integrating piezoelectric sensors for thermoacoustic … · 2019. 5. 7. · barbara schuppler...

Barbara Schuppler

Integrating Piezoelectric Sensorsfor Thermoacoustic

Computertomography

Diplomarbeit

Zur Erlangung des akademischen Grades einer Magistra

an der Karl-Franzens Universität Graz

Naturwissenschaftliche Fakultät

vorgelegt bei Ao. Univ. Prof. Dr. Günther Paltauf

Institut für Physik

Abteilung Magnetometrie und Photonik

im April 2007

Für meine Mama,

Anna Schuppler

Contents

1 Acknowledgments iii

2 Introduction 1

3 Theoretical principles of Optoacoustics 3

3.1 Historic Overview and Future Prospects . . . . . . . . . . . . . . . . . 3

3.2 Propagation of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2.1 Theory of Radiative Transfer . . . . . . . . . . . . . . . . . . . 6

3.2.2 Diffusion Equation . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3 Generation of Thermoacoustic Waves . . . . . . . . . . . . . . . . . . . 10

3.3.1 Optoacoustic Processes . . . . . . . . . . . . . . . . . . . . . . . 10

3.3.2 Thermal Confinement and Stress Confinement . . . . . . . . . . 12

3.3.3 The Correlation of Incident Light and Generated Pressure . . . 13

3.3.4 Thermoacoustic Wave Equation and Solution . . . . . . . . . . 14

3.4 Propagation of Acoustic Waves . . . . . . . . . . . . . . . . . . . . . . 16

3.4.1 Reflexion and Refraction . . . . . . . . . . . . . . . . . . . . . . 16

3.4.2 Sound Absorption and Dispersion . . . . . . . . . . . . . . . . . 16

3.4.3 Diffraction of Acoustic Waves . . . . . . . . . . . . . . . . . . . 17

3.4.4 Nonlinear Acoustic Effects . . . . . . . . . . . . . . . . . . . . . 19

4 Piezoelectricity and Piezoelectric Sensors for TACT 21

4.1 Principles of Piezoelectricity . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2 The Piezoelectric Line Sensor . . . . . . . . . . . . . . . . . . . . . . . 24

4.2.1 Piezoelectric PVDF Films . . . . . . . . . . . . . . . . . . . . . 24

4.2.2 The Construction of the Sensor . . . . . . . . . . . . . . . . . . 27

4.2.3 Electric Characteristics of the Sensor and Sensitivity . . . . . . 30

i

Contents

5 Integrating Line Sensors and Image Reconstruction 33

5.1 Point Detector vs. Large Plane/Line Detectors . . . . . . . . . . . . . . 33

5.2 Image Reconstruction for Line Sensors . . . . . . . . . . . . . . . . . . 35

6 Experiments to Characterize the Sensor 39

6.1 Testing the Sensor with a Point Source . . . . . . . . . . . . . . . . . . 39

6.1.1 Experimental Set-up and Procedure . . . . . . . . . . . . . . . . 39

6.1.2 Received Signals and Discussion . . . . . . . . . . . . . . . . . . 41

6.1.3 Testing the Line . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.2 Experimental Determination of the Sensitivity . . . . . . . . . . . . . . 45

6.2.1 Experimental Set-up and Procedure . . . . . . . . . . . . . . . . 45

6.2.2 Received Signals and Determination of the Sensitivity . . . . . . 46

7 Automation of Experiments for TACT 49

7.1 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.2 Procedure of the Experiment . . . . . . . . . . . . . . . . . . . . . . . . 50

7.3 Technical Assembling of the Control Box . . . . . . . . . . . . . . . . . 51

7.4 About the Microcontroller ATmega8 . . . . . . . . . . . . . . . . . . . 54

7.5 Programming an ATmega8 . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.6 Description of the Program Flow . . . . . . . . . . . . . . . . . . . . . 57

8 Tomographic Experiment with a Phantom 63

8.1 The Making of the Phantom . . . . . . . . . . . . . . . . . . . . . . . . 63

8.2 Experimental Set-up and Adjusting . . . . . . . . . . . . . . . . . . . . 64

8.3 Received Images and Discussion . . . . . . . . . . . . . . . . . . . . . . 67

9 Summary and Conclusions 73

10 Symbols and Abbreviations 75

10.1 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

10.2 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

List of Figures 79

Bibliography 81

ii

1 Acknowledgments

First of all, I would like to thank my supervisor, Prof. Dr. Günther Paltauf, for

giving me the opportunity to write my diploma thesis in his group, for supporting

my ideas and supervising my work. Furthermore, thanks go to Prof. Dr. Heinz

Krenn, who warmly integrated me in the group of "Magnetometrie und Photonik",

for the possibility to take part at the seminar Nano and Photonics. Mauterndorf 2006.

Thanks also go to the other students of the group for helping me technically in the

laboratory, for the fruitful discussions and for simply spending a good time together.

Thanks also go to Matthias Skacel, on the one hand, for helping me regarding

electronic and programming issues of the automation, on the other hand, for his

personal encouragement during all the years of studies.

Finally, I would like to thank my family. My brothers always supported my studies.

In the last months, my brother Martin even helped me with improving the quality

of the images included in this thesis. Special thanks go to my grandparents. They

supported me during all the years, financially and personally.

iii

1 Acknowledgments

iv

2 Introduction

Thermo Acoustic Computer Tomography (TACT), also known as photoacoustic or

optoacoustic tomography, is a technology in development for imaging semitranspar-

ent, light scattering media. Even though it is applied mainly to the diagnostics of

biological tissue, it is not yet established in medicine. The basic principle of TACT is

that first short laser pulses (pulse duration ≈ 10nm) are irradiated on the medium,

where the energy of the light gets absorbed in dependence on the optical characteris-

tics of the medium. A rapid thermal expansion of the medium causes an acoustic wave

(thermoelastic effect). This acoustic wave contains information on optical character-

istics and optical structures of the medium. Piezoelectric and optical sensors measure

the pressure signals outside the object. Computer algorithms are used to reconstruct

the distribution of absorbed energy and an image is received.

The choice of the wavelength of the electromagnetic radiation depends on what is

required to be imaged. Using wave lengths in the spectral range of infrared (800 −1200nm), or even microwave (1− 300mm) guaranties the imaging of deep structures,

as required for mammograms, but with a forfeit in contrast. Using light in the visible

spectrum (400 − 700nm) yields a higher contrast, but the penetration depth is only

in the range of some millimeters. For diagnostics of the skin preferably the visible

spectrum is applied [41].

Thermoacoustic computer tomography combines the advantages of optical imaging

and ultrasound imaging. Optical Coherence Tomography (OCT) has a very good res-

olution up to a depth corresponding to the diffusion length of the medium. After this

depth, the propagation of light becomes diffuse. Depending on the type of tissue this

length is about 1mm. Diffuse Optical Tomography (DOT) is the imaging technique

beyond this length. It gives the optical properties of the imaged tissue, but with a

poor resolution.

1

2 Introduction

Medical ultrasonography is a non-invasive imaging technique where ultrasound is

sent into the body where it is reflected from interfaces between tissues and an echo

is returned to a transducer. The used frequencies are between 2 and 13MHz, where

lower frequencies give greater penetration depth but less spatial resolution. The dis-

advantage of this method is that the acoustic contrast between soft tissues is low, but,

as the propagation of ultrasonic waves is less diffuse than of light, the resolution is

higher than when using DOT.

In TACT, incident electromagnetic radiation is transformed via the thermoelas-

tic effect into ultrasonic waves that leave the medium. Because of this, both, high

contrast and high spacial resolution can be obtained. Its advantage over X-ray com-

putertomography is the use of non-ionizing radiation that lies in the range of visible

and infrared light. The warming due to the propagation of the mechanical waves is

very low, as ultrasonic sensors of high sensitivity are used. Also the generation of

thermoelastic pressure is very efficient. Already a temperature rise of 1C leads to a

pressure of 5bar [41]. Its advantage over magnetic resonance is the relatively low cost

[5].

The aim of my diploma thesis was to construct and test a novel TACT set-up

using a piezoelectric line sensor and to develop an control box for the tomographic

experiment. The structure of the written work was chosen to be in chronological order

with the processes that occurred during the project. At the beginning of chapter 3

the focus lies on the propagation of light, then, understanding already absorption

in tissue, the thermoelastic effect will be treated, followed by the propagation of

acoustic waves. In a next step, these acoustic waves arrive at the piezoelectric sensor.

In Chapter 4, the attention will be given to piezoelectricity, its use for sensors and its

practical implementation in the construction of the sensor. Then, the line geometry of

the sensor and its consequences for the reconstruction will be discussed. In Chapter

6, experiments will be presented that allow to determine the characteristics of the

sensor. After describing the set-up of the tomographic experiments, the developed

automation, whose central component is a microcontroller, will be presented. Finally,

in the last chapter, images obtained of phantoms will be shown and discussed.

2

3 Theoretical principles of

Optoacoustics

In this chapter, some historical aspects of optoacoustics and its importance for medical

imaging will be treated. Chronologically following the generation of optoacoustic

waves, beginning with the propagation of light in medium, the processes of absorption

and scattering will be described. Then, processes that transform light into sound,

especially the thermoelastic effect, will be presented. After having understood how

pressure waves are generated, the focus will be on the propagation of acoustic waves

and its consequent influence on their waveform.

3.1 Historic Overview and Future Prospects

In 1880 and 1881 the first reports of experiments on the optoacoustic effect with

solids, liquids and gases were published by Alexander Graham Bell. He illuminated

thin discs with a beam of sunlight and interrupted the beam with a rotating slotted

disc. As the generated acoustic waves were in the range of audible frequencies, he

needed not more than his own ear as measuring instrument [34]. He found out that

by illumination with different wavelengths the measured sound yields a spectrum that

serves to characterize the absorbing components of the material [13].

Incidentally, Bell and his assistants developed the Photophone (Fig. 3.1). A mirror

was fixed on a membrane that served to generate vibrations of the mirror similar to

the vibrations in the voice. A light beam was radiated into this system, and so this

light beam was modulated with the sound. This modulated light beam, then, changed

the electric resistance of a gas cell, that was again transformed into sound. It worked

without wires, but since it only transmitted clearly up to distances of 100m, it did

3

3 Theoretical principles of Optoacoustics

Figure 3.1: Graham Bell´s Photophone [13]

not lead to a successful breakthrough [34].

As in these first experiments an audible acoustic wave was induced by a visible

electromagnetic field, the discoverers called the phenomenon Optoacoustic Effect [34].

In the field of spectroscopy the expression photoacoustic is nowadays more common.

However, the phenomenon was forgotten soon, as no great functional nor scientific

value could be found in the effect. It took fifty years until the optoacoustic effect

experienced a revival for the study of gases [45]. Important progresses were made

since the design and development of the first laser in 1960 [47]. From that time on,

a continuous interest on this effect in various fields of applications was notable and

efforts were made to explain the phenomenon theoretically.

Supporting the theory of Lord Rayleigh (1881), Bell elucidated his observations,

concluding that the principal source for the optoacoustic signal was the mechanical

vibration of the disc that was fixed on the membrane. This mechanical vibration, he

thought, was a result of uneven heating of the beam of light [45]. In the same year,

two more physicists worked on that field. On the one hand, Mercandier shared Bell´s

theory that the reason for the optoacoustic signal was mechanical vibration, on the

other hand, Preece suggested that the optoacoustic effect "is purely an effect of radiant

heat, and it is essentially one due to the changes of volume in vapors or gases produced

by the degradation and absorption of this heat in a confined space"([44]p.517). This

explanation already comes close to modern theories. The first attempt to mathemat-

ically describe the optoacoustic effect was not made until 1973 by Parker [45].

4

3.2 Propagation of Light

Contemporary photoacoustic spectroscopy still works on the same principles as

Bell’s apparatus, but with increased sensitivity by using lasers and microphones. It

can be used for gases, solids and fluids [13]. The actual technical range of appli-

cations of the optoacoustic effect is broad. In environmental engineering, it can be

used to measure the emission of plants and microbes, as well as industrial pollution.

In the field of materials testing, the optoacoustic measuring method is applied rou-

tinely e.g. for the characterization of impurities in semiconductors and to localize

inhomogeneities and cracks in materials [34].

Using radiation-induced ultrasound for biomedical studies was first realized by

Bowen et al. in 1981, utilizing microwaves [35]. Even though in medicine, thermoa-

coustic tomography is yet not utilized, the progress in research shows a high potential.

Sensor methods and reconstruction algorithms for imaging are continuously improving

[5, 10, 42], imaging of small animals and first successful in vivo images were achieved

[52]. Concerning medical applications for humans, thermoacoustic methods have been

tested examining skin vasculatures [29] and breast cancer [32]. Further ideas for the

technical realization are in test stage.


In this chapter, the propagation of light through a medium will be described. The

resulting distribution of light is given by the optical characteristics of the irradiated

medium. These are probabilities for absorption and scattering. The examination of

the absorption is especially important in our case, as this procedure is the reason

for the heating of the media and the resulting generation of a pressure wave. In the

description and explanation of the propagation of light, only the particle nature of

the light will be considered, since wave characteristics like coherence, polarization,

interference and diffraction do not play an important role in the case of optoacoustic

phenomena [34].

5


Figure 3.2: Illustration of the radiation density [34].

