2. 2
CONTENTS
1. Introduction………………………………………………………………………….… 5
1.1. Objectives of this thesis………………………………………………………… 5
1.2. Motivations……………………………………………………………………….. 5
2. Theory………………………………………………………………………………….. 7
2.1. Description of light propagation through matter…………………….………... 7
2.2. Basics of light scattering……………………………………………………….. 9
2.3. Introduction to the key variables µa, µs, µs', g………………………..………… 9
2.4. Theory of the spatial frequency domain……………………………………... 10
2.5. Fluorescence background…………………………………………………………. 13
3. Methods and Experimental Setup…………………………………………………........ 16
3.1. Data analysis method………………………………….………........................ 18
3.2. Expected measurement error……………………………………………………. 33
4. Results and Discussion……………………………………………….………………. 35
5. Conclusions……………………………………………………………………………. 44
6. Acknowledgements………………………………………………………………………. 44
7. References……………………………………………………………………………... 46
3. 3
Declaration
I herewith declare that I have produced this without prohibited assistance of third parties and without
making use of aids other than those specified as such. This paper has not previously been presented in
identical or similar form to any other German or foreign examination board.
The thesis work was conducted from 20-June-2014 to 12-November-2014 under the supervision of
Prof. Alwin Kienle at the University of Ulm.
Ulm,
Sela Shefy
4. 4
I am dedicating this thesis to Alona, my wife,
that through her sacrifice made it possible
and to my parents for all their support
the past two years.
5. 5
1. Introduction.
In this chapter I will cover the objectives and the motivation leading to this work. Under
the objective presentation section in this chapter I will enumerate my objectives and
clarify the meaning of each one. This will be the direction in which I will go and try to
achieve within the time and size frame of my master’s thesis. In the motivation section I
will show potential applications for fluorophore quantification and will demonstrate the
benefits it can encompass.
1.1. Objectives of this thesis.
In the framework for this thesis I will try to set basic concepts and methods
concerning the quantification of fluorophore molecules in turbid media using
spatial frequency domain imaging. This will be the primary objective. There are
two secondary objectives. One will be to determine the sensitivity of the spatial
frequency domain to small amounts of fluorophore and to determine the lowest
quantity detectable with the current setup. The other secondary objective will be to
determine the detection resolution of the fluorophore concentration, which that
method can achieve with the current setup.
1.2. Motivations.
Humanity as we all know, suffers from a variety of degenerative and mutant
diseases. Cancer and atherosclerosis bring about suffering and mortality in
significant percentages in the modern western world. In order to diagnose these
diseases, the conventional method is to perform biopsies and a histologic
examination of the sample by a certified pathologist. This is a very invasive
procedure that is time-consuming and requires highly trained professionals. All of
this results in the patient suffering both physically and mentally. For that reason
there is a need for basic screening before submission for biopsy. Moreover since
there is no applied real-time method for tissue classification (malignant, benign and
healthy), there is real difficulty for surgeons to be certain that they remove the
entire tumor. That of course requires the removal of "safety slices".
If there was a way to make a biopsy non-invasive, avoiding tissue removal and with
immediate results, it could give the physicians and surgeons more accurate and
efficient tools to prevent all this suffering. This is why efforts for optical biopsy
methods have been researched and developed for two decades now. Alfano and Pu
describe a number of methods in a chapter of "Lasers for Medical Applications
(2013)"[1]. Two of these methods involve the use of the auto-fluorescence of tissue
components (tryptophan, collagen, elastin, NADH i
, FAD ii
and porphyrins) to
determine the ratio between two or more of these components. It is shown in the
chapter that it is possible to distinguish between healthy and diseased tissue.
Experiments were performed on breast and prostate tissue (but not only),
comparing healthy and diseased samples for the same patient. The experiments
showed good correlation with the histological results, determining whether tissue is
cancerous or benign.
In the US alone breast and prostate cancer are the two most common cancers.
