Integrating Piezoelectric Sensors for Thermoacoustic … · 2019. 5. 7. · Barbara Schuppler...
Transcript of 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
2
Für meine Mama,
Anna Schuppler
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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
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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
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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.
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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.
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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.
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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
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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].
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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.
3.2 Propagation of Light
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].
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3 Theoretical principles of Optoacoustics
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-
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3.2 Propagation of Light
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
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3 Theoretical principles of Optoacoustics
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.
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3.2 Propagation of Light
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 =
õa
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
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3 Theoretical principles of Optoacoustics
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
3.3 Generation of Thermoacoustic Waves
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].
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3 Theoretical principles of Optoacoustics
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
3.3 Generation of Thermoacoustic Waves
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)
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3 Theoretical principles of Optoacoustics
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
3.3 Generation of Thermoacoustic Waves
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 Theoretical principles of Optoacoustics
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
3.4 Propagation of Acoustic Waves
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
3 Theoretical principles of Optoacoustics
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
3.4 Propagation of Acoustic Waves
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
3 Theoretical principles of Optoacoustics
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
4 Piezoelectricity and Piezoelectric Sensors for TACT
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
4.2 The Piezoelectric Line Sensor
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
4 Piezoelectricity and Piezoelectric Sensors for TACT
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
4.2 The Piezoelectric Line Sensor
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
4 Piezoelectricity and Piezoelectric Sensors for TACT
Figure 4.3: Steps in the construction of the sensor.
Figure 4.4: Real picture of the piezoelectric line sensor.
28
4.2 The Piezoelectric Line Sensor
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 Piezoelectricity and Piezoelectric Sensors for TACT
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
4.2 The Piezoelectric Line Sensor
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
4 Piezoelectricity and Piezoelectric Sensors for TACT
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.
5.2 Image Reconstruction for Line Sensors
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
5 Integrating Line Sensors and Image Reconstruction
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
5.2 Image Reconstruction for Line Sensors
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
5 Integrating Line Sensors and Image Reconstruction
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
6.1 Testing the Sensor with a Point Source
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
6 Experiments to Characterize the Sensor
Figure 6.3: Raw data at a distance of 5mm.
Figure 6.4: Raw data at a distance of 15mm.
42
6.1 Testing the Sensor with a Point Source
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
6 Experiments to Characterize the Sensor
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.
6.2 Experimental 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
6 Experiments to Characterize the Sensor
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
6.2 Experimental Determination of the Sensitivity
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
6 Experiments to Characterize the Sensor
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.
7.3 Technical Assembling of the Control Box
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
7 Automation of Experiments for TACT
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
7.3 Technical Assembling of the Control Box
Figure 7.3: Circuit diagram.
53
7 Automation of Experiments for TACT
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
7 Automation of Experiments for TACT
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.
7.6 Description of the Program Flow
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
7 Automation of Experiments for TACT
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
#define SW2_CLOSE PORTD |= (1<<PD4);
#define SW2_OPEN PORTD &= ~(1<<PD4);
// stepper motor 2( rotation):
//on/off SM2
58
7.6 Description of the Program Flow
#define SW3_CLOSE PORTD |= (1<<PD6);
#define SW3_OPEN PORTD &= ~(1<<PD6);
// 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
7 Automation of Experiments for TACT
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);
uart_puts("MSG \’\’\r");
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
7.6 Description of the Program Flow
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:
uart_puts("MSG \’\’\r");
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:
uart_puts("MSG \’\’\r");
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
7 Automation of Experiments for TACT
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
8 Tomographic Experiment with a Phantom
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.
8.3 Received Images and Discussion
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
8 Tomographic Experiment with a Phantom
Figure 8.5: Raw data.
Figure 8.6: Fourier reconstructed image.
68
8.3 Received Images and Discussion
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
8 Tomographic Experiment with a Phantom
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
8.3 Received Images and Discussion
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
8 Tomographic Experiment with a Phantom
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
10 Symbols and Abbreviations
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 Symbols and Abbreviations
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
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