3.2.1 Theory of Radiative Transfer

A mathematical ansatz for the description of scattering processes was first developed

by Chandrasekhar [6] for meteorological problems such as the propagation of light in

the atmosphere and in clouds. The aim of the derivation will be to describe processes

like absorption and scattering, as well as phenomena that include both. The theory of

the radiative transfer presented here describes the temporal dependence of the spacial

distribution of light, considering the direction of the beam. This dependence can be

expressed by the radiation density L, which is the power of radiation P per solid angle

dΩ that leaves an area df in direction s. Here the projection of s on the unit vector

~n of the area d~f , which is defined as d~f = ~n · df is considered [34].

The correlations of these vectors are shown in Fig. 3.2. The mathematical definition

of the radiation density is [34]

L :=dP

~s · d~fdΩ. (3.1)

The unit of L is W/m2sr. The irradiance E in a point in space described by ~r can be

defined using the radiation density L:

E(~r) =

∫4π

L(~r, ~s)dΩ. (3.2)

The irradiance has units of an intensity W/m2. Now, how the radiation density tem-

6


porally changes in total within a given volume V for a given beam direction ~s can be

described by

1

clight

∫V

∂L(~r, ~s, t)

∂tdV. (3.3)

This total change of the radiation density in the considered volume V consists of five

components, which form the Radiative Transfer Equation [34]:

1

clight

∂L(~r, ~s, t)

∂t= −~s · ∇L(~r, ~s, t)− µaL(~r, ~s, t)− µsL(~r, ~s, t) +

+ µs

∫4π

p(~s ′, ~s)L(~r, ~s ′, t)dΩ′ + ε(~r, ~s, t). (3.4)

The first term describes the part of the radiation density that was lost via the

surface of the volume. The second term describes the part of the radiation density

that was lost due to absorption, where µa is the absorption coefficient. µa describes

the probability for absorption per covered length of path. Its unit is cm−1. For a

purely absorbing medium the Lambert Beer´s Law relates the change of the intensity

I with the absorption coefficient, dependent on the distance z:

dI(z)

dz= −µa · I(z)⇒ I(z) = I0e

−µaz, (3.5)

where I0 is the initial intensity at z = 0. As will be shown in Chapter 3.3, the absorp-

tion coefficient also is important to characterize the transfer from electromagnetic- to

heat- energy.

The third term shows how much radiation density was lost in the considered vol-

ume due to scattering. µs is the scattering coefficient. In analogy to the absorption

coefficient, a relation of µs with the not-scattered intensity Is can be defined as

dIs(z)

dz= −µs · Is(z)⇒ Is(z) = I0e

−µsz. (3.6)

Scattering occurs due to partial reflection, transmission and diffraction, which are

processes that are a result of inhomogeneities of the refractive index n. In biological

tissue, these inhomogeneities are a result of the complex anatomy.

The fourth term in the Radiative Transfer Equation (Eq. 3.4) describes how much

radiation density can be gained in the considered volume due to scattering processes

7


of the surroundings. The function p(~s ′, ~s) gives the probability for a scattering from

a photon that is coming from the direction ~s ′ into the direction ~s in the considered

volume. As this function has a probability character, it has to follow the following

equation[34]: ∫4π

p(cos θ)dΩ = 1, (3.7)

where cos θ = ~s · ~s ′. (3.8)

The Henvey-Greenstein-Function pHG(~s ′, ~s), that was originally derived for the

propagation of light in interstellar nebulae, is also used commonly in tissue-optics:

pHG(~s ′, ~s) = pHG(cos Θ) =1

4π

1− g2

(1 + g2 − 2g cos Θ)3/2, (3.9)

with

g =

∫4π

pHG(cos Θ) cos ΘdΘ, (3.10)

where the parameter g, called anisotropy coefficient, is the average value of the cosine

of the angle of scattering Θ, and can therefore assume values between −1 and 1. For

g = 0, the characteristic of scattering is isotropic in average, which means that an

anisotropy could still exist within the averaged range. If g < 0, a dominant backwards

scattering is the case, if g > 0, the parameter indicates a dominant forward scattering.

In biological tissue, the forward scattering is strongly pronounced.

Considering the size of the particles in relation to the wavelength of the light, two

kinds of scattering can be distinguished. On the one hand, Rayleigh-scattering occurs

when the particle is small in comparison to the wavelength. Then, the scattered light

does not have any preferred direction, but rather comports isotropically (g = 0). On

the other hand, Mie-scattering occurs when the particles are at least the same size

as the wavelength, or bigger. The scattered light propagates dominantly in forward

direction (g → 1).

The fifth and last term ε(~r, ~s, t) of Eq. (3.4) is called source term and describes how

much radiation density the considered volume can gain due to light sources within

the volume. Such could be e.g light that was spontaneously emitted by fluorescence

[34].

To calculate the light transport in inhomogeneous absorbing and scattering media

the use of Monte Carlo Simulations is very common.

8


3.2.2 Diffusion Equation

Approximations are necessary, because the Radiative Transfer Equation is not solvable

precisely by analytical methods. A common ansatz for an approximate solution of

the above equation is to develop L(~r, ~s) and p(~s, ~s ′) with the spherical harmonics

Ylm(Θ, ϕ), so that a system of differential equations of rank 1 (for detailed description

see [33]) is received. Supposing that p(~s, ~s ′) is independent of ϕ, p(~s, ~s ′) can be

developed with Legendre polynomials Pl(cos Θ). The approximations are labeled after

the rank of the term Pl, after which the development is terminated. With the P1-

approximation satisfying results can already be achieved under the condition that

µa << µs(1− g2). This is the case in strongly scattering media, in which the incident

light propagates so diffusely that the irradiance ~E, as well as other functions of Eq.

3.4, lose their dependence on the direction of the incident light beam (~s). This leads

to the diffusion equation, which is a differential equation of rank 2 for the laser fluence

Ψ. Its unit is [Ψ] = J/m2. Ignoring the source term, the stationary diffusion equation

in one dimension along the axis of the laser beam z is [34]

∇ · (Ddiff (~r)∇Ψ(~r)) = −µaΨ(~r), (3.11)

and its solution has a similar form as the Lambert Beer´s law:

Ψ(z) = Ψ0(z)e−µeffz, (3.12)

where µeff is the effective optical energy attenuation coefficient, which is defined as:

µeff =

√µa

Ddiff

=√

3µa(µa + µs(1− g)) =√

3µa(µa + µ′s), (3.13)

where Ddiff is the diffusion constant, g is the anisotropy coefficient and µ′s is the

reduced scattering coefficient, defined by the anisotropy factor (µ′s = (1− g)µs). The

laser fluence is a term that is defined for the inside of the medium, as radiant energy

in every point of the space [34]. The definition of the laser fluence not only includes

the light reaching the considered area in the medium from the light source, but also

the scattered light that comes from all directions. Ψ0 is the fluence just underneath

the surface that, due to scattering, can be higher than the incident fluence. This

physical size is not to be confused with the irradiated light, described by the radiant

9


exposure [H(z)] = J/m2. Also for the incident radiant exposure a exponential law can

be defined, in analogy to Lambert Beer´s law:

H(z) = H0e−µaz, (3.14)

whereH0 is the incident radiant exposure at the surface of the absorbing liquid (z = 0).

The energy density is given by the negative gradient of the incident radiant exposure,

W (z) = −dH(z)/dz, or by the product of fluence and absorption coefficient:

W (~r) = µa(~r) ·Ψ(~r) (3.15)

3.3 Generation of Thermoacoustic Waves

3.3.1 Optoacoustic Processes

Many mechanisms exist that lead to the excitation of sound in matter due to inter-

action with laser radiation. In the following, only five of these mechanisms will be

mentioned, where the first two of them are nonlinear effects.

1. Plasma production, caused by a dielectric breakdown produces a shock wave

propagating the medium with supersonic speed. This dielectric breakdown only

happens at laser intensities above 1010W/cm2. It is the most efficient process

for converting electromagnetic energy into acoustic energy. The conversion ef-

ficiency η goes up to 30% for liquids. Unfortunately, this method is not usable

for diagnostic biomedical applications, since the intensities are too high [47].

2. If a threshold, whose value is determined by the thermal properties of the mate-

rial, is exceeded during the generation of acoustic waves, explosive vaporization

sets in. Material ablation occurs, normally accompanied by plasma formation.

This nonlinear effect has a efficiency η of about 1% [47].

3. Electrostriction occurs due to the capability of molecules to be electrically po-

larized by an electromagnetic wave, so that they start moving into and out of

regions with higher light intensity. As a result of these movements, a density

gradient and a following sound wave are generated. In weakly absorbing media,

electrostriction can be an important process [47].

10


Figure 3.3: Thermoelastic effect. The illuminated volume absorbs the electromagnetic

energy, which causes a thermal expansion and consequently a pressure field

[10].

4. When light is reflected, absorbed or scattered in a medium a transfer of impulse

of the photons takes place, which results in radiation pressure. In this process,

the radiation pressure itself serves as a sound generating mechanism [47]. This

effect leads to pressures in the range of mbar, but only when the laser intensity

is so high that it would already cause damage in biological tissue. As for ther-

moacoustic tomography laser intensities need to be low, the radiation pressures

are negligible [34].

5. The thermoelastic effect can be described the following way: A short laser pulse

is absorbed in a medium, where a quick heating and thermal expansion take

place. This results in a strain in the body, which relaxes to an acoustic wave.

Its efficiency is rather low (η can reach up to 1 · 10−3%). This effect dominates

the excitation of sound if the laser energies are below the vaporization threshold,

consequently this effect can be utilized for biological applications. Henceforth

the focus will be on the conditions that a system has to fulfill to make the

thermoelastic effect possible and efficient [47].

11


3.3.2 Thermal Confinement and Stress Confinement

The transformation from electromagnetic energy into sound energy is most efficient

when the here presented thermal- and stress- confinement requirements are fulfilled.

The former requires that the laser pulse duration tp is shorter than ttherm, which

means that the time in which the light acts on the medium is shorter than the time for

thermal relaxation. In other words, the time of the deposition of the electromagnetic

energy needs to be so short that the caused enhancement of temperature does not

have enough time to diffuse out of the radiated volume. Expressed mathematically

[49]:

tp < ttherm, (3.16)

ttherm =ρ · cV · δ2

λh, (3.17)

where ρ is the density of the medium, cV is the specific heat capacity, λh is the heat

conduction coefficient and δ is the characteristic length of the radiated volume, also

called penetration depth. In purely absorbing and optically homogeneous media, δ

is identical with the reciprocal of the absorption coefficient µa, whereas in scattering

media, δ equals the reciprocal of the effective attenuation coefficient µeff , which is a

combination of absorption and scattering (see Eq. (3.13)).

The stress confinement demands that the time tp is shorter than the time that the

volume would need to thermally expand. This means that the laser pulses have to be

so short that the radiated medium does not have the possibility to react mechanically

on the energy of the light [41]. This time shall be called acoustic relaxation time tac[49]:

tp < tac, (3.18)

tac =δ

c, (3.19)

where c is the speed of sound. This confinement guarantees that during the radiation

of light, no pressure equalization of the volume with its surrounding occurs. In general,

the heat conduction is not as fast as the acoustic propagation, so that the fulfillment

of the stress confinement is the superordinate condition [41].

To estimate the maximum time that a laser pulse might have, ttherm and tac are

calculated for the case of water. Its thermal and acoustic characteristics come close

12


to those of biological tissue, therefore serving as a good estimation [49]:

ttherm =1g/cm3 · 4.187J/K · g · (1 · 10−2cm)2

6 · 10−3WK · cm= 7 · 10−2s, (3.20)

tac =1 · 10−2cm

1.5 · 105cm/s= 6.7 · 10−8s. (3.21)

For tp < tac < ttherm the pulse duration needs to be in the range of some 10ns.

3.3.3 The Correlation of Incident Light and Generated

Pressure

Having explained how light propagates in media and the conditions for the generation

of thermoacoustic waves, the focus of the following will be on the correlation of the

incident light and the generated pressure.

When radiating a light absorbing medium and depositing an energy Q in a volume

V , the medium heats up (∆T ). This increase of temperature is directly proportional

to the deposited energy and inversely proportional to the volume, the density ρ of the

medium and the specific heat at constant pressure cp [49]:

∆T =Q

V · cp · ρ. (3.22)

Using the energy density W (~r) for the energy per volume yields

∆T =W (~r)

cp · ρ. (3.23)

In the general case of gases and liquids, the following relation can be given between

increase of temperature and resulting pressure:

p = −1

κ

(∆V

V

)+β

κ∆T, (3.24)

where β is the cubic expansion coefficient of the medium and κ is its compressibility.

As the stress confinement requires that during the deposition and absorption of the

energy the volume needs to stay constant (∆V = 0) at the time zero

p0 =β

κ∆T (3.25)

13


is valid [49]. Substituting Eq. (3.23) into former equation the relation between the

radiated energy density and the generated pressure becomes apparent:

p0(~r) =β

κ

W (~r)

cp · ρ= Γ ·W (~r). (3.26)

Γ is the dimensionless Grueneisen coefficient, which gives the relation of generated

pressure to the incident radiant exposure. The heating of the medium depends on its

absorption characteristics, therefore, this characteristic (Eq. 3.15) must be included

in the correlation of incident light and generated pressure.

W (~r) = µa(~r) ·Ψ(~r) (3.27)

Substituting former equation into Eq. (3.26) yields [40]

p0(~r) = Γ · µa(~r) ·Ψ(~r). (3.28)

In general, the pressure distribution is given by the distribution of the energy den-

sity. In homogeneous and purely absorbing media, the energy density follows the

distribution of the incident radiant exposure [40].