Approximately two hundred and thirty thousand new cases a year of each type of
cancer are diagnosed according to the American Cancer Society [2]. The methods
in "Lasers for Medical Applications (2013)"[1] suggest that if knowledge of the
biochemical composition in the organ is available, detection of deviations from the
norm is possible. Hence so are diagnostic tests for every organ in the body. Alfano
i
NADH – reduced nicotinamide adenine dinucleotide
ii
FAD – flavin adenine dinucleotide
6. 6
and Pu say, "During development from benign hyperplasia to premalignant
(dysplastic) and malignant stage, cells undergo proliferation and death, which
modify their biochemical content. The connective tissue frameworks of tissue can
be impaired during cancer evolution. Such alterations of tissue biochemistry and
morphology may be revealed in the tissue fluorescence."[1]
The idea of diagnosis of the cell using the auto-fluorescence of the tissue was explored in the
past with success. By using the combined fluorescence spectra and reflectance spectra
simultaneously, I. Georgakoudi was able to distinguish different states of the tissue and to
quantify biomarkers [3]. More than that, the possibility of diagnosing cancer cells
before histologic change took place is possible if we can be sensitive enough to the
biochemical changes in the tissue. As a vision, I see an optical biopsy hand device
enabling the physician or surgeon on all levels of the medical welfare system to
determine by imaging of tissue, whether it is malignant, benign or healthy with
spatial resolution. The work of my thesis is motivated in the light of this vision.
7. 7
2. Theory.
In this chapter I will describe in general lines the theories explaining light propagation. It is
important to understand intuitively the physical process governing the light propagation
mechanism and the assumptions that were introduced to the theory. This is necessary first in order
to consider the character of the solution (exact, statistical, approximate), which necessarily sets
limitations on the solution. This kind of limitation can be for example within which time limits
the solution is valid, whether it is satisfactory for all time regimes, only for very short times or
only after a long time. This knowledge of the different theories plays an important role in the
choice of the most suitable theory to describe and analyze the results of the experiment and to
understand discrepancies between the results and expected values. Other errors may occur in the
experimental setup itself and these errors will be discussed in the third chapter (chapter 3.4).
2.1. Description of light propagation through matter.
The interactions between light and electrical charges can be described using different
theories, involving different approaches to the very nature of light. Light can be described as
a wave or as particles and shows this dual feature in different interactions depending on the
light wavelength and the size scale of the system with which it interacts. Quantum Theory
takes light in its full complexity but while it provides a very good description at the
subatomic scale and describes the fluorescence phenomenon, it is not solvable for multi-
body systems with any mathematical tool available at this time.
Luckily in this case, we can take a few steps back and look at the system from a microscopic
perspective. It can be described and accurate predictions can be made using electromagnetic
wave propagation. In the book "Optics" written by Eugene Hecht [4] I found a nice analogy
to a train station during rush hour. That if you look at it from a distance you cannot
distinguish every person and that movement becomes a smooth stream predictable from one
day to another. This is an analogy to the way that the propagation of photons described by an
electromagnetic wave is given by the Maxwell equations. Correlation between propagation
of light to that of an electromagnetic wave comes together beautifully when comparing the
electromagnetic wave speed in vacuum (V) to the speed of light (C) value that was measured
in an experiment prior to the Maxwell equations.
= ≈ 3 ∙ 10
⁄
≈ (2.1.1)
The value of the electromagnetic wave speed in vacuum (V) is coming from the solution of
the wave equation, where µ0 is the permeability of vacuum, ɛ0 is the vacuum permittivity,
and C the speed of light in vacuum.
