengt Edlén. The Refractive Index of Air. Metrologia, 1966. Vol.2, No 2.

[2] Frank E. Jones. The Refractivity of Air. Journal of Research of National Bureau of Standards 1980. Vol.86, No 1.

[3] T.M. Dauphinee. Potentiometric Methods of Resistance Measurement. Temperature. lts Measurement and Control in Science and Industry. Ed. C.M. Herzfeld. Vol. III. 1962. Reinhold Publishing Corporation, New York.

-38-

Chapter 6.

APPENDICES.

6.1. NPL- Results.

6.2. PTB - Results.

6.3. THE - Results.

6.4. VSL - Results.

6.5. Results of recalculation of individual measurements to sample-place conditions.

-39-

6.1. NPL- Results.

The results are presented in the original form as the were supplied by the NPL-participants. Oncertainty calculations are presented on page 42.

OCR FUNDED AIR REFRACTOMETER INTERCOMPARISON

EINDilOVEN UNIVERSlTY

(JUNE 1983)

CELL All! DEW C02 (PPM) AIR REFRACtlVITY MEASURED- co2 co2 CORRECTED HEASIJRF.Il

PRESSUIIE (n-1) x 10 8 VA!.IJF.S TIME TEMPERAfURE •c POINT TIME EXTRAPOLATED CAt.CULATED CORRECTION MEASURED VAt.UE (PASCALS)

KB4 KB6 •c VA LUES CALCULATED (EDLEN) x 10-8 - CALCULATEO CORRF.C'I'F.ll '1'0 MEASURED (EOLEN) -8 VALUE (EOLF.N) NPI, 1'F.HPF.RA'I'IIRF.

'! 1o-8

Tuesday 7th 1130 680 - 5.6

1<100 101930 19.320 325 9.1 721 27365.0 27356.0 .. 9.0 - 6,2 + 2.8

1420 101926 19.331 335 9.2 727 27360.0 27353.6 t 6,4 - 6.3 • 0.1

1430 730

1450 101890 19,319 329 9.4 733 27348.8 27344.1 • <1.7 - 6.4 - l. 7

1510 101887 19.345 355 9.4 736 27343.7 27340.9 + 2.8 - 6.4 - 3.6

1525 101885 19.377 387 9.5 739 27342.5 27337.0 • 5.5 - 6.5 - 1.0

1535 101877 19.400 409 9.6 741 27340.0 27332.4 + 7,6 - 6.5 + 1.1 I

1555 101857 19.1176 488 9.9 744 27330,0 27318.7 + 11.3 - 6.6 t 4.7 ,j:l.

0 1600 745 I

1615 101842 19.500 508 10.2 750 27325.0 27311.6 + 13.4 - 6.6 + 6.8

1645 101844 19.553 564 10.4 758 27321.2 27306.4 + 14.8 - 6.8 • 8.0

1705 101830 19.552 564 10.6 764 27312.5 27301.9 + 10.6 - 6.9 + 3.7

1735 101001 19.682 695 10.7 769 27292.5 27281.6 + 10.9 - 6.9 + 4.0

1755 101781 19.692 707 10.7 1111 27283.8 27275.0 + 8.8 - 7,0 + 1.8

1800 780

1810 101785 19.717 735 u.o 703 27285.0 27272.6 + 12.4 - 7.1 + 5.3

Wednesday 8th 0900 380

0950 101688 18.604 596 8.6 490 27361.3 27360.5 • 0.8 - 2.9 - 2.1

1010 101?1<1 18.586 583 8.1 545 27368.8 27366.6 + 0.2 - 3.6 - 3.-1

1030 101705 18.639 641 8.8 596 27358.8 27360.6 - 1.8 - 4.4 - 6.2

1100 668

1115 101782 18.775 781 9.0 673 27368.8 27367.7 + 1.1 - 5.5 - 4.4

1130 101776 tl.a35 849 9.0 678 27365.0 27360.1 • 4.9 - 5.6 - 0.7

1200 101700 J.8.958 972 9.3 688 27330.0 27327.0 + 3.0 - 5.7 - 2.7

1230 :t01675 19.099 116 9.3 698 27313.7 27306.9 + 6.0 - 5.9 + 0.9

1330 101634 19.341 353 9.35 719 27281.3 27?.73.4 + 7,9 - 6.2 + I, 7

WedneRday continue~!

8t.h 1440

1500

1530

1600

lf\30

1715

'l'hurRrllty 9 th

Friday

1110

1120

11::10

1200

1230

1245

1345

1400

1500

1530

1600

1615

1630

1645

lOth

1000

1015

1030

1110

1135

1155

1230

121\5

101728

101720

101679

101685

101652

101711

102130

102132

102132

102127

102135

1021<15

102137

102132

102120

102107

102095

102089

102095

102100

101992

101984

101976

101970

101955

101950

101942

101930

19.504

19.626

19.709

604

646

731

19.760 779

19.915 933

19.972 983

20.045 047

20.032 036

20.035 041

20.108 114

20.121 131

20.169 180

20.304 311

20,316 322

20.482 482

20.516 526

20,561 5?2

20.601 608

20.585 593

20.642 652

19.603 595

19.574 570

19.574 572

19.696

19.?42

19.786

j9.872

697

748

801

882

19.895 909

9.6

9.6

9.6

9.7

9.8

9.8

9.8

10.0

9.9

10.0

10.0

10.1

10.1

10.0

10.3

10.2

10.2

10.2

10.3

10.5

9.5

9.5

9.5

9.!!