3.3.4 Thermoacoustic Wave Equation and Solution

So far, the photoacoustic pressure distribution at the time zero (Eq. 3.28) that was

caused by instantaneous heating has been derived. p0 is the source for the following

propagation of a pressure wave, that can be described by the inhomogeneous wave

equation [40]:

∇2ψ(~r, t)− 1

c2∂2ψ(~r, t)

∂t2=

β

ρcpS(~r, t), (3.29)

where ψ is the velocity potential and S(~r, t) is the heat source term that describes the

heat that is generated per unit time and per unit volume and has the unit [S(~r, t)] =

W/m3. As the fulfillment of the thermal confinement, which includes instantaneous

heating, can be assumed, S(~r, t) can be written as the product of the energy density

and a temporal Dirac delta function δ(t):

S(~r, t) = W (~r)δ(t), (3.30)

and substituting Eq. (3.27) for the energy density, the heat source term can be written

as

S(~r, t) = µaΨ(~r)δ(t). (3.31)

14


Using former equation, a term for the velocity potential ψ(~r, t) is received, which will

further on serve as the fundamental quantity to derive a solution of the wave equation:

ψ(~r, t) = − t

4πρ

βc2

cp

∫ ∫R=ct

W (~r ′)dΩ, (3.32)

derived from the Green´s function solution of Eq. (3.29). The position vector ~r defines

the point of observation, while ~r ′ defines the point where the source of the pressure

wave is located. When c is the speed of sound in the medium and t is the time of flight

from the pressure source point (~r ′) to the observation point (~r), then R = ct describes

the radius of the sphere around the observation point, over which the integration is

carried out. dΩ is the solid angle element.

The next step in the derivation is to find a correlation between the pressure and the

velocity potential. The pressure p(~r, t) can be derived from the velocity potentialψ

[40]:

p(~r, t) = −ρ∂ψ(~r, t)

∂t. (3.33)

Using Eq. (3.33),(3.32) and (3.26) yields

p(~r, t) =∂

∂t

[t

4π

∫ ∫R=ct

p0(~r′)dΩ

], (3.34)

or

p(~r, t) =βc2

2πcp

∂

∂t

[t

∫ ∫R=ct

W (~r ′)dΩ

]. (3.35)

These equations allow the calculation of the pressure distribution, depending on

the initial energy distribution. The integral can be calculated analytically for geo-

metrically simple sources. Otherwise numerical integrations need to be carried out

[41]. If the laser pulse duration is finite, a convolution of the pressure signal with the

temporal pulse profile is necessary. If the stress confinement is fulfilled (in the range

of 10ns, see Chapter 3.3.2), the pressure signal only suffers negligible changes due to

the laser pulse duration.

15


3.4 Propagation of Acoustic Waves

Henceforth, effects that influence the propagation of acoustic waves, whose generation

was described in the previous section will be considered. Such effects are sound reflex-

ion, refraction, absorption, dispersion, diffraction and in the case of finite amplitudes,

nonlinear acoustic effects.

3.4.1 Reflexion and Refraction

The speed of sound c is dependent on the compressibility κ and the density ρ of the

medium [53]:

c =1√κρ. (3.36)

In analogy to the propagation of light, refraction and reflexion of acoustic waves at

the boundary of two media with the speeds c1 and c2 can be described with

θi = θr, (3.37)

sin θisin θt

=c1c2, (3.38)

where θi is the angle of incidence, θr the angle of reflexion and θt the angle of the

transmitted, refracted acoustic wave.

The intensity Ir of the reflected wave depends on the impedances Z1 and Z2 of the

two media. For the case of normal incidence the intensity is [53]:

IrIi

=

(Z2 − Z1

Z2 + Z1

)2

, (3.39)

where the impedance is given by Z = ρc.

3.4.2 Sound Absorption and Dispersion

The absorption of sound in liquids is determined by the viscosity σ and the thermal

conductivity k. The absorption coefficient is [47] given by

α =8πν2

3c3ρ

[σ +

3

4

(cpcV− 1

)k

cp

], (3.40)

where ν is the frequency, and cp and cV are the specific heats at constant pressure

and at constant volume, respectively. For most liquids, the second term in the square

16


brackets is negligible. The ν2 dependence of the absorption that causes a waveform

distortion is important for all kinds of liquids. An acoustic pulse broadens while

propagating through media as its higher frequency components experience a higher

absorption [47]. In the case of ultrasonic waves, the frequency is in the range of

20kHz to 1GHz and the distances are in the range of several cm. This distortion of

the acoustic waveform can be neglected.

Furthermore, the waveform can be influenced by dispersion when the speed of sound

in a medium is dependent on the frequency of the wave. Sigrist comments that for

ultrasound frequencies the dispersion is negligible. Additionally, d’Arigio points out

that for H2O no dispersion is detectable down to minus 20C [47].

3.4.3 Diffraction of Acoustic Waves

During propagation through media, diffraction distorts the geometrical and temporal

wave profile of an initially plane acoustic wave. Such a plane acoustic wave can be

obtained by radiating a medium of one-dimensional or layered structure with a laser

beam, whose radius is much larger than the optical propagation depth of the medium.

Then, the initial distribution of the energy density exclusively depends of the distance

z of the surface. Integration of Eq. (3.34) yield the solution of a plane wave [41]:

p(z, t) =Γ

2[W (z − ct) +W (z + ct)] . (3.41)

The first term in the square brackets describes a wave in positive z-direction, whereas

the second term describes the wave propagating in negative z-direction. The formula

is only true for acoustically matching materials at the boundary at z = 0, which

guaranties a reflexion free transition.

In the context of diffraction, the wavelength of the acoustic wave λac is the crucial

parameter. It is necessary to distinguish two cases [47]:

• When the penetration depth δ = 1µa

of the laser beam into the liquid is shorter

than the distance z = ctp, the acoustic wavelength is given by λac = 2ctp, where

tp is the laser pulse duration.

• When the penetration depth is longer than z = ctp, the acoustic wavelength is

given by λac = 2µa.

17


Figure 3.4: a) Near field b) Far field [41]

Diffraction limits the generation of plane thermoelastic waves, as it occurs at the

border of the source volume, where the pressure was induced, and respectively at the

border of the laser beam. In z-direction, the distribution of the energy density (W ) is

given by the Lambert Beer´s law. In r-direction, the energy density is nearly constant

and a high gradient at the borders is the source for diffraction. Consequently, the

initially plane wave becomes spherical. In the case of a constant laser intensity across

the beam diameter, the influence of diffraction can be described by the diffraction

parameter [41, 47]

D =

∣∣∣∣zλaca2

∣∣∣∣ , (3.42)

where λac is the acoustic wavelength, z is the distance between sensor and source

and a is the radius of the laser beam. For D < 1 the measurement happens in the

near field, for D > 1 in the far field [41]. In the case of homogeneous absorbers, the

acoustic wavelength is λac = 2/µa, where µa is the absorption coefficient [41].

The boundary between near and far field is located at the propagation distance [40]

zf =D2

4λac. (3.43)

This equation is only valid for acoustic wave lengths that are much smaller than the

diameter of the source.

Fig. 3.4.a shows that if the detector is close to the source, the sphere of integra-

tion with the radius R = ct (see Eq. (3.35)) will reach the depth borders of the

18


source, which are given by the acoustic wave length, but will not reach the lateral

borders. Therefore, the detector measures a planar thermoelastic wave, as no in-

formation originating of the boundaries is received. The detected pressure signal is

directly proportional to the absorbed energy.

Fig. 3.4.b shows the case of a far field measurement. The part of the sphere that

intersects the source is nearly a plane, so that the detector measures the temporal

derivation of the plane wave signal. Therefore, the direct proportionality of pressure

signal and energy distribution is not valid anymore.

Using the near field measurement, a good representation of the depth distribution of

the absorbed energy can be achieved, whereas far field measurements can be utilized

to obtain defined borders of structures with different absorbing characteristics [41].

3.4.4 Nonlinear Acoustic Effects

The nonlinearity parameter B/A, which was introduced by Beyer, gives information

about the nonlinearity of a liquid. Sigrist [47] presents a novel method to determine

B/A. Whereas in previous measurements, one single acoustic pulse was recorded at

several distances of the source, he analyzed numerous pulses of different amplitudes

at the same distance. Therefore, as diffraction effects are dependent on the propa-

gation distance, he could avoid a simultaneous detection of both effects. He could

observe that the wavefronts steepen due to nonlinear effects. This steepening can be

interpreted as an increase of the propagation speed [47]:

c = c0 +p

ρ0c0+B/A · p2ρ0c0

. (3.44)

The first term describes the initial speed of sound for small amplitudes, the second

one the particle velocity and the third term the influence on the speed due to nonlinear

effects. Henceforth, the steepness of the wavefront rises with the pressure, the Beyer

parameter and the distance z.

19


20

4 Piezoelectricity and Piezoelectric

Sensors for TACT

The focus of this chapter lies in the piezoelectric effect. After a general overview,

theoretical descriptions and calculations of special cases of the effect will be presented.

Finally, the attention will be given to the construction and features of the piezoelectric

line sensor that is used in the here presented experiments.

4.1 Principles of Piezoelectricity

The piezoelectric effect describes the interplay of mechanical pressure and electrical

voltage in crystals. The word piezo derives from the Greek word piezein, which means

to press. This effect is based on the phenomenon that a directed deformation of certain

materials causes electric charges on the surface of the material, which is called direct

piezoelectric effect. Then, the barycenter of charge is displaced, and, in consequence,

microscopical dipoles emerge within the unit cell. The summation of these dipoles

over all unit cells of the crystal leads to a macroscopically measurable voltage [1]. In

1880, Jacques and Pierre Curie discovered that in tourmaline crystals, the applied

pressure and the resulting voltage were directly proportional.

In contrast, certain crystals are deformed by a voltage that is impressed on them

(inverse piezoelectric effect). In physics, the piezoelectric effect is at the intersection

of electrostatics and mechanics [9].

Fig. 4.1 shows the most famous piezoelectric crystal, Quartz (SiO2). Every Si-atom

is situated in the center of a tetrahedron of oxygen atoms. The Si-atoms have four

positive elementary charges. The oxygen atoms have two negative charges. Therefore,

the quartz crystal is neutral in total [1].

21

4 Piezoelectricity and Piezoelectric Sensors for TACT

Figure 4.1: a) Quartz crystal [15]. b) Deformation and movement of charges at a

quartz crystal [37].

Having already distinguished between direct and inverse piezoelectric effect, another

differentiation is made concerning the direction in which the force, and the electric field

act. It is called longitudinal piezoelectric effect, if the pressure acts parallel to a polar

axis of the crystal. In contrast, the transversal piezoelectric effect (Fig. 4.1) occurs

when the force acts parallel to a neutral axis. If the force acts in direction of the optical

axis, no piezoelectric effect is measurable [15]. Similarly, the same principles apply to

the inverse piezoelectric effect, which is also classified as longitudinal or transversal,

depending on the direction of the electromagnetic field. Two more characteristics of

the piezoelectric effect shall be mentioned at this point:

• Inverse and transversal piezoelectric effect always occur together. When a crys-

tal is mechanically deformed transversally, an electric field is generated, which,

because of the inverse effect, causes a secondary deformation of the crystal,

which acts against the principal force. This secondary effect is negligible in the

most cases.

• The signs of the piezoelectric effect change when the causation changes its sign.

If e.g. pressure changes to tension, the polarity of the charges change.

The piezoelectric effect can only appear in non-conductive materials. In crystals, a

lack of center of symmetry is the criterion for piezoelectricity [14]. If the crystal

has several polar axes, it is piezoelectric, whereas if it has one single polar axis, the

material is pyroelectric, which means that it can polarize itself spontaneously. By

22

4.1 Principles of Piezoelectricity

changing the temperature of the material, this effect can be enhanced and the surface

charges can be detected [30].

It is common to mathematically describe the piezoelectric effect by the following

coupled equations [14]:

Di = dij · Tj + εTj

ij · Ei and (4.1)

Sj = dij · Ei + sEiij · Tj, (4.2)

where Di is the dielectric displacement, Tj is the mechanical stress, Ei is the electrical

field strength, Sj is the strain, εTj

ij is the permittivity at constant or zero mechanical

stress and sEiij is the elasticity modulus at constant or zero electrical field strength.

The most important material parameter for the piezoelectric effect is the piezoelectric

constant dij that describes the correlation between the electric field strength and the

strain of the material [14]. The index i corresponds to the direction in which the

electric field acts, whereas the indexj gives information about the direction of the

mechanical force [8].

Direct Piezoelectric Effect

Focusing again on Eq. (4.2)and (4.1), the first formula describes the direct piezoelec-

tric effect, where the first term of the formula describes the primary effect, i.e. that

the acting pressure or the mechanical stress causes a dielectric displacement. The

generated electric field E3 again causes a stress on the material that is orientated

in opposite direction to the initial pressure/stress (inverse piezoelectric effect). This

secondary effect is negligible compared to the primary effect. Depending on whether

the effect is lateral or transversal, either d31 or d33 is the constant of main interest.

Inverse Piezoelectric Effect

For the inverse transversal piezoelectric effect, the coupled equations (Eq. (4.2))

reduce to the form

S1 = sE311 T1 + d31E3, (4.3)

where the mechanical force and the electric field strength are normal to each other.