Maxwell comments on this agreement between the two, "This velocity [i.e., his theoretical
prediction] is so nearly that of light itself (including radiant heat, and other radiations if any)
is an electromagnetic disturbance in the form of waves propagated through the
electromagnetic field according to electromagnetic laws."[4]. The classic wave description
using the Maxwell equations is considered accurate for the scattering absorption of any
interaction between light and matter (or vacuum). It also lets us look at the matter as a
distribution of refractive indices, directly connected to the speed of light propagation in
matter. Still analytical solutions for Maxwell's equations are available for very limited highly
symmetrical systems like a single sphere (Mie Theory) and an infinite cylinder. Numerical
methods for the solution of the Maxwell equations are the FDTDiii
and DDAiv
, but this
solution is only good for stationary systems, and for large volume calculation time it is very
long.
iii
FDTD - finite difference time domain
iv
DDA - discrete dipole approximation
8. 8
In light of these limitations, comparison to experiment would require an exact distribution of
refractive indices that is not really available for non-uniform material. Since we do not
control the position of every particle that is inserted into the media and even if we would,
there are still thermal vibrations in the material. So there would be a need to solve for all
potential possibilities of the media states and average all of them to get a solution
comparable to measurement. This would take a relatively long time to compute for all
positions of the particles in time. This is highly impractical due to the long time of
calculation per each state, disregarding the missing knowledge on particle locations.
Nevertheless with these methods (Mie, FDTD, DDA) there is the possibility of calculating
for a single scatterer the solid angles and distribution of the light scatter from a single object
or a small group of objects at a microscopic scale. In order to make use of this distribution,
practical phase functions or scattering functions were used as an approximation of the
information that was obtained in experiments and simulations. In this work I used the
Henyey-Greenstein scattering function that was originally created for diffuse radiation in the
galaxy. I will discuss the Henyey-Greenstein function further in the section of "basics of
light scattering" (chapter 2.1).
A method that has the ability to overcome the difficulties with the solution of Maxwell's
equations is the radiative transport equation (RTE). The basic idea of the transport equation
is to observe the system in mesoscopic scale and use a statistical approach. The transport
equation is based on the Boltzmann equation. It can be described as the balance equation for
the energy flux of light. Transport Theory is based on phenomenon observation and an
assumption made at first to describe the observation, but in 2006 Mishenko demonstrated in
his book the derivation from the Maxell equation to the transport equation [5].
The radiative transport equation as part of the statistical approach uses coefficients to
quantify bulk properties. This approach is good under some assumptions and allows to
describe volume of media by its optical index (n), absorption coefficient (µa), scattering
coefficient (µs) and phase function (p(θ)). I will discuss these coefficients in the basics of
light scattering) and the introduction to key variables (chapter 2.2).
There are three available solutions for the transport equation. The first is by using the Monte
Carlo simulation. Using the Monte Carlo simulation method produces very good
approximation results for low spatial frequencies, but presents some problematic
disadvantages. The second known solution for the transport equation is the SPNv
solution,
one problem with it is that the solution does not converge for a large N. I did not choose to
use this solution for this thesis. The third solution known to me is the PNvi
solution; it
produces analytical and accurate solutions for the transport equation in the limit of a high
computation order N. At ILMvii
there is an available solution that I will use for the analysis
of the non-fluorescence part, but at the moment I have no applicable solution for the
fluorescence part. The transport equation is valid under the following assumptions.
Assumption 1 is that the distribution of the scatterers, absorbents and in this case the
fluorescence, is randomly structured in the media. The second assumption is that the
concentration of the particles is low and therefore the particles are independent scatterers.
The third assumption is that the distribution of particles in the media is uniform.
The next step that can lower the level of difficulty of the mathematical problem is the
diffusion approximation. The diffusion equation is an approximation of the radiative
transport equation but instead of considering the phase function, the phase function is taken
into account only by using a reduced scattering coefficient (µs') instead of the scattering
coefficient (µs) itself. Further discussion of this coefficient will be in the introduction to key
variables (chapter 2.2). The reduction of the phase function removes the initial
directionality dependence and results in the equation of energy diffusion in the material. In
v
SPN – simplified spherical harmonics
vi
SP - spherical harmonics
vii
ILM – Institute for Laser Technologies in Medicine and Metrology
9. 9
order for this approximation to be valid, we must assume that the detector is far from the
light source, the absorption coefficient is significantly smaller than the reduced scattering
coefficient (µa<<µs') and that it is after a "long" interaction time. For Spatial Frequency
Domain (SFD) measurement this is not a problem in the measurement time frame (chapter
2.4). All of these assumptions are made to make sure that the light will have a large number
of scattering events prior to the detection. Only under these conditions it makes sense to
compare results of experiments with this solution. In case we push these boundaries it may
be shown as discrepancies between the experiment and the solution. Nevertheless the
advantage of having an analytic solution makes the diffusion equation attractive for
comparison with the experiment.