9.5

9.7

9.9

10.0

1600

743

750

760

770

772

776

1800 780

0900

1130

1400

1600

0900

410

609

625

640

649

656

662

660

690

730

750

770

780

785

788

430

470

460

490

1100 510

1240

510

576

614

661

700

710

27276.2

27275.0

27256.3

27252.5

27233.7

27242.5

27346.3

27346.3

27346.3

27335.0

27340.0

27336.2

27322.5

27318.8

27297.5

27293.8

27287.5

27280.0

27262.5

27276.3

27343.8

27347,5

27346.3

27341.2

27332.5

27327.5

27317.5

273f?7.5

27274.6

27266.5

27249.6

27246.2

27222.6

27233.4

27339.5

27340.5

27340,5

27332.0

27332.7

27330.6

27315.8

27313.8

27294.3

27287.5

27280.2

27275.0

27277.6

27272.9

27345.4

27345.7

27343.5

27329.3

27321.6

27315.2

27304.6

27298.6

• 1.6

+ 6.5

t 6.7

+ 6.3

+ 11.1

+ 9.1

+ 6.8

.. 5.8

+ 5.8

.. 3.0

• 7.3

+ 5.6

t 6.7

• s.o • 3.2

.. 6.3

• 7.3

+ 5.0

+ 4.9

+ 3.4

- 1.6

• 1.8

+ 2.6

+ 11.9

+ 10.7

• 12.3

+ 12.8

• 6.9

- 6.5

- 6.6

- 6.0

- 6.9

- 7,0

- 7.0

- 4.6

- 4.8

- s.o - 5.1

- 5.3

- 5.4

- 5.6

- 5.8

- 6.3

- 6.6

- 6,9

- 7.1

- 7.2

- 7.2

- :!.5

- 2.6

- 2.6

- 3.1

- 4.1

- 4.6

- 5.6

- 6.1

- 4,9

- 0.1

- 0.1

- 0.6

• 4.1

• 2.1

+ 2.2

• 1.0

• 0.8

- 2.1

• 2.0

+ 0.2

+ 1.1

- 0.8

- 3.1

- 0.3

+ 0.4

- 2.1

- 2.3

- 3.8

- 4.1

- 0.6

0

Air smple • 8. 8 t:al<en~t Elrd-tlltm + 6 • 6

valve am filter

+ 7.7

• 7.2

+ 2.8

1'1'11 i'7?.7R.8 R ( N!>I,-I"I'B -1 , f. x 10- )

I'"1'FI ?73411.5 -8 ( NPI-PI'Il - 0. 2 x 10 )

rrn i'73Y•·o R ( NPL-1'"1'FI 41.0 x 10- )

I

""' PTB 2?318.5 8

(NPI~PTB +0., x 10- ) Pre 2?293·? 8 (NPL-PTB +3~ x 10- ) Pt'B n. ::>.o -8

{NI'I-PTB 11, x 10 )

PTB 27~3·9 -8 (NPL-PTR -Ö.1 x 10 )

(1) UNCERTAINTIES ASSOCIATED WITH MEASURED VALUES OF REFRACTIVITY

Souree

UNCERTAINTY IN CELL LENG TH

UNCERTAINTY IN FRINGE COUNT DUE TO

(1) ambient drift (1)

(2) fringe count reading

Parameter uncertainty

:t 14.5 J.IJil

:t 0.045 counts

:t 1.2s x tö8 ( 2 )

Uncertainty in (n-1) x toB

Random systematic

:t 1. 45

:t 1.12

:t 1.25

(1) refers to parameter drift during maasurement cycle.

(2) parameter uncertainty quoted in tenns of (n-1)

99\ Confidence interval

(n-1) x toB

:t 2.17

:t 2.07

± 1.25

Tbtal uncertainties in (n-1) x 108

Random Systematic

:t 2.42 :t 2.17

Total uncertainty in (n-1) x 108

for measured refractivities

± 3.25

I ~ N I

-43-

6.2. PTB - Results.

Original results as supplied by PTB-participants.

Summary of uncertainty calculations for measured values of N: Resolution of the interferometer: +1*10-9

Uncertainty in N due to the interf;rometer ~1*10-8 . Contribution of temperature measurement to uncertainty: ~4*10-8 . !e3-e2Ji0.5K. Overall uncertainty of the refractometer used with temperature measurement: ±5*10-8

For the values of N, calculated from Edlens formula, an uncertainty of ±8*10-S has been claimed.

table 1a tempera tures, pressure, de\" point, co2abttndance from 7.6.83 time meas. air ajr air press. de1r1 co2 (n-1)

temp .. temp. temp. temp. point x10 11

PTR PTB TH8 in let (Edlén) -{}31oC .a. 1°C 2 ·1°C .a. 1°C 1 /mbar /°C /ppm

14.20 19.o3 19.238 1o19.27 9.o 73o 2.7368 14.4o 19.o6 19.263 1o18.95 2.7359 1S.oo 19.o8 19.311 1o1.U. So 2.7349 15.2o 19.11 19.338 1o18.77 2.7346 15.40 19.13 19.378 1018.72 9.6 2.734o I

ob. ~ 16.oo ·19 .16 t9.4o8 1o18. 5 ï 745 2.7333 I

t6.2o 19.19 19.453. 1o18. 5o 2.7327 ,.__"-~---------· ...