The following formula is used to describe the longitudinal case, where mechanical

23


force and electric field strength act in parallel directions [12]:

S3 = sE333 T3 + d33E3. (4.4)

4.2 The Piezoelectric Line Sensor

At the beginning of this section, the use of PVDF films for sensors and the character-

istics of the used PVDF film will be treated. Then, the construction of the sensor that

was used in the experiments will be illustrated. At the end of this section, attention

will be given to details of the sensor and the calculation of its specifications.

4.2.1 Piezoelectric PVDF Films

Polyvinylidene fluoride (PVDF) films are commonly used as transducers. The field of

applications is wide: infrared sensors, stress gauges, vibration detectors, etc. PVDF

was first created in 1969 . The polymer PVDF has to be prepared to obtain piezo-

electric properties. The film is heated, stretched, and, at the same time, polarized

in an electrical field. The dipoles align with the electrical field. Then, the PVDF

film is cooled down below the Curie-Temperature (80C). At this temperature, the

film stays electrically polarized. If, in the polarization process, the PVDF film is

stretched only in one defined direction under the influence of the electrical field, the

piezoelectric coefficient is higher in this direction. These films are called uniaxial.

Biaxial films have been stretched with the same force in two directions at the same

time. In general, the piezoelectric properties of PVDF films weaken over time due to

aging processes [38].

The thickness of PVDF films is between 6µm and 1mm. The surface coating of

aluminum has a thickness of between 150Å [27] and 500Å [34]. The coating is needed

to contact the piezoelectric material and to pick off the charges. The utilized PVDF

films are polarized in z-direction. Table 4.1 shows important characteristics of the

used PVDF film.

The piezoelectric specifications are affected by temperature influences. After 100

days at room temperature, a depolarization takes place and d33 suffers changes up

to 5%. The same 5% distortion is noticeable after only one day at 60C. Moreover,

24


thickness of the film dfilm: 25µm [48]

piezoelectric constant d33

for electric fields and mechanical

strain in direction of d: 16pC/N at room temperature [48]

piezoelectric constant d31 = d32

for mechanical strain normal to d: 8pC/N at room temperature [48]

relative dielectric coefficient εr: 11 at 1000Hz [48]

speed of sound c: 2000m/s [27]

density ρ: 1800kg/m3 [27]

elasticity modulus s: 2000MPa [48]

Table 4.1: Important Specifications of PVDF Films.

PVDF is not only piezoelectric, but also pyroelectric. For this reason, it is recom-

mended to take care during measurements that no laser light is radiated directly on

the PVDF surface, since electrostatic induction charges caused by thermal differences

would also show a signal [27].

In the following, some of the advantageous characteristics of PVDF films that make

this medium so suitable for the use as an ultrasound detector will be discussed:

Mechanical Capacitance

PVDF films are very flexible and robust. In lateral direction, these films do not

disrupt under pressures until 180MPa. This value is similar to the capacitance of

bones and hair. The elasticity modulus (see Table 4.1) is ten times higher than of any

biological tissue. This characteristic is important, as laser induced pressure waves can

reach high amplitudes. The mechanical capacitance of PVDF films is sufficiently high

to use PVDF films as pressure sensors for measurements on biological tissues [34].

Acoustic Impedance

Comparing PVDF with other piezoelectric materials, the acoustic impedance is low.

The film used for this work has an impedance of

ZPV DF = c · ρ = 3.6 · 106kg/m2s, (4.5)

25


Figure 4.2: Propagation of acoustic waves through the sensor layers [26].

which is the same order of magnitude as the impedance of water (ZH2O = 1.48 ·106kg/m2s) and biological soft tissue (Ztissue = 1.3 to 1.6 · 106kg/m2s). Due to this

similarity, the acoustic matching conditions that guarantee that a sufficient part of

the pressure amplitude can be transmitted into in the film are provided [34]. If the

the acoustic impedances were of a different order of magnitude, a significant part of

the signal would be reflected at the surface of the sensor and would be lost for the

measurement. In these experiments, the sensor has direct contact to water. The

reflectivity R for the acoustic wave between water and the piezoelectric film is given

by

R =ZPV DF − ZH2O

ZPV DF + ZH2O

=3.6 · 106kg/m2s− 1.48 · 106kg/m2s

3.6 · 106kg/m2s + 1.48 · 106kg/m2s= 0.417. (4.6)

The transmissivity between water and the PVDF film is

T =2 · ZPV DF

ZPV DF + ZH2O

=2 · 3.6 · 106kg/m2s

3.6 · 106kg/m2s + 1.48 · 106kg/m2s= 1.42. (4.7)

Furthermore, it is necessary to consider the transition of the acoustic wave (wave

length λac) from the PVDF film (thickness d = 25µm) to the material that lies behind

the PVDF film in the sensor (Z3). Fig. 4.2 shows the transition of the wave, arriving

at the sensor with an incident angle ϕi. For the case λac < d, the sensor layer is

acoustically transparent. Hereby, the pressure amplitudes before and after the film

are the same. The pressure measured inside the PVDF film is dependent on the

26


characteristics of the bordering media [26]:

pPV DFpH2O

=p3

pH2O

=2Z ′3

Z ′H2O+ Z ′3

, (4.8)

Z ′i =Zi

cosϕi. (4.9)

This leads to the conclusion that, if the bordering materials have the same acous-

tic impedance, the pressure measured with the PVDF film (pPV DF ) is the same as

the incident, initial pressure. Moreover, it is independent of the incident angle [26].

For this reason, Plexiglas (Polymethylmethacrylat, PMMA), which has an acoustic

impedance of Z3 ≈ 3.2 · 106kg/m2s (value from [18]), was used as the third medium.

4.2.2 The Construction of the Sensor

Preparation of the PVDF Film

After planning the sensor, the first practical step in the construction is the preparation

of the PVDF film. The required geometric form (a rectangle of 4cm × 7mm) of the

film is cut out of the A4-sheet with a sharp razor blade (Fig. 4.3.b). It is essential to

take care that during the cutting of the film the Al-coatings do not come into contact

with each other. Before going on to further steps, it is advantageous to check the film

with a multimeter.

Then, a mask out of adhesive tape is prepared. For this purpose, a rectangle is

drawn onto the tape, which is then applied to a metal bar, where it then is cut with

a razor blade. Thereupon, the mask is removed from the metal bar and fixed on the

film (Fig. 4.3.c), and the two pieces together are placed onto a piece of paper. Now,

one drop of FeCl3 is put on the small rectangle that is to be etched, and the liquid

is evenly distributed using a cotton swab. After several seconds, the FeCl3 is washed

off the PVDF film with distilled water. Finally, the mask is removed from the film

carefully (Fig. 4.3.d).

Realizing the Line

The active surface of the PVDF film is the part of the film where both sides of the film

are in contact to a conducting material. In the case presented here, a line geometry

27


Figure 4.3: Steps in the construction of the sensor.

Figure 4.4: Real picture of the piezoelectric line sensor.

28


of the sensor is to be obtained. One possibility for realizing a thin line would have

been to remove all of the Aluminum-coating except for the sensor´s contact line. This

could have been achieved either by etching or by ablating with laser pulses. The

disadvantage of these methods is that especially for thin lines under ≈ 300µm width

the electrical contact is easily disrupted.

The chosen method is to first remove the Aluminum on one side of the PVDF

film, as described in Chapter 4.2.2, and then use the quoin of a thin Aluminum

film (200µm) as the electrode. The Aluminum film is pressed between two blocks of

Plexiglas. The surface of the whole block is polished to achieve an even surface (Fig.

4.3.e). Now, the rectangular strip of the piezoelectric material can be glued onto the

Al-line (Fig. 4.3.f). For gluing, a two-component adhesive is used. Is is important

to apply a very thin coating of adhesive and to evenly press the PVDF film onto

the Plexiglas. Moreover, wrinkles of the film should be avoided, and a continuous

end-to-end contact with the electrode is to be obtained. The depth (z-direction) of

the Plexiglas block is chosen to be at least in the range of severalcm. Hereby, pressure

waves that are reflected at the back end of the block would arrive late enough to be

distinguishable from real signals. A detailed explanation of the reasons for the sizes

of certain components of the sensor will be given in Chapter 5.

Achieving Waterproofness

Since in the experiment, the sensor is situated in a water tank, it is necessary to

guide the electric conductors through a waterproof metallic cage which also provides

shielding against electrical noise. One conduction is connected with the Al-film inside

the cage, the second conduction is the cage itself, to which the Al-coated upper side

of the PVDF film is connected. The whole block of Plexiglas, Al-film and PVDF film

is pressed into a cage and sealed with silicone. A tube connected to the cage-box

allows the sensor to be fixated for the experimental set-up and connects the sensor

with a coaxial cable to the amplifier and to the oscilloscope. The cage is equipped

with additional possibilities to screw on further kinds of tubes, so that the sensor is

applicable in various experimental set-ups. Fig. 4.4 shows the constructed sensor.

29


4.2.3 Electric Characteristics of the Sensor and Sensitivity

In this section, the focus of attention will be set on the electric characteristics of the

signal generation, dependent on the features of the used sensor. The aim is to be

able to calculate back from the obtained voltage signal to the original pressure wave

amplitude that arrived at the sensor. By following the pressure wave through the

sensor, the important components that influence the signal can be determined.

Focusing again on Fig. 4.3.a, it is obvious that the PVDF film acts as a plane-

parallel capacitor. Its capacitance is given by [34]

Cfilm = ε0εr ·Afilmdfilm

, (4.10)

where ε0 is the permittivity of free space, εr is the relative dielectric coefficient, Afilmis the active area of the PVDF film (the line), and d the thickness of the dielectric, in

this case PVDF. The capacitance of the sensor is:

Cfilm = 8.854187817 · 10−12F/m · 11 · 5.6 · 10−6m2

25 · 10−6m= 21.82pF. (4.11)

The relation between the detected pressure and the received voltage is linear if

• during the influence of the pressure, no external electric field acts on the piezo-

electric material, e.g. in case of a short-circuit.

• the pressure transient arrives normal to the film, so that only the d33 compo-

nents, those in direction of the thickness of the film (z-direction), have to be

considered [34].

Then, Eq. (4.1) for the general case of piezoelectricity can be reduced to the case of

the direct piezoelectric effect

Di = dij · Tj + εTj

ij · Ei, (4.12)

where the second term describes the secondary inverse piezoelectric effect which can

be neglected as it is insignificant compared to the primary effect. For this reason,

εTiij ·Ei ≈ 0. The mechanical stress Tj has opposite sign to pressure and has the same

unit ([Tj] = [p] = N/m2). Assuming that the pressure transient arrives normal to the

film, the dielectric displacement induced in the piezoelectric film can be calculated as:

D3(z, t) = d33 · p(z, t), (4.13)

30


where d33 is the piezoelectric constant´, the index 3 indicates z-direction and p(z, t)

is the pressure that acts normal to the surface of the active sensor area. Higher

precision of the calculation could be achieved by including the d31 and d32 directions.

They are important for pressure transients that do not arrive normal to the surface

of the sensor. One more interesting detail shall be mentioned: For piezoelectric films,

only these three piezoelectric constants are of importance, since the electrodes are

fixed in the 1 − 2 area (the aluminum coating). Therefore, the charges are always

taken in the 3- direction.

For a capacitor, the relation of dielectric displacement and charge is D(z, t) =

Q(z, t)/A. This yields

D3(z, t) =Q(z, t)

A= d33 · p(z, t) (4.14)

and consequently

Q(z, t) = d33 · A · p(z, t). (4.15)

The surface charge Q(t) is given by a spacial averaging of the pressure inside the

film multiplied with the active area of the sensor [34]:

Q(t) = d33 · Apressure ·1

dfilm·∫ dfilm

0

p(z, t)dz = d33 · Apressure · p(t). (4.16)

Depending on the geometry of the sensor, the active area, Apressure, can have different

interpretations. If the size of the active area of the sensor is larger than the lateral

size of the pressure wave, Apressure is the active area of the pressure wave, otherwise it

is the active area of the PVDF film. The size of the pressure wave in the near field of

the sensor is given by the size of the acoustic source [8]. In the case of the sensitivity

measurement (Chapter 6) it is ≈ 4 · 10−8m2, as the line is only 200µm thick.

As the film thickness has a finite value, the pressure wave needs a finite time to

cross the film. In this case, for d = 25µm, the transit time is

d

c=

25 · 10−6m

2000m/s= 12.5ns. (4.17)

In the preceding equation, the spacial averaging of the pressure also means that pres-

sure variations that are shorter than this transit time are averaged [8].

The surface charges are not measurable, but the voltage is. Substituting the relation

C = Q/U in Eq. (4.16) yields

U(t) =1

Ctot· d33 · Apressure · p(t), (4.18)

31


where Ctot is the total capacitance, which includes the input capacitance of the oscil-

loscope, the capacitance of the cable and the capacitance of the sensor [8]:

Ctot = Cosc + Ccab + Cfilm. (4.19)

The capacitance Ccab of a coaxial cable is dependent on its length. Typical values

are 100pF/m. Using an active probe (i.e. impedance converter), which is directly

connected to the sensor, the high capacitance of the coaxial cable can be avoided.