2.2. Basics of light scattering.
Light scattering of a single scatterer may be considered as basic. As mentioned before, the
small volume dealing with a single immobile scatterer can be solved analytically or
numerically using solutions of Maxwell's equations. In any case, it can provide a three-
dimensional distribution of light after engaging the scatterer. Nevertheless some simple
function describing this distribution was made in order to simplify the direction of light
propagation. One of those functions is the Henyey-Greenstein (HG) function that I will be
using in this work. This is written out as follows:
=
! "# $%
(2.2.1)
Where g is a parameter that can have values between -1 to 1. The Henyey-Greenstein
scattering function (HG) function shows the effect of total backscattering for g=-1, isotropic
scattering for g=0 and full forward scattering for g=1. Total forward scattering is equal to no
scattering at all since the light moving in the original direction without change. Integration
of the HG function over full shell is normalized to 1. Some take into account also the initial
light and then the phase function should be normalized to zero. This normalization is valid in
cases where there is no source inside the sphere.
2.3. Introduction to the key variables µa, µs, µs', g.
In order to describe the media, as I wrote before, the use of variables that relate to the
volume quality and not to every particle in particular makes our conception of the bulk
easier and more intuitive.
The first variable is the optical index n, a very basic variable that we know is the index that
describes the influence the bulk has on the light propagating through it. The optical index is
the ratio between the propagation speed of light in vacuum (C) and the propagation speed of
light in media.
& =
'
(
(2.3.1)
Since the maximum speed of light is in vacuum it is obvious that the optical index (n) can
vary from 1 and above. In its scalar form it may be the most basic optic coefficient, but this
is not a full description of it, and then, calculated from the electromagnetic properties of the
material the next equation forms:
& = √*+,+ (2.3.2)
with ɛr, relative permittivity and µr, relative permeability. The ɛr is a complex number
depending on the frequency of the light, and therefore the optical index is complex as well.
This fact has more of an effect for conductive media. In this work I will not use the complex
10. 10
form to describe the basic media, which in low concentration of scatterers and absorbers µs
and µa are used respectively. As a convention, µs is called the scattering coefficient and µa is
called the absorption coefficient. Both coefficients are defined in units of one divided by
distance (customary to use: mm-1
). Intuitively these coefficients are inverse to the mean
distance a photon will pass through the media between interaction, scattering or absorption.
As I explained in the section of basics of light scattering (chapter 2.1), another parameter
that plays an important role in describing the scattering of particles in the media is the phase
function p(θ). The HG phase function is governed by a parameter we call g, that effectively
determines the light statistical distribution to the different angles (θ). In the diffusion theory
we neglect the phase function and use in its place a reduced scattering coefficient (µs'),
defined by the following simple equation:
μ!
.
≡ μ!(1 − g) (2.3.3)