16.4o 19.22 19.496 1o18.42 2.7323 1'/.,oo 19.26 19.548 1o18. 3o 1o.o 2.7316 1'1. 2o t9.3o 19.587 1ot8.o7 2.73o2 17.40 19.34 19.628 1o17.95 2.7294 18.oo 19.37 19.658 . tot? .81 2.7287 18.20 19.41 19.688 1o17.85 1o,2 2.7284

table 1b ( 1) tempera t•1res, pressure, dew point, co2abundance from r-.6.83

time meas. air air air press. dew co2 (n-1) temp. temp. temp. temp. point x10 4

PTB PTB THE in let (Edlén) IJ 1°C 3 1'21oC /°C a l 0 c 1 /mbar /°C lppm

9.2o 18.56 18.549 18.647 18.5o4 1o1'/ ,28 38o 2.7381 9.4o 18.52 18.568 18.677 18.514 1o17,o4 8,6 2.7373

to.oo 18.51 18.598 18. '/o7 18.554 1ot7.32 8.7 2.7379 ' to.2o t8.5o 18.628 18.727 18.623 tot7.24 8.8 2.7370

1o.4o t8.5o 18.667 18.777 18.699 tot':• .42 2.7367 11.oo 18.52 18.728 18.827 18.794 1o17.84 9.o 54o 2.7365 I

""" 11.20 18.54 18.774 18.877 18.874 1o17.79 9,o 2.7361 U'l I

11.4o 18.57 18.838 18.937 18.954 totï.51 2.7346 12.oo 18.61 18.898 19.oo7 t9.o44 to17 .o6 9.3 2.7325 t2.2o 18.65 18.963 t9.o47 19.135 1o16.64 2.73o6 12.4o 18.7o 19.o56 19.155 19.233 1o16.85 2.73o2 13.40 18.87 19.227 19.346 19.413 1ot6.4o 9.3 68o 2. 7274 14.oo 18.95 19.3o2 19.427 19.486 tot7.7o ·2.7275 14.2o t9.o1 19.370 19.495 19.566 1o17.17 2.728o 14.40 19.o8 . 19.465 19.574 19.645 1o17.12 9.6 2.7271 15.oo 19.14 19.518 19.637 19.699 1o17.13 2.7267 15.2o 19.2o 19.585 19.717 19.776 1o16.66 9.6 2. 724 7

15.40 19.26 19.637 19.787 19.824 1o16.7o 2.7248

table 1b (2) temperatures, pressure, dew point, co2abllndance from 8.6.83

time meas. air air air press. dew co2 (n-1)

temp. temp. temp. temp. point x10 4

PTB PTB THE: in let (E:dlén) IJ. /°C 3 IJ.. /°C 2 /°C f) /°C 1 /mbar /°C /ppm

16.oo 19.32 19.698 19.83o 19.889 1o16.83 9.7 77o 2.7241 I

16.25 19.39 19.768 19.92o 19.954 1o16.62 2.7229 lli:lo 0"1 I

16.40 19.46 19.818 19.976 19.999 1o16.64 9.8 2.7226 17 .oo. 19.51 19.866 2o.o35 2o.o54 1o16.82 2.7225 17.3o 19.58 19.948 2o.1o4 2o.114 1o17.52 2.7238 17.40 19.63. 19.978 2o.177 ~o.144 1o1·/.5o 9.9 2.7235 18.oo 19.69 20;.045 2o.2o4 2o.214 1o1·· .32 78o 2.7223

table 1c temperatures, pressure, dev1 point, cu2aoundance fror:1 ·9.6.83

time meas. air air air press. de\.; co2 (n-1) temp. temp. temp. temp. point X10 4

PTB PTB THt; in let (Edlén) /} /°C 3 ~ /°C 2 /°C a.. /°C 1 /mbar /°C /ppm

9.4o 19.9o1 19.968 2o.154 19.974 1o21.o4 41o 2. 7341 1o.oo 19.897 19.975 2o.164 19.974 1o21.25 9.6 2. 734 7 1o.2o 19.89o 19.978 2o.172 19.976 1021.41 2.7352 11.oo 19.888 19.994 2o.184 2o.o28 1o21.26 9.8 2. 7341 11.2o 19.891 2o.o18 2o.2o7 2o.o52 1o21.3o 64o 2. 7343 11.40 19.9oo 2o.o58 2o.25o 2o.o74 1o21.17 9.9 2.7338 12.oo 19.915 I 2o.o88 2o.264 2o.12o 1021.15 2.7333 .::..

-...1

12.20 19.93o 2o.115 2o.294 2o.156 1o21. 3o 2.7334 I

12.4o 19.955 2o.158 2o.33o 2o.199 1o21. 31 2.733o 13.4o 2o.o35 2o.24o 2o.434 2o.324 1o21.27 1o.1 2.7317 14.oo 2o.o61 2o.27o 2o.454 2o.335 fo21.27 69o 2.7316 14.3o 2o.o95 2o.315 2o.492 2o.382 1o21.3o 2.7310 15.oo 2o.135 2o.373 2o.524 2o.444 1o21.1o 1o.3 2.7301 15.25 2o.18o 2o.433 2o.S74 2o.499 1o2f.91 2.7291 15.So 2o.199 2o.468 2o.614 2o.544 1o20.85 1o.2 2.7286