Furthermore, then, the capacitance of the active probe (CSHA = 3.5pF) is relevant,

and not the capacitance of the oscilloscope. The total capacitance is

Ctot = CSHA + Cfilm = 25.32pF. (4.20)

The sensitivity S of the PVDF film is a term that describes the relation between the

measured voltage and the amplitude and frequency of the incoming pressure wave. If

this relation is independent of the frequency and linearly dependent on the amplitude,

the term S is given by a constant factor. This is true for PVDF films, if they are

used to detect pressure amplitudes that are in the range of bar, which is the case for

pressure waves that are generated by thermoelastic effects in biological tissue [34].

Then, the sensitivity is given by [34, 47]:

S :=dU

dp=

U

p(t)=d33 · Apressure

Ctot. (4.21)

Substituting the values for the experimental set-up of the sensitivity measurements

(Chapter 6) yields

S ≈ 16pC/N · 4 · 10−8m2

25.32pF≈ 2.528mV/bar. (4.22)

This is only an approximation, as the measurement was not made in the near field

of the sensor, where Apressure could have been determined exactly. In this relation,

the transit of the pressure wave from water to the PVDF film is not yet considered.

The transmissivity in Chapter 4.2.1 was calculated as: T = 1.42. The sensitivity S

increases with this factor to: S = 3.589mV/bar

This theoretical sensitivity is only reachable if the electric shielding of the whole

system is optimal, and if ground loops are avoided [34]. In Chapter 6 the sensitivity

will be determined experimentally.

32

5 Integrating Line Sensors and

Image Reconstruction

To understand the chosen line geometry of the here presented sensor, the reasons for

the size of the active PVDF line and the consequences for the measurement and for

the reconstruction of the original absorption distribution, the attention will be given

to the consequences of near and far field measurements for detectors in general and

for the case of integrating large plane and line sensors. Finally, the reconstruction

algorithm that is adapted to the line symmetry and that is used to obtain images

from the measured pressure signals will be treated qualitatively.

5.1 Point Detector vs. Large Plane/Line Detectors

Image reconstruction requires solving the inverse problem that is reconstructing the

original energy density distribution from the detected acoustic signals. The recon-

struction method depends on the mode of operation of the sensor. The development

of new detector shapes and novel reconstruction algorithms are two strongly associated

fields of investigation.

Generally speaking, regarding two measurement cases, two types of detectors can

be distinguished. On the one hand, an object is situated in the far field of the

detector. In this case, the size of the detector should be much smaller than the object,

which ensures a high spatial resolution. More precisely, for all acoustic wavelengths

generated in the object the far field conditions must hold. Ideally, the detector, and

for piezoelectric sensors the active area of the PVDF film, is a point. Fig. 5.1.a shows

a point detector and the object that is to be imaged. A successful reconstruction

algorithm for this case is the Time Domain Back Projection [42]. The point detector

33

5 Integrating Line Sensors and Image Reconstruction

Figure 5.1: a) Point detector b) Large plane detector [3].

measures the pressure signal for a given time, which represents the integral of the

energy density distribution. This integral is carried out over a sphere with the radius

R = ct, where c is the speed of sound and t is the time of flight (see Eq. 3.35). t = 0

is the point in time when the laser pulse irradiates the object. The detector receives

a signal that is the approximate projection over this sphere [5].

Even when using exact frequency domain reconstruction algorithms, the finite de-

tector size is a general limitation of the spacial resolution. In a tomography set-up

where the detector rotates around the object the resolution for points of the object

that are further away from the rotation axis, thus closer to the sensor, is worse than

for points close to the rotation axis [4]. Moreover, the electrical signal is weak, so that

the signal to noise ratio can be problematic [3].

On the other hand, large area detectors can be used to guarantee that the object

is in the near field of the detector, where the size of the detector must be larger than

the object. Fig. 5.1.b shows a large planar detector. The horizontal lines symbolize

parallel planes to the detector that have a distance of z = ct from the detector. The

generated signal of such detectors are an integral of the pressure distribution over

these planes. The received signal S(t) contains the information of all sources that are

at the distance z = ct from the detector, and it is proportional to the average pressure

p(z) [3]:

S(t) ∝ p(z), (5.1)

34

5.2 Image Reconstruction for Line Sensors

Figure 5.2: Condition for the size of a sensor for near field measurements.

where p(z) =

∫p(~x, t)dxdy, and z = ct. (5.2)

Therefore, S(t) is correlated to the exact projection of the absorbed energy density

along the plane at the distance z. By rotating the detector around the object, a set of

signals is received that allows the implementation of the inverse Radon transformation,

which is a well known reconstruction algorithm, originally used in X-ray computer

tomography. For line detectors, however, the relation of the received signal with

the Radon transform is more complex [3]. Incidentally, the mathematical basis of

the Radon transformation was defined by the Austrian Johann Radon in 1917 and

revolutionized the X-ray tomography when sufficient computing power was reached

in the sixties [2].

While the resolution of measurements with point detectors is limited by the fi-

nite detector size, the spatial resolution of large plane detectors only depends on the

bandwidth.


In Chapter 3.4.3, the border between near and far field was defined, using the diffrac-

tion parameter

D =

∣∣∣∣λacza2

∣∣∣∣ , (5.3)

where z is the distance between the source and the detector and a is the radius of

the source volume, for the case of a point geometry of the detector. For extended

detectors, this formula is still true for point sources, where a is the length of the

sensor.

35


Figure 5.3: Integrating line sensor. Definition of axes and integration over a cylinder

with the radius R = ct [3].

Line sensors are a combination of point sensors and large planar sensors, since the

length of the line has large dimensions, as those of plane detectors, but the width has

small dimensions, as those of point detectors. So the object is in the near field of the

detector concerning the direction of the y- direction, but in the far field, concerning the

x-direction. Ideally, the line should be of infinite length. Since this is not possible,

the sensor must fulfill the conditions that are shown in Fig. 5.2, which allow the

determination of the required line length of the sensor and the distance of the object

to the sensor.

If the signal that propagates normal to the sensor arrives prior to the earliest arrival

time of the wave at the edge of the sensor (g > ct), the first one is detected as if the

sensor had infinite size. A small negative peak appears that is caused by the end of

the sensor. If the length of the line is long enough (in this case 2.8cm), the peak does

not interfere with the pressure signal.

For explaining the reconstruction, a definition of the coordinate axes is necessary,

shown in Fig. 5.3. The x-axis describes the vertical direction, in which either the

sensor or the phantom moves. Due to this motion, the line sensor emulates an array

of parallel line sensors. The y-axis lies in direction of the active line of the sensor, over

which the incoming signal is integrated. The z-axis is in direction of the incoming

pressure wave. Signals are acquired by moving the phantom in x-direction and then

changing the angle by a certain angle step width. These steps are repeated, until the

phantom has rotated a full 360. These motions are required, for obtaining sufficient

information to image a three-dimensional object [4].

36


Figure 5.4: Schematic illustration of the image reconstruction algorithm.

Fig. 5.3 shows that, using a line detector, the pressure signal p(~x) is integrated along

a line y. The received signal S(t) is proportional to the average pressure p(x, z, t) [3]:

S(t) ∝ p(x, z, t), (5.4)

where p(x, z, t) =

∫p(~x, t)dy, (5.5)

Since no source exists along the line y, it is permitted to apply Green’s formula:

∫ ∞−∞

∆yp(~x, t)dy = 0. (5.6)

This yields for the two dimensional wave equation [4]:(∂2

∂t2− c2∆y,z

)p(x, z, t) = 0, (5.7)

solved by using

p(x, z, t = 0) =

∫p0(x, y, z)dy and

∂p

∂t= 0. (5.8)

In the experiment, a pressure signal (pz=0(x, θ, t)) is received that is a function of x,

θ and the time t. For the image, the original pressure distribution at the time t = 0,

the point in time of the generation of the pressure wave, is required (pt=0(x, y, z)). A

general overview over the steps in reconstruction is shown in Fig. 5.4. The first step

(Fig. 5.4.a) is a frequency domain reconstruction algorithm, which was first presented

by Koestli and Beard [28, 31] and by Xu, Feng and Wang [54]. The Fourier transform

of the measured signal is calculated by [4]

Aθ(kx, ω) : =

∫ ∞0

∫ ∞−∞

pθ(x, 0, t)e−ikxx cos(ωt)dxdt, (5.9)

37


which correlates in the spatial frequency domain to

Pθ(kx, kz) =2c2kzω

Aθ(kx, ω), (5.10)

kz =

√(ω

c)2 − kx, (5.11)

where ~k is the wave vector, given by the dispersion relation ω = c ·∣∣∣~k∣∣∣. Then, for

each angle θ, the initial pressure distribution at t = 0 can be reconstructed using the

inverse Fourier transformation (IFFT):

pθ(x, z, 0) =1

4π2

∫ ∫Pθ(kx, kz)e

i(kxx+kzz)dkxdkz, (5.12)

which corresponds to the projection of the absorbed energy on the y-axis.

The second step (Fig. 5.4.b) in the reconstruction is the inverse Radon transforma-

tion (see [36, 2]), which is carried out for every x-plane, so that the three dimensional

initial pressure distribution p0(x, y, z) is finally received.

38

6 Experiments to Characterize the

Sensor

This chapter will treat experiments that were made to test and to characterize the

constructed line sensor. The first experiment, using a point source as object, serves to

show geometric characteristics of the sensor, i.e. how it behaves in parallel and normal

direction to the piezoelectric line. Then, the sensitivity of the sensor (Eq. 4.21) will be

determined experimentally, by measuring an object of a well known optical absorption

coefficient.

6.1 Testing the Sensor with a Point Source

6.1.1 Experimental Set-up and Procedure

Fig. 6.1 shows the experimental set-up schematically. The sensor and the point

source are positioned in a water tank. The experiment is undertaken in a water tank

because it is necessary to acoustically match the system to the object. Similarly,

in the tomographic experiments (Chapters 7 and 8) the water tank is used for the

same reason. Since in this case, ideally, no reflexions occur, this guaranties that the

major part of the pressure amplitude leaving the object also reaches the sensor. Both

biological tissue and testing phantoms have an acoustic impedance close to water, so

it shall be the embedding medium. Furthermore, the attenuation of ultrasonic waves

in water is low, so that this effect can be neglected, at least in this work.

The point source is realized by a glass fiber, whose end was dipped into black color.

The diameter of the point source is 137µm. The fiber is fixed on a plastic cylinder

that is connected to a stepper motor. Therefore, the point source can be moved

continuously in vertical direction. Also, the two glass fibers (diameter 600µm) that

39

6 Experiments to Characterize the Sensor

Figure 6.1: Point source: Experimental set-up.

guide the laser pulses, are fixed to the same mount as the point source, so that they

move exactly together with the point source. This is necessary because the source

must be illuminated evenly and constantly during the whole measurement.

Both ends of the illuminating glass fibers and the point source have to be positioned

exactly on a line. The alignment is quite difficult, as the diameters of all components

are only in the range of a couple of hundred µm. In the first step of the alignment,

the point source is illuminated only by laser pulses from one side. A signal is sought

by positioning the laser fiber. Then, the other glass fiber is activated. Again, a signal

is sought. The resulting signal of illumination with both laser fibers should reach the

double amplitude compared to single fiber illumination.

The definition of the coordinate axes is as described in Fig. 5.3. In start position,

the point source is located 7mm below the line of the sensor in x-direction and at a

distance of 5mm of the sensor in z-direction. Then, while being illuminated by 280

laser pulses, the point source is moved with constant speed 14mm in x- direction by

a stepper motor that moves 50µm between two laser shots. The signals are stored on

a digital oscilloscope. Another two sets of signals are measured, while lowering the

source back to the starting position and then raising it 14mm up again. Then, the

complete procedure is repeated for an initial z-distance of 10mm and 15mm.

40


Figure 6.2: Single pressure signal.

A quality Q-switched Nd:YAG laser is used to generate the laser pulses. This is a

solid-state laser, where neodymium-doped yttrium aluminum garnet is the crystal used

as the lasing medium [11]. This laser emits radiation in the infrared range (wavelength

= 1064nm). The frequency-tripled output (355nm wavelength) is used to pump an

Optical Parametric Oscillator (OPO), which generates continuously tunable radiation

from 420 to 2500nm wavelength. A wavelength of 500nm was used for the experiment.

The pulse width of our system is tp = 8ns and a pulse repetition rate is 10Hz. The

energy of the laser pulses in this experiment are ≈ 2mJ.

6.1.2 Received Signals and Discussion

Fig. 6.2 shows one single pressure signal received while moving the object 1.4cm in

x-direction. The sensor-source distance is the product of measured time of flight and

speed of sound (c = 1485m/s). The signal shows typical characteristics for a 2D wave

form from a points source detected with a line sensor [7]. Noise and electrical reflexions

and noise disturb the signal. A discussion and a comparison of signals received with

the constructed sensor with signals received from a simulating program is given in

Section 6.2.2.

41


Figure 6.3: Raw data at a distance of 5mm.

Figure 6.4: Raw data at a distance of 15mm.

42


Figures 6.3 and 6.4 show the raw data at two different distances. The pressure

amplitudes are given by the colors. The color bar shows the corresponding mV value

to the different colors. For higher initial z-distances, the hyperbolic arc is broader.

This is a purely geometric effect, and shows that the proportion of x to z becomes

smaller.

After reconstruction of the signals by a two dimensional Fourier Reconstruction

Algorithm [28], Figures 6.5 and 6.6 are received. These figures demonstrate that the

original point broadens the further away the object is from the sensor. To be precise,

the resulting image is not exactly circular. The reason for this behavior is that the

object is not a real point, but a cylinder, which is illuminated from the side, and not at

the circular base area. Comparing the received images at distances of 5mm and 15mm,

it is obvious that the ellipse gets smaller in z-direction but broader in x-direction.