2.4. Theory of the spatial frequency domain.
The spatial frequency domain imaging method is a method of obtaining the optical
properties of turbid media. In general outlines the idea at the base of this method is to
illuminate a sample with a known spatial light pattern on the surface and take measurements
(images) of the light pattern remitting from the sample. The difference that we obtain
between the projected pattern and the captured pattern holds the optical information of the
sample. Intuitively it will be probably best to start with imagining a point source. In that case
there is photon or ray propagation in initial direction in the material. These photons will
continue in the same direction until they will interact with an absorber or scatter area of the
material. When interaction occurs, the photon will absorb or change its direction
respectively. If scattered, the photon will continue the movement in a new direction. Let us
imagine this line of events repeats itself many times. Eventually all photons will be absorbed
or will escape the material considering that in a semi-infinite bulk, the only option of photon
escape in the material will be from the same surface where the light source is. Under this
assumption there will be a pattern of light emerging from the material surface. This pattern
(position and intensity) is a result of the absorption and scattering of the material. Isotropic
material will show a circle of light with decreasing intensity as the distance from the point
source increases. For materials that have non-isotropic optical properties (for simplicity’s
sake, let us say in x and y directions), the pattern on the surface will be ellipsoid and not
circular. Imagining the effect of scattering and absorption is slightly more difficult since the
effect is combination of the two parameters but it is possible to "hold" one parameter
constant and imagine the effect caused by changing the other. Let me start by holding
absorption constant. Increasing of scattering creates more scattering events at a small
distance and therefore a photon is more likely to escape the material closer to the source than
in the case of low scattering. This effect causes faster decrease of the intensity when getting
further away from the source and smaller scattering will allow more photons to escape the
material at a longer distance from the source. The other option, of course, will be to hold the
scattering constant while changing the absorption. As the absorption increases, there is a
higher probability of a photon being absorbed in the bulk so that its energy is converted to
another form of energy. Obviously the amount of photons escaping the material will
decrease. The obvious effect will be that the integration of intensity over space will decrease
with every increase of the absorption. The question is, how will this increase in the
absorption affect the chance of a photon to escape the material at a different distance from
the source? To consider that, the longest path the photon can make through the material in
order to escape at a specific point must be examined. The conclusion must be that the
minimum path for a short distance from the source is shorter than for a longer distance from
the source, but the maximum length is theoretically unlimited in semi-infinite media. This
leads to the fact that the change in absorption will have a bigger effect on light emitting
11. 11
farther away from the source than on one emitting closer to it. Therefore the intensity will
decrease with a bigger factor for longer distance from the source.
After considering the different effects the coefficients have on light propagation from a point
source, let us imagine superposition of many point sources. I will limit this discussion to a
one dimensional sine pattern with the extreme case of frequency zero. Not because other
patterns are impossible but because I use the one-dimensional sine pattern and do not see a
need to discuss the general case here.
In the extreme case of frequency zero (uniform illumination) the surface of the sample
illumination can be considered as an infinite number of point light sources with equal
intensity spread on the surface at a finite distance, as small as we wish for, under the
assumption of isotropic material. The light diffused from one source is compensated for by
other light sources around it and the surface will emit a uniform image that is different from
the projected image in intensity, due to the light absorbed in the bulk. Theoretically in semi-
infinite material with scattering and no absorption at all, the projection and the image will be
equal. Another option to have equal projection and the image is the usage of extremely high-
scattering material, this way the light has almost no penetration depth into the material.
Under this condition all the projected light is scattered from the surface theoretically without
any absorption.
With these two extreme cases (point source and uniform illumination) it is easy to move to
the next step and think of a one-dimensional sine function. In one dimension the projection
is uniform, in theory to infinity. Let us say for this discussion that this is the x-axis, and in
the other dimension there is an assembly of point sources with intensity that is modified
periodically to match the sine function, let's say for this discussion that this is the y-axis.
(figure 2.4.1)
Therefore on the x-axis the points compensate for the light propagation in this direction but
on the y-axis there is light that is re-emitted from the material after propagating from its
entry point. This combination will look like "blurring" of the sine function. Evaluation of
this "blurring" effect is quantified by two parameters, the offset, which is called the DC
value and the amplitude, which is called the AC value. To remove any doubt, it is only an
analogy and no electrical current is involved. Every image that is captured is the sum of the
DC and AC components so mathematically it is possible to represent every image in the
following way: (if the phase of the sine wave is neglected)
I = I34 + I64 (2.4.1)
From every three points on the sine curve, with a phase shift of 2π/3, it is possible to obtain
the AC and DC value are given by the following equations:
M648f:; =
<%
=
> I − I # + I − I=# + I= − I # ?