. 16.2o 2o.251 2o.524 2o.664 2o.6o5 1o2o.8o 77o 2.7279 17.1o 2o.366 2o.628 2o.685 2o.716 1o2o.92 17.3o 2o.658 2o.7o5 2o.734

table 1d temperatures, pressure, dev.J point, co2abundance from 1o.6.83

time meas. air air air press. de\" co2 (n-1) 4 temp. temp. temp. temp. point xil.O

PTB PTB THE in let (Edlén) I) I°C 3 I). 1°C 2 1°C {}. ;oe

1 /mbar ,. /°C /ppm

9.25 19.537 19.555 19.6oo 19.446 1o19.9o 9.5 43o 2.7359 9.45 19.5o5 19.550 19.594 19.439 1019.83 2.7357

1o.oo 19.49o 19.548 19.592 19.457 1o19.92 2.7361 I ... (I)

1o.2o 19.477 19.558 19.6o2 19.471 1-o19. 75 9.5 2.7355 I

1o.4o 19.470 19.573 19.617 19.489 1o19.68 51o 2.7352 11.2o 19.473 19.635 19.686 19.584 1o19.7o 9.6 2. 7343

11.40 19.482 . 19.668 19.727 19.648 1o19.57 9.6 2.7335 12.oo 19.495 19.7o9 19.753 19.713 . 1019.48 2. 7327 12.2o 19.527 19.772 19.834 19.784 1o19.38 9.9 2.7317

12.4o 19.555 19.818 19.884 19.86o 1o19.28 1o.o 7oo 2. 73o7

-49-

table 2a (1)

results from 7.6.83

. time meas. (n-1) ref. (n-1)

temp. x10 4 temp. x10 4

{}3/.oC at .,.,.3 -8- / 0c 2 at "2

14.3o 19.o4 2.73918 19.251 2.73718

14.34 19.o4 2.73938 19.256 2.73738

14.39 19.o5 2.73885 19.263 2.73695

14.43 19.o5 2.73885 19.27o 2.73681

14.48 19.o5 2.73826 19.282 2. 736o9

14.52 19.o6 2.73817 19.291 2.736o3

15.oo 19.o7 2.7379o 19.311 2.73566

15.o4 19.o8 2.73799 19.316 2.73580

15.10 19.o8 2.73773 19.325 2.73546

15.19 19.1o 2.73790 . 19.338 2.73569

15.25 19.10 2.73744 19.348 2.73521

15.3o 19.12 2.73749 19.358 2.73528

15.36 19.12 2.73689 19.37o 2.73457

15.42 19.13 2.737o8 19.382 2. 734 74

15.48 19.14 2.73643 19.39o 2.73411

15.52 19.14 2.73641 19.396 2.734o3

15.59 19.15 2.73573 19.4o8 2.73334

16.o4 19.16 2.73584 19.417 2.73345

16.o9 19.16 2.73538 19.428 2.73289

16.13 19.17 2.73547 19.437 2.73299

16.2o 19.18 2.73528 19.453 2.73275

16.22 19.19 2.73528 19.457 2.73280

16.27 19.19 2.73481 19.467 2.73224

16.35 19.21 2.73490 19.485 2.73235

16.41 19.21 2.73463 19.495 2.73198

16.44 19.23 2.73444 19.5o6 2.73188

16.50 19.23 2.73397 19.521 2.73127

16.54 19.24 2.73391 19.532 2.7312o

17.11 19.27 2.73423 19.570 2.73144.

17.17 19 •. 28 2.73331 19.582 2.73o5o

17.20 19.29 2.73316 19.588 2.73o4o

17.26 19.30 2.73283 19.6o3 2.73oo2

-50- i

table 2a (2)

results from 7.6.83

time meas. (n-1) ref. (n-1)

temp. x10 · 4 temp. x10 4

-{}~ / 0c 3 -

at f)-3 {} /oe 2 at f)-2

17.35 19.32 2.73310 19.626 2.;73o32

17.42 19.34 2.73285 19.631 2.73o15

17.46 19.34 ·2. 73292 19.637 2.73o16

17.51 19.35 2.73258 19.645 2.72965

17.55 19.36 2.73210 19.651 2.72940

18.o1 19.37 2.73183 19.658 2. 72915

18.o5 19.38 2.73191 19.666 2.72925

18.11 19.34 2.73164 19.675 2.729o9

18.15 19.40 2.73230 19.681 2.72959

18.21 19.41 2.73224 19.688- 2.72966

-51-

table 2b (1)

results from 9.6.83

time meas. (n-1) ref. (n-1)

·temp. x10 4 temp. xlO 4

{}. /oe 3 .