This occurs because the sensor-source distance is enlarged but the scan length in x-

direction is kept constant, so that the aperture becomes smaller. The light lip-shaped

line around the imaged point source is a result of the reconstruction algorithm. To

obtain a good image of an object, for line sensors, it is required to measure at small

sensor-source distances and to increase the scan length in x-direction. Ideally, the

sensor line should be of infinite length, experimentally the maximum length that is

possible in the set-up should be chosen. Furthermore, scanning also along a second

line in z-direction would minimize the broadening of the point and the non-clear

boarders of an object in that direction.

6.1.3 Testing the Line

For this experiment, the same set-up was used as described in Chapter 6.1.1, but the

object was moved in y-direction at a sensor-source distance of 5mm, i.e. parallel to

the sensor line. Since the sensor has the same sensitivity along the whole line, the

amplitude of the pressure signal does not change. In the experiment, a difference in

the time of flight of 0.4µs was detectable, which is such a small value that it rather

arises from a not-exact parallelism of the assembling than from imperfections of the

sensor.

43


Figure 6.5: Fourier reconstructed image at 5mm.

Figure 6.6: Fourier reconstructed image at 15mm.

44

6.2 Experimental Determination of the Sensitivity

Figure 6.7: Experimental set-up for the determination of the sensitivity.


To determine the sensitivity of the line sensor, the pressure transient of an absorber

of known optoacoustic characteristics is measured. The ratio of measured voltage to

calculated pressure amplitude for this absorber will yield the sensitivity.

6.2.1 Experimental Set-up and Procedure

Fig. 6.7 shows the experimental set-up (developed by Passler [43]). A ring of Plexiglas

served as outer walls and a thin plastic film as bottom of a water tank.The plastic

film provides is well matched to water. The water tank is in direct contact with the

sensor and a drop of water on the sensor guarantees good acoustic coupling. Another

recipient, built the same way but smaller, contains the absorber (Orange G, dilution

of 10 g/l in distilled water). It is mounted at a distance of 1.2cm of the sensor surface.

The glass fiber is submerged inside the absorber. The distance between the glass fiber

and the sensor is 2cm.

In a first step, the laser energy that leaves the glass fiber ( 600µm) was determined

(0.47mJ). Then, the pressure signals were detected for three different modes of how

the oscilloscope was connected to the sensor:

45


Figure 6.8: Averaged signal of Orange G.

• by interposing an amplifier,

• by interposing an active probe (i.e., an impedance converter), or

• by interposing only a coaxial cable.

6.2.2 Received Signals and Determination of the Sensitivity

Fig. 6.8 compares the signals obtained when an amplifier is used with the case when

only a coaxial cable connects the sensor to the oscilloscope. These signals show how

the amplifier not only amplifies but also modifies the signal. First of all, the signal is

inverted. Logically, the measured voltage is higher and changes from the range of mV

to the range of V. Furthermore, reflexions that are probably coming from the cable

are reduced.

For the estimation of the sensitivity, the signals received with the active probe were

used. Fig. 6.9 shows the measured pressure signals and the simulated signals. The

simulation calculates bipolar signals, as would be received from a point sensor. Since

the measured signal is obtained from a line sensor, the first peak is higher than the

second, negative peak. Another characteristic for line sensors is visible: the measured

pressure amplitude returns to its initial value slowly. Ideally, for an infinite line, it

never reaches the initial value again.

A laser beam does not have an equal intensity I along the whole radius of the beam.

Near the optical axis the intensity is maximum (I0 at r = 0) and falls off laterally.

46


Figure 6.9: Pressure signal of Orange G and simulated pressure signal.

The lateral distribution is a cylindrical symmetric Gaussian [51]:

I(r) = I0e− 2r2

w2 , (6.1)

where w is the radius of the beam cross section measured to the points at which the

intensity falls to 1/e2 of its maximum value [46]. This Gaussian laser beam profile

is included in the simulation. The Gaussian wing gw is the width of the edges of

the laser beam profile. The following parameters of the experiment were used in the

simulation program:

absorption coefficient: µa = 9 · 104m−1

distance between source and sensor: z = 2.005 · 10−2m

radius of the glass fiber: a = 3 · 10−4m

Gaussian wing: gw = 3 · 10−5m

speed of sound in water: c = 1485m/s

incident radiant exposure: H0 = 1662.29J/m2

Grueneisen parameter: Γ = 0.12 (6.2)

The simulation leads to an expected pressure amplitude of 18.1bar at the distance

z of the source volume. Using Eq. (3.26) for the pressure at the time t = 0 we get a

pressure of

p0 = Γ · ElaserpulseVsource

= 0.12 · 0.47mJ

(300µm)2π · 19· 10−4

= 179.53bar, (6.3)

47


where Elaserpulse is the measured energy of the laser pulse and Vsource is the volume of

the irradiated source, given by the area of the glass fiber times the penetration depth

for the given absorber (Orange G). Measuring at nearly direct contact of source and

sensor would not yield a pressure signal of 179.53bar, but exactly half of that value,

as the wave propagates in opposite directions simultaneously. At a distance of only

2cm, after a propagation time of t = 1.35 · 10−5s, the amplitude of the pressure wave

has already decayed by ≈ 80%.

With this simulated pressure amplitude and the measured voltage, the sensitivity

for the system (sensor, active probe and oscilloscope) can be calculated using Eq.

(4.21):

S =0.0107V

18.1bar= 0.5912 mV/bar. (6.4)

This value is six times smaller than the theoretically calculated value (Chapter 4.2.3:

S = 3.589 mV/bar), which can have various reasons. The used PVDF film is already

15 years old, so that aging processes (see Chapter 4.2.1) may have changed the piezo-

electric constant. Furthermore, by gluing the film on the Plexiglas block wrinkles and

an unequally thick layer of adhesive could have occurred. Moreover, the adhesive is

not considered in the theoretical description at all, as well as other components of the

sensor.

48

7 Automation of Experiments for

TACT

The focus of this chapter will be on the development of the control box. First, atten-

tion will be given to the set-up of the experiment that is to be automated. The succes-

sion of steps in the experiment will be explained, which is prerequisite for creating a

control box for the experiment. Then, the technical assembling and the programming

of the control box will be treated.

7.1 Experimental Set-up

As already discussed in Chapter 5, to obtain a 3-dimensional image using a line sensor,

either the object or detector must be moved in x-direction and rotated a full 360.

Here, it is chosen to move the phantom and not the sensor, which is easier to realize

technically (Fig. 7.1). These movements are carried out by stepper motors, where

one is used to drive a linear stage. After each pulse the stepper motors turns 0.9.

Sensor and phantom are situated in a water tank. The laser pulses are lead through

two glass fibers from the Nd:YAG laser to the phantom, which is illuminated from

two opposite sides. An amplifier is connected between the sensor and the oscilloscope.

The oscilloscope is used to save the measurement. It is triggered by the laser pulses

and records one signal for every laser pulse that is shot toward the phantom. All

signals from one sequence (one linear scan) are saved together in one file.

49

7 Automation of Experiments for TACT

Figure 7.1: Experimental set-up: Sensor and phantom.

7.2 Procedure of the Experiment

First of all, the operator adjusts the positions of sensor, phantom and laser beam

so that a good illumination of the phantom is obtained, avoiding light irradiating

directly the PVDF film of the sensor. After setting the oscilloscope, the measurement

begins. In a not-automated experiment, only the linear movement is carried out by

stepper motors, while the rotation of the phantom is done by hand. The operator

would execute the following three steps of measurement:

1. Simultaneously turning on the stepper motor that moves the phantom in vertical

direction and the laser by pressing the buttons of their control systems. After

a given number of laser pulses, both stop automatically.

2. Saving the measurement by pressing the buttons "do save" and "clear sweeps"

on the oscilloscope and noting the file number.

3. Rotating the phantom by a certain angular increment. Changing the moving

direction of the stepper motor for the linear movement by tilting a switch.

These steps of the measurement are repeated until the phantom has rotated a full

180 or 360. The duration of the measurement, however, increases proportionately

50

7.3 Technical Assembling of the Control Box

Figure 7.2: Communication directions between the instruments and the control box.

with the factor by which the angular increment is decreased, and, therefore, with the

precision of the measurement.

Increasing the precision of the measurement and minimizing the time and effort of

the operator was the motivation to build an automation device that undertakes the

repetitive parts of the experiment. The central component of the control box is a

microcontroller (denoted as µC) that controls the instruments.


In this section, the focus will be on the instruments the microcontroller communicates

with, and on the technical realization of this communication. Fig. 7.2 shows all in-

struments that either give input to the µC, or receive signals from it. These directions

are symbolized by the arrows.

The stepper motors, one for moving the phantom in vertical direction and one for

rotating it in a certain angular increment, each have their own control unit. The

stepper motor that moves the phantom in vertical direction is turned on by receiving

a 5V TTL signal from the microcontroller. From an external frequency generator

it receives a square wave signal of chosen frequency. The rotational stepper motor

51


is turned on during the whole measurement, but it only moves the phantom when

it receives pulses from the µC. The microcontroller generates a 10Hz square wave

signal of a length given by the required number of pulses, depending on the angular

increment that is chosen by the operator (0.9 are equivalent to 1 pulse). Furthermore,

the control units of the stepper motors receive TTL-signals from the µC that define

the direction of the movement.

The microcontroller also communicates with the control units of the Nd:YAG laser.

On the one hand, the laser is started by a TTL-signal. The laser is stopped by

its own control unit after having shot a defined number of laser pulses. On the

other hand, while the laser is on, the µC counts the laser pulses, which is possible

because it receives a TTL-pulse every time a laser pulse leaves the laser. Thereby,

the microcontroller is able to stop the movement of the stepper motors exactly after

a required number of laser pulses has hit the sample.

Another important instrument of the experiment is the oscilloscope. The UART

(Universal Asynchronous Receiver and Transmitter) of the microcontroller enables

the communication to a serial interface, and the used oscilloscope supports remote

control via an RS232 interface. Since the µC provides 5V for a logic 1 and 0V for

a logic 0, but the RS232 interface of the oscilloscope uses −12V and 12V, a level

converter (MAX232) is necessary [50]. In the experiment the oscilloscope receives the

command to save measurements and serves as an output screen for messages from the

microcontroller.

The push buttons are used to start (RST) and end (RST) the experiment, to

simulate the laser pulses in test stages (button T2) and to confirm the chosen angular

increment (button T1).

Fig. 7.3 shows the circuit diagram of the control box, which was created using the

CAD (Computer Aided Design) program Eagle. This software was also used to create

the printed circuit board. Fig. 7.4 shows the real printed circuit board assembly.

Since the automation device is constructed in a modifiable way, it can be easily

adopted to other set-ups. The system presented here is the one used in the experiment

described in Chapter 8. By performing small changes in programming and technical

assembling on this system, it could be used for experiments of different sensors and

scanning geometries. The circuit board offers the possibility to add a third stepper

52


Figure 7.3: Circuit diagram.

53


Figure 7.4: Assembling of the control box.

motor (Fig 7.3: PB0 and PB1). Then, scanning geometries that include a movement

in z-direction would be possible. Furthermore, one more interrupt is available.

7.4 About the Microcontroller ATmega8

ATmega8 is an 8-Bit RISC microcontroller of the AVR family of the company Atmel

and is a very common microcontroller. It is a single integrated circuit with micropro-

cessor, EEPROM, RAM, Analog to Digital converter, various digital input and output

lines, timers, UART for RS232 communication and many other useful components. It

is used here for several reasons:

• It meets all the technical requirements of the automation device.

• It is built as a DIP device (Dual Inline Package). Therefore, it is possible to

solder by hand, in contrast to microcontrollers with SMD (Surface Mounted

Device) cases.

• The GNU Compiler is available, thus, the development of the program is possible

in C programming language, and there is no need to use assembler.

54

7.5 Programming an ATmega8

Figure 7.5: Harvard(left) and Von-Neumann Architecture [23].

• ATmega8 is a commonly used model. Therefore, many field reports, tips and

libraries are available.

The ATmega8 is built in Harvard Architecture. Fig. 7.5 shows the difference of

the Harvard Architecture to the Von-Neumann Architecture. Since it offers separate

memories for data and program, data and instructions can be loaded within only one

clock cycle, whereas Von-Neumann Architecture needs two [23]. Within one command,

the µC can process data of 8 bit length.

The maximum system fed clock rate is 16MHz, for the control box 3.6864MHz are

used. This frequency is an integer multiple of the baud rate and sufficiently fast for the

requirements of the experiment. The ATmega8 has one UART and provides 5V TTL

signals. The ATmega8 microcontroller has a Flash-Rom, which can be reprogrammed

several thousand times [22].

7.5 Programming an ATmega8

For programming an AVR microcontroller, adequate software is required. WinAVR is

a freeware package that includes an AVR-GCC-Compiler, the Programmer´s Notepad

and AVR specific libraries that ensure the communication of the microcontroller with

the other instruments and specify the pin-addressing of the ATmega8. These have

to be included in the header of the program, and can be downloaded from [16, 17].

Furthermore, a programmer software (AVR-Dude) is needed to load the code onto

55


the Flash-Rom of the microcontroller.