@
A%
(2.4.2)
M34 =
=
I + I + I=# (2.4.3)
12. 12
Where MAC is the measured AC value (the amplitude), MDC is the DC value (offset) and I1,
I2, I3 represent the IAC values in three different positions along the curve (the y axis) with a
2π 3⁄ phase difference between the positions. It is important to know that MDC is not
dependent on the spatial frequency and therefore can be produced from the image of the
uniform illumination projection and from any other image of frequency projection. One
more important conclusion is that the resolution for the AC value is also frequency
dependent. The higher the frequency is the distance over the x-axis between the three
positions that are used is smaller. If all three points are taken from the same image the
distance between the first and the third point will be 3/4 of the wavelangth, which grow
shorter as the frequency goes higher. This is not preferable for a homogeneous sample but
averages optical properties over space for non-homogeneous samples. This has a very
elegant solution. By shifting the projection by a phase of 2π 3⁄ and taking three images of
the sample it is possible to obtain the information from a single point, or pixel, depending on
camera limitations.
Figure 2.4.1: Illustration of the projection on top as 2D (x-axis and y-axis) on the sample surface
and at the bottom the intensity change in the x-axis (spatial axis).
13. 13
It does not directly determine the spatial resolution due to the fact that the optical properties
are not fully local, but involve the volume in which the light is propagated through before re-
emission. Here will be a good place to mention that the higher the frequency we use, the
more information we obtain is of a thinner layer from the surface. This is due to the fact that
the higher the frequency, the shorter the distance the photon needs to propagate through the
material between the points of maximum projection intensity and the minimum projection
intensity. Intuitively it is possible to understand that the photons that propagate a long
distance in the material statistically average the maximums and minimums and therefore
contribute to the DC value, and only the photons that propagate a short distance and
therefore move through a thinner layer, contribute to the AC value of high spatial frequency.
Using this method it is possible to obtain from every image two points along the SFD curve.
These two points are enough to find a theoretical curve in my case from the RTE and extract
the optical coefficients µa and µs' from it (solution for the inverse problem). Although it is
possible to use only two points, I prefer to use more frequencies in order to have a better fit
and more error compensation.
2.5. Fluorescence background
Fluorescence is an effect of a molecule that involves the absorption of a photon and
conversion of its energy to take an electron from a low energetic state to a higher state. The
Figure 2.4.3: Illustration of the three phase projection. When taking the three images the sine
function have three different values for the same spatial position. These three values have the 2π/3
phase shift and are used in equation 2.4.2 and equation 2.4.3 to calculate the DC and AC
values.
Figure 2.4.2: Illustration of the three phase projection on top as 2D (x-axis and y-axis) on the
sample surface and at the bottom the intensity change in the x-axis (spatial axis). From left to right
there the three projection (phase=0, Phase=2π/3 and Phase=4π/3), an image is taken for every one
of the phases. (The axis are the same as in figure 2.4.1)
14. 14
higher energetic state is an unstable state and therefore after a short time, the electron drops
back to the ground energetic state. This electron transfer requires that the excess energy of
the electron be converted through non-radiative losses and spontaneous emission of a photon
with lower energy than that of the photon that was absorbed. This is called a Stokes shift.
In bigger more complex molecules there are more options for the electrons to drop to lower
energy bands. We observe a continuous spectrum that has a high probability in a specific
wavelength, therefore a peak is observed in the spectrum for that wavelength. Another
conclusion that can be made is that the highest wavelength of light emitting corresponds to
the lowest energy gap between the ground energy level and the next energy band.
Figure 2.5.1: Typical fluorescence spectrum. In the image the excitation wavelength and the
emission peak are marked, and between these two, the Stokes shift. It is also visible that unlike the
quantum description the spectrum is not quantized but continues with decay towards a longer
wavelength (lower energies).
15. In this work I used rhodamine 6G
made from 65 atoms with the formula C
rhodamine 6G is dissolvable in water, butanol, ethanol, methanol, propanol, isopropanol,
ethoxyethoxy ethanol and others.
changing due to stress,
Figure 2.5.2: Example for
transfers in a molecule, with radiative
i – photon absorption
ii – fluorescence (emission)
iii – internal conversion
S – singlet state
15
rhodamine 6G as a fluorophore. Rhodamine 6G is an
made from 65 atoms with the formula C28H31N2O3Cl. It is strong red pigment. The
dissolvable in water, butanol, ethanol, methanol, propanol, isopropanol,
hoxyethoxy ethanol and others. The energy states of a molecule in solvent or in resin are
changing due to stress, pressure and bonds to the environment.