at {j-3 {}/oe 1

at {jol

9.43 19.9oo 2.7~503 19.974 2.73417

9.52 19.9oo 2.73544 19.974 2.73457

9.57 19.898· 2.73544 19.974 2.73453

1o.o7 19.894 2.73593 19.974 2 •. 73498

1o.to 19.893 2.73588 19.975 2.73492

1o.19 19.89o 2.736o4 19.976 2.735o6

11.12 19.888 2.73599 2o.o42 2.73439

11.17 19.891 2.73592 2o.o48 2.73428

11.25 19.892 2.736o4 2o.o56 2.73455

11.3o 19.896 2.736o8 2o.o63 2~73434

11.41 19.9oo 2.73564 2o.o74 2.73384

11.45 19.9o1 2.73568 ·2o.o85 2.73380

11.52 19.9o5 2.73544 2o.1o2 2.73344

11.59 19.910 2.73544 2o.12o 2.73331

12.o7 19.916 2.73535 2o.133 2.73316

12.15 19.925 2.73546 2o.14 7 2.73321

12.23 19.932 2.73562 2o.162 2.73331

12.3o 19.939 2.73573 2o.177 2.73333

12.37 19.948 2.73571 2o.192 2.73325

12.41 19.952 2.73562 2o.199 2.73313

13.53 2o.o47 2.73459 2o.332 2.73175

13.59 2o.o54 2.73417 2o.335 2.73137

14.o3 2o.o6o 2.73428 2o.34o 2.73149

14.o9 2o.o68 2.73463 2o.35o 2.73182

14.15 2o.o77 2.73461 2o.36o :2.7318o

14.39 2o.1o9 2.73390 2o.4oo 2.73101

14.52 2o.127 2.73383 2o.427 2.73o87

14.55 2o.131 2.73310 2o.434 2.73o:t1

15.o1 2o.138 2.73290 2o.444 2.72987

15.o4 2o.143 2.73350 2o.451 2.73o47

15.11 .. 2o.154 2.73319 2o.464 2.73o14

15.2o 2o.168 2.73257 2o.48o 2.72995

15.24 ·2o.176 2.73237 2o.499 2. 72918

-52-

table 2b (2)

results from 9.6.83

time meas. (n-1) ref. (n-1)

temp. x10 4 temp. x10 4

-8: /oe 3 at -8-3 -3: / 0c 1 at -8-1

15.34 2o.192 2.73324 2o.515 2. 73oo6.

15.43 2o.2o7 2.73280 2o.531 2.72960

15.48 2o.218 ·2.73255 2o.54o 2. 72936

15.5o 2o.221 2.73276 2o.544 2.72957

16.oo 2o.236 2.73252 2o.564 2.72928

16.o4 2o.243 2.73260 2o.572 2. 72935

16.12 2o.255 2.73229 2o.589 2.72899

16.18 2o.266 2.73253 2o.6o1 2.72922

16.27 2o.28o 2.73222 2o.631 2.72877

16.30 2o.284 2.73268 2o.642. 2'.72918

16.35 2o.294 2.73259 2o.661 2.72899

-53-

table 2c

results from 1o.6.83

time meas. (n-1) ref. (n-1)

temp. x10 4 temp. x10.

4

IJ. /°C 3 at 8 3 IJ.. /°C 1 at 81

9.54 19.5oo 2.73520 19.450 2.73549

1o.ó4 19.488 2.73573 19.460 2.73584

1o.1o 19.485 2.73540 19.464 3.73544

1o.18 19.480 2.73529 19.470 2.73521

1o.22 19.480 2.73542 19.473 2.73529

1o.3o 19.4 73 2.73536 19.48o 2.73512

1o.32 19.473 2.73527 19.482 2.735o2

1o.41 19.47o 2.73525 19.489 2. 73489

1o.56 19.469 2.73520 19.527 2.73448

11.o5 19.467 2.73538 19.548 2.73444

11.13 19 .. 469 2 •. , ~555 19.567 2.73445

11.21 19.471 2.73522 19.584 2.73398

11.23 19.473 2.73531 19.594 2.73398

11.30 19.474 2.73528 19.616 2.73378

11.42 19.482 2.73546 19.655 2.73368

11.5o 19.488 2.73498 19.680 2.733o1

11.53 19.492 2.73498 19.69o 2.73295

11.59 19.49ï 2 •. /3452 19.713 2.73229

12.o2 19.5oo 2.73458 19.720 2.73235

12.1o 19.5o6 2.73443 19.749 2.732o2

12.12 19.512 2.73443 19.756 2.732oo

12.18 19.518 2. 73441 19.777 2.73183

12.21 19.524 2.73459 19.784 2.73198

12.28 19.532 2.73417 19.814 2.73136

12.3o 19.536 2.73415 19.821 2.73130

12.42 19.55o 2.73375 19.865 2.73o66

12.44 19.556 2.734o4 19.873 2.73o91

. -54-

table 3 ( 1)

results from 8.6.83

time meas. (n-1) ref. (n-1)