A central topic of the development of programs for microcontrollers is the access to

ports. A µC has many registers. Most of them are readable and writable registers,

which means, that the program can read the content of the registers, as well as

write on the registers. The names of the registers are defined in the header of the

program, according to the type of AVR controller. By defining the type of the MCU

in the makefile and by including the general I/O header (#include <avr/io.h>), the

compiler automatically chooses the appropriate data file that defines the registers.

In general, I/O registers of AVR microcontrollers can be written and read like

variables, because they have a Memory Mapped I/O. The I/O registers of electronic

devices are mapped in the central memory. For this reason, the devices can be accessed

by normal memory access routines [20]. To access to the ports of the microcontroller,

three registers for each port are necessary. These are shown in Table 7.1.

DDRx Data Direction Register for the port x.

If the bit in the register is set to 1 the port works as output.

If it is set to 0 it works as input.

PINx Input direction of the port x.

The bits in PINx show the current state of a port being

used as input. Use bit 1 for high, and bit 0 for low.

PORTx This register is used to access the outputs of a port.

If a Pin is set by using DDRx as input, PORTx can be used to

activate (bit 1) or disable the internal Pull-Up resistors.

Table 7.1: Registers to access ports [20].

Furthermore, for programming a µC, it is important to be aware of the limited

bytes of RAM provided. For this reason, neither the use of large data structures nor

the inclusion of complicated function calls or recursions are recommended [25].

For programming an AVR microcontroller, it is recommended using integer data

types, since the integer arithmetic is realized by the hardware. Therefore, even though

the use of floating point data types is possible, it would cause long processing times

[19]. In our case, int and char data types are used, when necessary in combination

with the modifier unsigned and the qualifiers const and volatile. The modifier

56

7.6 Description of the Program Flow

Figure 7.6: Interrupt service routine [21].

volatile prevents the variable from being optimized by the compiler. Supposing,

a variable has the value 0, then its value is changed to 1 and then again to 0, the

compiler would make optimizations and set the value to 0. volatile is for dynamic

use, e.g. in the case of data that is to be moved to an I/O port [24]. Note that the

use of volatile is crucial for programming a microcontroller.

Generally speaking, two different methods of programming microcontrollers are

distinguishable.

1. Sequential program flow : Using this method, an infinite loop is developed, which

has the following progression of events: First, each potential source of input is

"asked" to find out its operational status (i.e. Polling). Then, the processing

follows, and finally, the outputs are assessed. Afterward, the loop begins again

with polling etc.

2. Interrupt-driven program flow : Using this method, at the beginning of the pro-

gram, the wanted source for the interrupt must be activated. The program goes

on into the infinite loop, where non-time-critical actions are processed. Once an

interrupt is initiated, the dedicated interrupt-function will be processed. This

is shown schematically in Fig. 7.6 [21]. In the case of this control box, the

interrupt-driven program flow is used.


In Fig. 7.7, a general overview of the structure of the program is given. In the following

section, parts of it will be explained explicitly by code examples. Here, the focus will

not be on the code of the used functions, like for example delay_ms() to make a

57


time break between the actions that the microcontroller proceeds, uart_puts() to

realize an output via the serial interface, or sei() to activate an interrupt, but on

the succession of function calls in the main program. Also, in the original code, these

functions are removed from the main program to separate files.

Figure 7.7: Flow chart of the program.

First of all, the ports are assessed:

// Access ports for stepmotor1(vertical direction)

// direction SM1

#define SW1_CLOSE PORTD |= (1<<PD5);

#define SW1_OPEN PORTD &= ~(1<<PD5);

//on/off SM1



// stepper motor 2( rotation):

//on/off SM2

58




// direction SM2:

#define SM2_CLOSE PORTD |= (1<<PD7);

#define SM2_OPEN PORTD &= ~(1<<PD7);%

Then, the frequency of the CPU, the baud rate and the number of laser pulses per

linear scan are set in the macros and the features of the interrupt routine are defined.

The counted laser pulses are the interrupts.

// define CPU frequency in MHz here if not defined in Makefile

#ifndef F_CPU

#define F_CPU 3686400 UL

#endif

//9600 baud - velocity of the serial port:

#define UART_BAUD_RATE 9600

// define number of laser pulse per linear scan here:

#define WARTEPULSE 10

volatile uint16_t laserCount;

SIGNAL (SIG_INTERRUPT1)

laserCount ++;

if (laserCount >1000) laserCount =0;

The first step of the main program is the setting of the data directions for laser and

stepper motors:

DDRD |= ((1 << PD4)|(1 << PD5)|(1 << PD6)|(1 << PD7));

DDRB |= (1 << PB1);

In succession, the interrupts are activated. The laser pulses are the interrupts for the

real experimental case, and, respectively, the button T2 in the testing stages.

DDRD&=~(1<<PD3);// access ExtInt as Input

PORTD |= (1<<PD3);// Pullup active. Deactivate!with laser use.

MCUCR |= (1<<ISC11)|(1<<ISC10);//INT1 reacts on rising edge

GIMSK |= (1<<INT1); //INT1 activate for test stage only

Furthermore, the angular increment is defined. The stepper motor receives either 1, 5

or 10 pulses, which correspond to 0.9, 4.5or 9. From now on, attention will be given

in detail on the development of the program for these repetitive actions. Basically, it

59


is necessary to know precisely in which order the instruments should start their work.

Thereafter, the ports are opened and closed at the right time in the right order.

During every step of the experiment, comments are written on the screen of the

oscilloscope, using uart_puts("MSG \’text\’\r"). This feature guarantees that, on

the one hand, the operator can follow the steps, and, on the other hand, that in

cases of defects, the operator can trace back their origin. The commands for the

communication with the oscilloscope via the RS232 are taken from the oscilloscope´s

handbook [39] and implemented and adapted to the C-code. uart_puts("") is the

command to make an output by the UART-interface of the µC. Using the command

uart_puts("STO\r"), the oscilloscope saves the measurement into a file that is elected

before the experiment is started. STO is a oscilloscope specific command, \r is the

terminator that the oscilloscope requires for commands sent via the RS232.

In the main loop, all repetitive actions of the experiment are done until the phantom

has rotated 360 once, where the number of runnings through the loop is defined

through the chosen angular increment. In this part of the program, the matching of

the time delays is important, as different instruments react more or less quickly.

The first step in the main loop is that the phantom moves in vertical direction, while

being irradiated by a defined number of laser pulses. This number of laser pulses is

defined at the beginning of the program. Then, the stepper motor is stopped:

uart_puts("MSG \’\’\r");

delay_ms (500);

uart_puts("MSG \’Laser+SM1 are working\’\r");

delay_ms (1000);


delay_ms (500);

uart_puts("MSG \’Waiting on pulses , Dir1\’\r");

SW1_CLOSE //SM1 in direction upwards.

delay_ms (2000);

laserCount =0;

SW4_CLOSE //laser needs only short pulse to start

delay_ms (100);

SW4_OPEN

SW2_CLOSE //move SM1

do

while (!( laserCount == WARTEPULSE));

60


SW2_OPEN //stop SM1

delay_ms (1000);

In the second step, the signals are saved on the oscilloscope. With the command CLSW

(clear sweeps) the oscilloscope is ready for the next measurement step:


delay_ms (500);

uart_puts("MSG \’saving measurement \’\r");

delay_ms (500);

uart_puts("STO\r");

delay_ms (3000);

uart_puts("CLSW\r");

delay_ms (500);

Then, the phantom is rotated with the chosen angular increment:


delay_ms (500);

uart_puts("MSG \’SM2 rotates\’\r");

for (int i=0; i<pulszahl; i++)

SW3_CLOSE

delay_ms (100);

SW3_OPEN

delay_ms (100);

These three steps of the main loop are repeated until the phantom has rotated a full

360. Then, all ports are opened and the experiment is finished. Since the microcon-

troller does not have any operating system, an infinite loop has to be appended at the

end of the program.

61


62

8 Tomographic Experiment with a

Phantom

With the aim of testing the complete system of the control box and the constructed

sensor, a model sample for biological tissue was scanned. Such model samples are

called phantoms. In this chapter, first, the making of the used phantom will be

described. Then, the experimental set-up and its adjusting will be treated. Finally,

the received images of the experiment will be shown and discussed.

8.1 The Making of the Phantom

The phantom consists of two components: A base material that has optical and

mechanical characteristics of biological tissue and into which small light absorbing

objects are embedded. Since a phantom serves to test a tomographic system, including

experimental set-up and applied reconstruction algorithm, the geometric shape and

the optical characteristics of the embedded objects should be selected to serve the

testing of the system.

Gelatin mixed with soy bean oil emulsion as scattering medium has characteristics

that are close to those of biological tissue, and will serve as base material. Further-

more, the scattering dilution guaranties that the phantom is evenly illuminated, even

though it will only be irradiated from two sides. For preparing the base material,

25ml of water mixed with 5g of grained gelatin is heated up in a water bath to 45C.

Then, 1.6g of soy bean oil emulsion (Introlipid with 20% fat content) is mixed into

the gelatin carefully as not to cause air bubbles. This mixture is kept warm at 40C.

Small sperical droplets (diameter: 1mm to 0.5mm) of red oil color mixed with castor

oil represent the to be imaged objects.

63

8 Tomographic Experiment with a Phantom

Figure 8.1: The used phantom: Schematic illustration.

The gelatin mixture is filled into a plastic tube up to a height of 35mm. For the

two color spheres of the first plane, the color is injected with a hypodermic needle

slightly underneath the surface of the liquid gelatin. After the gelatin has hardened,

another 4mm of gelatin are filled into the tube and a second set of red balls is injected.

Once the gelatin has been allowed to cool, the remaining space in the plastic tube is

filled up with the base material. If the layers were not solid before pouring in more

gelatin, the balls would raise within the gelatin. A schematic and a real picture of the

phantom are shown in Fig. 8.1. The reason for positioning the objects at a height

of 35mm is that at the bottom of the plastic tube the plastic wall is thicker, which

would disturb the signal. So it is to be avoided to scan close to the end of the tube.

The phantom is scanned beginning from 10mm below the center of the objects up to

10cm above the objects (it is moved in x-direction, coordinate system as described in

Fig. 5.3).

8.2 Experimental Set-up and Adjusting

Fig. 8.2 shows the experimental set-up as it was basically already described in Chap-

ter 7. Two illumination units are used to illuminate the phantom. They are fixed

opposite to each other to the same mount as the phantom so that they move exactly

synchronously with the phantom.

The illumination units consist of a guidance and an adjustable fitting for the glass

fibers (diameter 600µm) and a convex lens (focal length f = 10cm), whose distance to

the fiber exit can be changed. The energy of a laser pulse is 4mJ for each glass fiber.

64

8.2 Experimental Set-up and Adjusting

Figure 8.2: Experimental set-up: Phantom, sensor, stepper motors and illumination

units.

The pulse width of the laser system is tp = 8ns, the pulse repetition rate is 10Hz and

a wavelength of 503nm was used. The sensor is connected to an amplifier (bandwidth

30MHz, amplification factor 1000), which in turn is connected to the oscilloscope.

Since the accurate timing of the signal acquisition is essential, the trigger signals

that the oscilloscope receives from a photo diode have to be optimized. Fig. 8.3

shows the used trigger signal. The amplitude can be adjusted by lightly changing the

position of the photo diode. The second, smaller peak at a position of 20ns is a signal

caused by optical reflexions.

By using an Helium-Neon laser bean that is coupled into the optical fibers, the

convex lenses of the illumination units are positioned in a way that the diameter of

the beam at the position of the phantom is as broad as the phantom and that a clear

65


Figure 8.3: Trigger signal.

image of the beam is obtained.

As described in Chapter 6.1, a good reconstruction of the object is achieved at

distances of the objects to the sensor up to a maximum of 15mm. Best results could

be achieved at 5mm. The used phantom has a diameter of 12mm, and the red droplet

that is the furthest away has a distance of 10mm to the sensor. The sensor-phantom

distance is 3mm. In the next step, an acoustic signal is sought with illumination by

laser pulses. For this purpose, the sensor line and the phantom are positioned at the

same height, where it is expected that the pressure signal has its maximum. The fine

adjustment of the relative position between sensor line and phantom is carried out by

seeking the best pressure signal. The sensor is fixed, but the phantom can be moved,

and the distance can be read from a scale. To find an optimal signal, it is convenient

use an averaging, as then the signal is more clearly visible. Fig. 8.4 shows the original

pressure signal and an arithmetical average over 15 shots for the case of sensor line and

objects being at the same height. Electrical reflexions and noise as well as scattered

light toward the PVDF film disturb the signal. The high voltage amplitude in the

first 2µs is a pyroelectric signal (see Chapter 4.2.1) that caused the light that was

scattered toward the PVDF film. The first negative and positive peak of the averaged

pressure signal are a typical pressure signal for a spherical shaped absorber detected

with a line sensor. Since the phantom consists of four spheres, more peaks are appear

66

8.3 Received Images and Discussion

Figure 8.4: Raw pressure signal and zoom into the averaged signal.

After having obtained a good signal, the operator chooses the file, where the saved

sequences of the following automated measurement will be saved to. By pressing the

button "RST" on the control box, the measurement starts.

In one sequence, the phantom is moved during 400 laser pulses in vertical direc-

tion. Feeding stepper motors with 467Hz, results in a phantom motion of 50µm per

laser pulse in x-direction so that in total it moves 20mm per sequence. An angular

increment of 5.4 is chosen which corresponds to 6 pulses which the rotational stepper

motor receives from the microcontroller. After 72 sequences, the phantom returned

exactly at the same position (accuracy in µm range), which proves that the interplay

of interrupts which the microcontroller receives from the laser, and the movement of

the stepper motor is very exact.