Figure 2.5.3: Rhodamine 6G molecule
schematic drawing: The formula is
C28H31N2O3Cl. Rhodamine 6G is a relatively
big molecule with aromatic rings. The aromatic
rings show that the molecule has more than
one configuration for the ground energetic
state and it shifts between these configurations.
(The image was produced with “online
chemical editor, Marvinsketch”)
: Example for a Jablonski diagram, which is a schematic representation of the
transfers in a molecule, with radiative and non-radiative transitions.
photon absorption
fluorescence (emission)
internal conversion
singlet state
an organic molecule
It is strong red pigment. The
dissolvable in water, butanol, ethanol, methanol, propanol, isopropanol,
The energy states of a molecule in solvent or in resin are
schematic representation of the energy
16. 16
3. Methods and Experimental Setup.
3.1. Experimental setup.
The experimental system is made in order to project a sine function. Different
frequencies regarding one spatial axis and uniform projection on the second axis
create an image of the sine wave on the sample surface. The scattered and the
remitting light is then detected with a camera and analyzed.
The components of the system are:
• Halogen lamp
• Filter wheel for the incident light
• Two optical arrays of lenses
• Mirrors
• Digital Micromirror Device (DMD)
• Charge Coupled Device (CCD) camera
• Computer
The source of light is a halogen lamp the light is white and non-coherent, the
intensity is changing with wavelength and also periodically in time due to the AC
voltage of the power supply. Since the frequency of this voltage change is in 50 Hz
for a camera exposure time of more than 0.2 sec it is possible to disregard this
change. The incident light wavelength has been chosen using the filter wheel. The
filter wheel in this setup has 8 positions and for this experiment only 3 position are
being used, one for shutter, the second for the excitation wavelength of 532 nm and
the third for the emission peak wavelength of 550 nm. The light source is coupled to
the rest of the system with an optical bundle at the end of which the filter wheel is
positioned.
After the filter wheel, the light goes through a set of optical lenses. The purpose of
this array is to make the light as uniform as possible. The light is deflected with a
mirror to the DMD. The DMD element is used to produce the different frequency
and the shape of the projection. The principle by which the DMD works is by
deflecting the light in the direction of the projection or away from it. This is done
by changing the angle of the micromirror elements that it is made of. Every
micromirror is a pixel of the image. The intensity of every pixel is determined by
the amount of time the mirror is directed to reflect the light to the sample.
The light from the DMD goes to another mirror, deflecting it through the second
optical lens array. The purpose of this array is to focus the image on the surface of
the sample. It is a challenge because of the oblique projection angle. The angle
brings about a different distance between the lenses and the surface. The oblique
angle is necessary in order to prevent the direct reflection from the surface from
reaching the camera’s angle of detection.
The camera that is being used in this setup was made for astronomical use.
Therefore it is designed for long exposure times. It is highly sensitive, as required
for astronomical observations, but not designed for short exposure times. For the
SFD, it is sufficient.
The control of the camera, DMD and the filter wheel is done by computer and
software that was made to control the setup and to do part of the image analysis.
17. Figure 3.1.1: On top a schematic description
1. Halogen lamp
2. Optical bundle
3. Filter wheel for the incident light
4. Data and control cables
5. Optical arrays of lenses
6. Mirrors
7. DMD
17
chematic description and at the bottom an image of the experiment system setup:
3. Filter wheel for the incident light
8. Optical arrays of lenses
9. Sample
10. Detection bandpass filter
11. Camera objective
12. CCD camera
13. Computer
of the experiment system setup:
filter
18. 18
3.2. Data analysis method.
The objective of the measurement is to extract the fluorophore quantum efficiency
of the bulk as a whole and the total absorption coefficient of the bulk in the
excitation wavelength. The quantum efficiency of the bulk is defined as the ratio
between the amount of light at the excitation wavelength absorbed by the bulk and
the amount of light emitted from it as a result of fluorescence. With these two
parameters and the knowledge of the fluorophore (molar mass, density, quantum
efficiency and emission spectrum) that is being detected, we can calculate the
quantity of the fluorophore in the bulk. In order to have all of those needed
parameters, we need to set measurements and references:
i. AC reference.