temp. x10 ·4 temp. x10 4

IJ. / 0c 3 at {}3 IJ.. / 0c 1 at {).1

9.52 18.52 2.73943 18.538 2.73938

1o.oo 18.52 2.73916 18.554 2.73875

1o.o2 18.51 2.73876 18.561 2.73838

1o.o6 18.52 2.73968 18.575 2.739o8

1o.o9 18.51 2.73971 18.585 2.73901

1o.16 18.51 2.73962 18.599 2.73879

1o.2o 18.5o 2.73972 18.623 2.73858

1o.26 18.51 2.74oo8 18.646 2.73882

1o.31 18.51 2.74o3o 18.665 2.73886

1o.37 18.51 2.74o81 18.688 2.73916

1o.42 18.51 2. 74o73 18. 7o9 2.73888

1o.49 18.51 2.74o19 18.742 2.738o3

1o.54 18.52 2. 74o19 18.765 2. 73791

1o.59 18.52 2.74o61 18.794 2.738o9

11.o4 18.52 2.74o59 18.810 2.7379o

11.11 18.52 2.74180 18.838 2.73885

11.13 18.53 2.74169 18.846 2.73875

11.18 18.54 2. 74o87- 18.866 2.73784

11.21 18.54 2..74o87 18.874 2.73777

11.26 18.55 2.74o9o 18.898 2.73767

11.29 18.55 2.74o87 18.910 2.=73753

11.35 18.56 2.74o87 18.934 2.73740

11.42 18.57 2. 74144 18.963 2.73779

11.4" 18.58 2.73937 18.986 2.73560

11.50 18.59 2.73930 18.999 2.73550

11.56 18.6o 2.73832 19.o26 2.73436

12.oo 18.61 2.73819 19.o44 2. 73416

12.o5 18.62 2.73699 19.o67 2.73284

12.o9 18.63 2.73739 19.o85 2.73316

12.15 18.64 2.73575 19.112 2.73138

12.17 18.65 2.73597 19.121 2.73159

12.31 18.68 2.73650 19.189 2.73177

12.33 18.69 2.73566 19.199 2.73o93

-55-table 3 (2)

results from 8.6.83

time meas. (n-1) ref. (n-1)

temp. x10 4 temp. x10

4

a / 0c 3 '

at a3 {Jo l 0 c 1

at a1

12.36 18.7o 2.73494 19.213 2.73o17

12.38 18.71 2.73553 19.222 2.73o76

12.43 18.71 ·2.73540 19.248 2.73o4o

13.46 18.91 2.73276 19.436 2.72787

13.5o 18.92 2.73347 19.441 2.72683

13.52 18.93 2.73320 19.458 2.72829

13.55 18.94 2.73298 19.470 2.728o6

13.57 18.94 2.73298 19.478 2.72798

14.o1 18.95 2.73274 19.489 2.72773

14.o3 18.96 2.73320 19.5o1. 2.72817

14.o8 18.97 2.73241 19.52o 2.72730

14.11 18.99 2.7323o 19.531 2.72727

14.16 19.oo 2.73284 19.551 2. 72772

14.18 19.o1 2.73325 19.559 2.72814

14.24 19.o2 2.73333 19.579 2. 72814

14.25 19.o3 2.73329 19.585 2.72813

14.31 19.o4 2.73296 19.6o6 2. 7277o

14.33 19.o6 2.73318 19.611 2.728o6

14.39 19.o7 2.73314 19.627 2.72797

14.41 19.o8 2.73316 19:.645 2. 72791

14.47 19.o9 2.73285 19.664 2. 72752

14.49 19.10 2.73296 19.669 2.72767

14.54 19.12 2.73276 19.683 2.72753

14.57 19.13 2.73296 19.691 2.72775

15.o2 19.14 2.73263 19. 7o7 2.72736

15.o5 19.15 2.73285 19.718 2.72757

15.11 19.17 2.73210 19.741 2.72680

15.13 19.18 2. 73215 19.749 2.72686

15.24 19.21 2.73164 19.786 2.72629

15.30 19.23 2.73127 19.8oo 2.72597

15.32 19.24 2.73122 19.815 2.72588

15.45 19.27 2.73o22 19.840 2.72449

15.47 19.28 2.73144 19.847 2. 72587'

-56-

table 3 (3)

results from 8.6.83

time meas. (n-1) ref. (n-1)

temp. x10 4 temp. x10 4

8 /°C 3 at {).3 8 / 0c 1 at 81

17.o5 19.53• 2.73o28 2o.o64 2. 72532

17.1o 19.54 2.73o59 2o.o74 2.72563

17.13 19.55 2.73o54 2o.o8o 2.72561

17.18 19.56 2.73983 2o.o9o 2.72593

17.21 19.57 2.73116 2o.o96 2.72627

17.25 19.58 2.73131 2o.1o4 2.72644

11.28 19.59 2.73140 2o.11o 2.72657

17.33 19.61 2.73111 2o.123 2. 72634

17.36 19.61 2.73120 2o.132 2.72635

17.42 19.63 2. 73o74 2o.151 2.7259o

17.47 19.65 2.73188 2o.168 · 2.72657

17.55 19.67 2.73o54 2o.197 2.72564

18.oo 19.68 2.73o87 2o.214 2.72591

18.1o 19.71 2.73o24 2o.249 2.72523

-57-

6.3. THE - Results.

Summary of uncertainty calculations.

Measured values. Refractive index bas been calculated from:

K * Ày N = 1 + L * 400

K: the number of counts measured by the interferometer. L: the actual length of the sample-cell. K and~L have to be corrected for temperature influence. Àv: vacuum wavelength used in the interferometer.

Uncertainty in K

Random: 3 counts Systematic: 3 counts

Uncertainty in L

Systematic: 5 IJm Random: 2 IJm

.... Uncertainty in

Systematic: 5*10-8

Relative 2*10-8 Random:

Total uncertainty (95\ confidence interval)

Uncertainty in N*108

1 r 5 1 1 5

0,8 0,4

negligible

negligible

4

THE - Results of 19830607 co2-content: 740 ppm.