In this section, not only the resulting images of the phantom will be shown and

discussed, but also the images received after every step of the computerized recon-

struction algorithm that was theoretically described in Chapter 5.

Fig. 8.5 shows the raw data at the position Θ = 356.5. The x-direction is the

direction of the linear scan and, therefore, is between 0 and 20mm. The sensor-

source distance is the product of measured time of flight and speed of sound (c =

1500m/s). The pressure values are represented by the gray scales. For each sphere

67


Figure 8.5: Raw data.

Figure 8.6: Fourier reconstructed image.

68


Figure 8.7: Determination of the rotation axis.

in the phantom, one hyperbolic arc is visible. Comparing these curves with the ones

obtained from the measurement with the 135µm point source (Figures 6.3 and 6.4),

here the arcs are quite broad. The reason for this occurrence is that the distance of

the color droplets and the sensor is between 7mm and 10mm. Technically, it was not

possible to decrease this distances down to 5mm.

The signals of the first 3µs were set to zero, as they contained electrical noise and a

signal caused by heating of the PVDF film (pyroelectric effect). From the remaining

pressure signals, the mean pressure value was subtracted, which lowers background

signals on the image. After reconstruction of the signals by the two dimensional

Fourier Reconstruction Algorithm [28], one x-z- section for each angle is received. Fig.

8.6 shows an x-z-section at the angle Θ = 356.5. It shows all typical characteristics,

as already discussed in Chapter 6.1.2, but for the case of four spherically shaped

extended objects.

Since a 3-dimensional image is to be obtained, the information about the rotational

positions needs to be included. This is realized by applying the inverse Radon trans-

formation. Before this transformation can be carried out, the position of the rotation

axis must be determined with such a high precision that is not reached by measuring

it directly from the set-up.

69


Figure 8.8: Real picture and reconstructed image at an x-position of 13250µm

Figure 8.9: Real picture and reconstructed image at an x-position of 9250µm

70


Therefore, the array of data obtained after the Fourier reconstruction, serve to de-

termine the position of the rotation axis. Fig. 8.7 shows pressure signals received

along the scanning in x-direction assigned to the corresponding angle Θ. The re-

construction program is written in a way that by clicking at the maximum and the

minimum of the sinusoidal curve, the program calculates the baseline of the sine and

sets it as position of the rotation axis.

Then, the inverse Radon transformation is carried out and y-z slices are received.

Figures 8.8 and 8.9 show two slices that are chosen at those positions where they

coincide with the two layers containing the red oil droplets. In each case, it can be

seen that the bigger droplet is represented by a ring. This occurs, as the sphere

radius is bigger than the penetration depth, which is the reciprocal of the absorption

coefficient. The radial lines originating at the objects are a typical artifact of the

inverse Radon transformation. The angle between the lines is exactly the angular

increment of 5.4. For comparison, figures 8.8 and 8.9 also show the real picture of

the phantom. To obtain these pictures the plastic tube was sawed apart close to the

objects and the gelatin was cut with a scalpel. Then the gelatin with the objects was

pressed out of the tube and cut in slices. Since on these pictures the plastic tube is

removed, the radius of the phantom presented here is smaller, as described in section

8.1.

Figures 8.10 and 8.11 show a 3-dimensional rendering of the phantom images from

two different views. A typical characteristic for scanning in x-direction with a line

sensor is obvious: Since no signals were measured in z-direction, the originally spher-

ically shaped oil droplets appear elongated in x-direction. This artifact could be

minimized by using a third stepper motor to move the phantom also in z-direction.

As the control box offers the possibility to scan that way, it is applicable also in future

experiments.

Further improvements of the image could be achieved by increasing the scan length,

which was not possible in the present set-up because the maximum length of the

movement of the vertical stepper motor is 25mm. Regarding the sensor, and increase

of resolution could be achieved by using a thinner PVDF film and by covering the

PVDF film with another film to lower the signals received from light scattered onto

the sensor active area.

71


Figure 8.10: 3D image of the four red oil droplets.

Figure 8.11: 3D image of the four red oil droplets.

72

9 Summary and Conclusions

The aim of this diploma thesis was to construct and test a piezoelectric line sensor and

to design a control box for automating tomographic experiments. The entire system

was to be tested with a self-made phantom and the received images should shed light

on the interplay of the instruments and the compatibility of the experiment with the

applied reconstruction algorithm.

A description of the construction of the sensor and an explanation of the reasons

for the chosen materials and sizes are given in Chapter 3. Since making such a sensor

by hand is quite hard, it was decided to use easy-handling materials. Therefore,

a 25µm film was used instead of a 9µm film which would have provided a higher

resolution. The experiments with the point source show that the behavior of the

sensor in parallel and normal direction to the active line is as expected. Then, by

using a known absorber, the sensitivity was determined. Even though six times smaller

than the theoretical value, it is still satisfying, as the determination of the theoretical

sensitivity does only include the material and the size of the active PVDF line and

the active probe, but does not include other components of the sensor nor effects

caused by certain construction failures, as for example small wrinkles of the PVDF

film caused by the application of the two-component adhesive.

The design of the control box led to satisfying results. Various testing stages led

to the presented system. The communication with the oscilloscope proved to be

especially problematic. Discovering the problem in a non-functional system was quite

tricky, as many components could be responsible for the failure. Furthermore, in

some cases, it was even difficult to find out if either the programming or the hardware

caused the defect.

73

9 Summary and Conclusions

The advantages of the presented control box over manual driven experiments are:

• The advancing of the angular increment by sending pulses by the microcontroller

is more exact than manually with a scale.

• The steps of the measurement proceed in the time limit given by the instruments,

which is faster than a person can do. Therefore, the total time of the experiment

decreases.

• For the rotation of the phantom, smaller angular increments can be chosen,

without greatly increased time for the operator.

• It´s simply automated! Go and get yourself a coffee! :)

To test the system of the line sensor and the control box, a phantom was imaged.

The phantom consisted of four spherically shaped droplets of red oil color that were

injected into gelatin. The measurement showed that the interplay of interrupts and

stepper motors is very exact, since the initial position of the phantom did not change

after 72 linear scans (accuracy in the µm range). The received images are as expected

for the used sensor, whereas the use of the control box led to results way above

the expected. Since it is built in a modifiable way, a third stepper motor could be

added, which would make it possible to realize scanning geometries that include the

z-direction. Moreover, in prospective experiments, the control box could be used with

different kinds of sensors as for example piezoelectric sensors of various geometries of

the active PVDF film or interferometric, optical detecting methods.

74

10 Symbols and Abbreviations

10.1 Symbols

Symbol (alphabetical) Unit Physical Value and Description

a m radius of the laser beam

A m2 area

α 1/cm sound absorption coefficient

B/A – Beyer′s nonlinearity parameter

β 1/K cubic expansion coefficient

c m/s speed of sound

clight m/s speed of light

cp J/kg·K specific heat at constant pressure

cV J/kg·K specific heat at constant volume

C F capacitance

d m diameter, thickness

dij C/N piezoelectric constant

df m2 infinitesimal area

D – diffraction parameter

DiC/m2 dielectric displacement

Ddiff cm diffusion constant

δ m penetration depth

δ(t) – Dirac delta function

E W/m2 irradiance

Ei V/m electrical field strength

η % conversion efficiency

75


εij C/V·m permittivity

ε0 C/V·m permittivity of free space

εr – relative dielectric coefficient

ε(~r, ~s, t) W/m3 source term

f cm focal length

g – anisotropy coefficient

gw m radius of the Gaussian wing

Γ – Grueneisen coefficient

H J/m2 radiant exposure

I W/m2 intensity

I0 W/m2 initial intensity

Is W/m2 not scattered intensity

k W/m·K thermal conductivity∣∣∣~k∣∣∣ m wave vector

κ Pa compressibility

L W/m2sr radiation density

λac m acoustic wavelength

λh W/K·g heat conduction coefficient

µa 1/cm absorption coefficient

µeff 1/cm effective optical attenuation coefficient

µs 1/cm scattering coefficient

µ′s 1/cm reduced scattering coefficient

ν Hz frequency

ω Hz angular frequency

Ω sr solid angle

p Pa pressure

p(~s ′, ~s) – probability function

p0 Pa generated pressure at t = 0

P W power of radiation

PHG(~s ′, ~s) – Henvey-Greenstein function

Ψ J/m2 laser fluence

76

10.1 Symbols

Q J heat energy

Q(z, t) C charge

R – reflectivity

ρ kg/m3 density of media

sij Pa elasticity modulus

S V/Pa sensitivity of a piezoelectric sensor

S(t) V signal received from sensor

Sj – strain

S(~r, t) J/m3·c heat source term

σ Pa · s viscosity

t s time of flight

tac s acoustic relaxation time

tp s laser pulse duration

ttherm s thermal relaxation time

T – transmissivity

∆T K change in temperature

Tj N/m2 mechanical stress

Θ rd angle of scattering

V m3 volume

W J/m3 energy density

Ylm(Θ, ϕ) – spherical harmonics

zf m distance of the near- and far field boundary

Z kg/m2s impedance

77


10.2 Abbreviations

CAD Computer Aided Design

DDR Data Direction Register

DIP Dual Inline Package

DOT Diffuse Optical Tomography

EEPROM Electronically Erasable Programmable Read-Only Memory

GCC GNU Compiler Collection

I/O Input/Output

MCU Micro Controller Unit

µC Microcontroller

Nd:YAG Neodymium-doped Yttrium Aluminum Garnet

OCT Optical Coherence Tomography

OPO Optical Parametric Oscillator

PMMA Polymethylmethacrylat, Plexiglas

PVDF Polyvinylidene Fluoride

RAM Random Access Memory

RISC Reduced Instruction Set Computer

RST Reset

TACT Thermo Acoustic Computer Tomography

TTL Transistor Transistor Logic

SMD Surface Mounted Device

UART Universal Asynchronous Receiver and Transmitter

78

List of Figures

3.1 Graham Bell´s Photophone [13] . . . . . . . . . . . . . . . . . . . . . . 4

3.2 Illustration of the radiation density [34]. . . . . . . . . . . . . . . . . . 6

3.3 Thermoelastic effect. The illuminated volume absorbs the electromag-

netic energy, which causes a thermal expansion and consequently a

pressure field [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.4 a) Near field b) Far field [41] . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 a) Quartz crystal [15]. b) Deformation and movement of charges at a

quartz crystal [37]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2 Propagation of acoustic waves through the sensor layers [26]. . . . . . . 26

4.3 Steps in the construction of the sensor. . . . . . . . . . . . . . . . . . . 28

4.4 Real picture of the piezoelectric line sensor. . . . . . . . . . . . . . . . 28

5.1 a) Point detector b) Large plane detector [3]. . . . . . . . . . . . . . . . 34

5.2 Condition for the size of a sensor for near field measurements. . . . . . 35

5.3 Integrating line sensor. Definition of axes and integration over a cylin-

der with the radius R = ct [3]. . . . . . . . . . . . . . . . . . . . . . . . 36

5.4 Schematic illustration of the image reconstruction algorithm. . . . . . . 37

6.1 Point source: Experimental set-up. . . . . . . . . . . . . . . . . . . . . 40

6.2 Single pressure signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.3 Raw data at a distance of 5mm. . . . . . . . . . . . . . . . . . . . . . . 42

6.4 Raw data at a distance of 15mm. . . . . . . . . . . . . . . . . . . . . . 42

6.5 Fourier reconstructed image at 5mm. . . . . . . . . . . . . . . . . . . . 44

6.6 Fourier reconstructed image at 15mm. . . . . . . . . . . . . . . . . . . 44

6.7 Experimental set-up for the determination of the sensitivity. . . . . . . 45

79

List of Figures

6.8 Averaged signal of Orange G. . . . . . . . . . . . . . . . . . . . . . . . 46

6.9 Pressure signal of Orange G and simulated pressure signal. . . . . . . . 47

7.1 Experimental set-up: Sensor and phantom. . . . . . . . . . . . . . . . . 50

7.2 Communication directions between the instruments and the control box. 51

7.3 Circuit diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.4 Assembling of the control box. . . . . . . . . . . . . . . . . . . . . . . . 54

7.5 Harvard(left) and Von-Neumann Architecture [23]. . . . . . . . . . . . . 55

7.6 Interrupt service routine [21]. . . . . . . . . . . . . . . . . . . . . . . . 57

7.7 Flow chart of the program. . . . . . . . . . . . . . . . . . . . . . . . . . 58

8.1 The used phantom: Schematic illustration. . . . . . . . . . . . . . . . . 64

8.2 Experimental set-up: Phantom, sensor, stepper motors and illumina-

tion units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

8.3 Trigger signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

8.4 Raw pressure signal and zoom into the averaged signal. . . . . . . . . . 67

8.5 Raw data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

8.6 Fourier reconstructed image. . . . . . . . . . . . . . . . . . . . . . . . . 68

8.7 Determination of the rotation axis. . . . . . . . . . . . . . . . . . . . . 69

8.8 Real picture and reconstructed image at an x-position of 13250µm . . . 70

8.9 Real picture and reconstructed image at an x-position of 9250µm . . . 70

8.10 3D image of the four red oil droplets. . . . . . . . . . . . . . . . . . . . 72

8.11 3D image of the four red oil droplets. . . . . . . . . . . . . . . . . . . . 72

80

Bibliography

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