Time Dewpoint Pressure Temp. Interf erometer N N t:.N~to8 0 (Pa) 0

Calculated Measured temp. ( C) air ( C) counts

14.30 9.4 101894 19.29 70195 1.00027355 1.00027368 -13.4

15.15 9.4 101886 19.33 70176 1.00027349 1.00027361 -11.4

15.30 9.6 10f880 19.38 70156 1.00027342 1.00027353 -11.1

15.45 9.9 101864 19.40 70133 1. 00027335 1.00027344 - 8.7 I

VI CIO

17.00 10.5 101836 19.53 70083 1.00027313 1.00027325 -11.8 I

17.15 10.7 101805 19.62 70037 1.00027296 1.00027307 -11.1

17.35 10.8 101800 19.63 70028 1. 00027293 1.00027303 -10.4

17.45 10.7 101800 19.64 70016 1. 00027292 1.00027298 - 6.3

18.00 10.9 101777 19.72 70002 1.00027278 1.00027293 -14.8

18.15 11.1 101780 19.81 69980 1.00027270 . 1.00027278 -14.3

THE - Results of 19830608

Time Dewpoint co2 Pressure Temp. Interferometer N N /illd08 0 air (°C) temp. ( C) (ppm) (pa) Counts Calculated Measured

10.40 8.9 540 101746 18.79 70208 1.00027361 1.00027373 -12.0

11.30 9.0 560 101733 18.91 70171 1.00027346 1.00027359 -12.0

12.00 9.3 580 101654 19.01 70083 1.00027314 1.00027325 -10.8

13.30 9.6 680 101660 19.35 70009 1.00027285 1.00027296 -10.8

13.45 9.6 690 101660 19.35 69999 1.00027285 1.00027292 - 6.9 I

14.40 9.6 720 101708 19.54 69994 1.00027280 1.00027290 - 9.6 VI ' \.0

I

15.05 9.6 730 101662 19.64 69935 1.00027259 1.00027267 - 8.0

16.00 9.6 740 101680 19.82 69902 1.00027248 1.00027254 - 6.4

16.30 9.8 750 101650 19.97 69853 1.00027225 1.00027235 -10.2

17.25 9.9 770 101745 20.07 69890 1.00027249 1.00027249 - 0.3

17.50 10. 1 780 101735 20.17 69864 1.00027299 1. 00027239 -11.4

THE - Results of 19830609

Time Dewpoint co2 Pressure Temp. Interfarometer · N N 6N:~1o8 temp. (°C) (ppm) (Pa) air (°C) Counts calculated Measured

11.00 10.0 600 102130 20.25 70130 1.00027325 1.00027343 -17.9

11.45 9.9 645 102131 20.28 70108 1.00027322 1.00027334 -12.1

12.00 10.0 650 102127 20.31 70098 1.00027319 1.00027330 -12.0

12.40 10. 1 660 102131 20.33 70094 1.00027317 1.00027328 -11.5

16.00 10.4 770 102094 20.80 69950 1.00027264 1.00027273 - 8.3 I

0'1

THE - Results of 19830610 0

I

10.15 9.6 480 101984 19.66 70156 1.00027340 1.00027353 -12.9

10.45 9.6 500 101965 19.68 70142 1.00027334 ; 1.00027247 -13.3

11.10 9.8 510 101968 19.71 70132 1.00027331 1.00027344 -12.3

11.35 9.7 576 101954 19.75 70109 1.00027326 1.00027335 - 9.0

11.55 9.7 614 101946 19.79 70094 1.00027320 1.00027329 - 9.3

12.30 9.9 681 101935 19.85 70076 1.00027310 1.00027322 -11.4

6.4. VSL - Results.

Summary of uncertainty calculations. Measured values of N.

K * Àv N - 1 = L*1440

-61-

K : the corrected number of measured counts from tbe interferometer. Àv: the vacuum wavelengtb used in the interferometer. L : tbe actual length of the sample-cell.

Uncertainties

Relatieve uncertainty in K: Random: 1.2*10-5

Systematic: 1.8*10-4

Relative uncertainty in ~: Systematic : 10-8 Random: 3*10-9

Relative uncertainty in L: Systematic : 5*10-5

Random: 6*10-6

Total uncertainty: (95% confidence interval)

Uncertainties in N

3.6*10-9

5.6*10-8

negligible negligible

1.5*10-8

0.2*10-B

VSL - Results of 19830609

Time Dew-point Pressure Temperature Interf erometer N N 6Nz108 (OC) (Pa) measuring-cell Counts Calculated Measured

11.50 10.0 102117 20.22 172955 27324 27347 -23.0

12.10 10.0 102122 20.20 173004 27327,5 27352 -24.5

13.00 10.1 102135 20.28 172982 27323,5 27335 -11.5 I

14.35 10.3 102113 20.49 172828 27298 27323 -25.0 0'1 N I

15.15 10.3 102044 20.52 172743 27290 27313 . -23.0

15.35 10.2 102986 20.54 172718 27287 27300 -13.0

16.05 10.2 102079 20.59 172716 27281 27298 -17.0

16.35 10.5 102082 20.65 172662 27276 27290 -14.0

17.10 10.5 102094 20.72 172607 27272 27283 -11.0

VSL - Results of 19830610

Time Dew-point Pressure Temperature Interferomet.er N-Calculated N-Measured AN~lo-8 (OC) (Pa) air-inlet(°C) Counts (N-1)~108 (N-1) x1o8

11.15 9.7 101970 19.56 172890 27345.9 27345.4 + o.s

11.22 9.7 101970 19.59 172886 27343.8 27344.8 - 1.0

11.35 9.7 101958 19.62 172866 27337.9 27336.9 + 1.0

11.40 9.6 101958 19.65 172831 27335.6 27336.2 - 0.6 I 0"1

11.45 9.6 101954 19.66 172816 27334.0 27333.7 + 0.3 w 1

12.00 9.6 101948 19.72 172776 27326.8 27327.5 - 0.7

12.20 9.9 101939 19.78 172751 27317.9 27323.5 - 5.6

12.25 10.0 101939 19.80 172769 27316.7 27326.4 - 9.6

12.43 10.0 101933 19.86 172626 27309.6 27319.6 - 9.9

12.50 10.0 101928 19.88 172681 27306.5 27312.4 - 5.9

-64-

6.5. Recalculation of individual results to sample-place conditions.

19830607 Recalculations of results to conditions near PTB-refractometer.

Near PTB-refractometer conditions PTB NPL THE

Time p P~62) co2 Oewpoint N N t:lN N ÀN N ÀN 0 ~108 ~108 ~108 (pa) ( C) (ppm) temp. ( C) Calculated Measured Measured Measured

I 0'1 U'l I

14.30 101905 19.251 730 9.4 1.000273616 1.000273718 -10.2 1.000273601 1.5 1.000273745 -12.9

15.30 101875 19.358 742 9.6 1.000273429 1.000273528 - 9.9 1.000273423 0.6 1.000273557 -12.8

17.05 101830 19.560 764 10.5 1.000273091 1 . 000273136 - 4.5 1.000273117 -2.6 1.000273212 -12.1

17.35 101801 19.626 769 10.7 1.000272945 1.000273032 - 8.7 1.000272977 -3.2 1.000273032 - 8.7

18.15 101780 19.681 785 11.1 1.000272825 1.000272959 -13.4 1.000272870 -4.5 1.000272959 -13.4

19830608 Recalculation of individual results to sample-place conditions.

Sample-place conditions

Time p T {Pa} {oC}

10.30 101733 18.665

11.30 101765 18.910

14.40 101712 19.627

17.15 101717 20.080

19B30609

11.10 102128 20.041

12.00 102115 20.120

12.40 102131 20.200

15.00 102110 20.444

16.00 1020BO 20.564

o) NPL-PTB same inlet

s) NPL-THE same inlet

co2 (ppm)

590

6BO

740

770

610

650

660

730

770

]?TB NPL

Dewpoint N N AN N 0 ~lOB temp. ( C) Calculated Measured Measured

B.B . 1.000273703 1.000273BB6 -1B.1 1.000273639

9.0 1.000273565 1 • 00027227B liL 7 1.000273551

9.6 1.000272739 1.000272797 - 5.B 1.000272680

9.8 1.000272327 1.000272577 -25.0 1. 0002 72 340

9.B 1.000273439 1.000273439 0.3 1.000273467

10.0 1. 000273332 1.000273331 0.1°)1.000273307

10.1 1.000273298 1.000273313 - 1.5 1.000273296

10.3 1.000273017 l.0002729B7 3.o0 >1.000272986

10.2 1. 000272834 1.000272928 - 9.3 1. 000272838

THE

AN N AN ~toB Measured ~1oB

-6.4 1.000273810 -10.7

1.4 1.000273675 -11.Q'

5.9 1.000272830 -9..1

-1.3 1.000272411 - B.4 I

0"1 0"1 I

-2.5 1.000273613 -17.1

2.5°} 1.000273443 -11.1

0.2 1.000273400 -10.2

3.1°) ------------0.4~) 1.000272818 1.6~)

19830609 Recalculation ofVSL-results to sample-place conditions.

Sample-place conditions VSL

Time p T co2 Dewpoint N N .ó.N (Pa) (OC) (ppm) temp. (°C) Calculated Measured *108

11.50 102117 20.08 650 10.0 . 1.000273375 1.000273580 -20.5

12.10 102122 20.14 650 10.0 1.000273332 1. 00027 3575 -24.3 l

13.00 102135 20.22 670 10. 1 1.000273292 1. 0002 7 3406 -11.4 0'1 -..J I

14.35 102130 20.38 700 10.2 1.000273192 1. 000273377 -24.8

15.15 102100 20.47 730 10.2 1.000272970 1.000273192 -22.2

15.35 102087 20.52 740 10.2 1.000272890 1.000273016 -12.6

16.05 102082 20.57 770 10.2 1.000272833 1. 000272992 -15.9

16.35 102085 20.65 770 10.3 1. 000272763 1. 000272892 -12.9

17.10 102092 20.72 780 10.5 1.000272718 1.000272824 -10.6

19830610 Recalculation of individual results to sample-place conditions.

Sample-place conditions PTB NPL THE

Time p T co2 Dewpoint N N Llli N Llli N Llli (OC) 0 x108 x108 x108 (pa) (ppm) temp. ( C) Calculated Measured Measured Measured

I

10.15 101979 19.466 480 9.5 1.000273572 1.000273521 5.1 1.000273576 -0.4 1.000273695 -12.3 83 -8.3*)

l 11.10 ·101970 19.584 510 9.8 1.000273432 1.000273445 -1.3 1.000273515 1.000273561 -12.6

11.35 101957 10.648 576 9.5 1.000273357 1. 000273374 -1.7 1.000273417 -6.o*> 1. 0002 7 34 52 - 9.5

11.55 101948 19.690 614 9.7 1.000273292 1.000273295 -0.3 1.000273359 -6.7x) 1.000273387 - 9.5

12.30 101942 19.821 681 9.9 1. 000273156 1.000273130 2.6 1.000273222 -6.6*) 1.000273260 ..:.10.4

x) NPL-THE same inlet.

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