ii. Collimated transmission spectrum of the filter.
iii. Fluorescence spectrum of the target fluorophore.
iv. Projection intensity measurement.
v. Spectralon reference for excitation and emission wavelength.
vi. Spectralon reference for time interpolation.
vii. Dark reference.
viii. Optical properties for excitation and emission wavelength.
ix. Fluorescence intensity measurement
i. AC reference.
The AC reference is used to correct for inaccuracy and blurring in the sinusoidal light
projection pattern. It corrects the amplitude (MAC) values of the measurements. The
projection from the DMD is not given as a clean-cut sine function that varies in
intensity from MDC plus MAC to zero (MDC minus MAC). Due to the optical lenses and
the challenges of the oblique angle of incidence, the projection is offset from zero so
that the AC reference will give the factor for the correction. The AC reference is made
by taking three phase images of aluminum producing MAC and MDC and using the ratio
MDC to MAC to correct the AC value of the measurement. I use the names DCAl and
ACAl for MDC and MAC of aluminum respectively.
Aluminum is used for this measurement since it has a very high absorption coefficient
that allows only the photons scattered from the surface level of the material to re-emit.
The image obtained is only from the surface without contribution of volume scattering.
Since the image is without contribution of light propagation through the aluminum,
MDC and MAC should be equal, but due to the challenges of the oblique projection and
the lenses, it is not. Using the ratio of MDC to MAC and multiplying it by the MAC of the
measurement corrects for this inaccuracy in the projection.
ii. Collimated transmission spectrum of the filter.
In order to quantify transmission through the filter, I use a collimated light
spectrometer. It is vital to know the transmission percentage in order to calculate the
filter factor for the normalization factor. It is also possible to have the factor as a part of
the image of the Spectralon reference for excitation and emission wavelength (chapter
3.2 v) and I do that where it is possible, but for the fluorescence measurement, it is not
applicable since the Spectralon has no fluorescence properties.
The procedure for the collimated light transmission spectrum requires taking of a
reference spectrum in order to calibrate the sensitivity level of the detector for different
wavelengths, the absorption of the media surrounding the sample and the intensity of
the light source for different wavelengths. These references with the transmission
through the sample, in this case the filter of the fluorescence emission wavelength, are
used to create a scaled transmission function. I also use a filter for the excitation
19. 19
wavelength, but this filter transmission takes care of the Spectralon reference (chapter
3.2 v), where it is needed so there is no need for it to be measured in this method.
iii. Fluorescence spectrum of the target fluorophore.
In the process I used the "Cary Eclipse" spectrometer for two ends. One is to determine
the excitation and emission wavelength that I would be using, and the second, in order
to have the emission spectrum in order to determine a factor between the amount of
light emitted and the amount of emitted light passing the detection bandpass filter.
In order to decide which wavelength to use for excitation and detection (the peak
wavelength of emission), I take 3D spectra in fluorescence mode. This technically
means that the spectrometer scans the excitation wavelength with a user-defined delta
and for every excitation wavelength, it measures the emission spectrum. This mode
gives the ability to make a 3D map (figure 3.2.1) and to easily determine the
wavelength that has the most significant fluorescence effect for the target fluorophore
(for this experiment, rhodamine G6).
In order to determine the full fluorescence emission spectrum in the chosen excitation
wavelength (in this case, 532 nm), I take the spectra in fluorescence mode once for a
sample of resin with the fluorophore and once of the resin without any added materials.
I obtain the two spectrums, comparing the intensity of the two for the excitation
wavelength (532 nm) and subtracting that from the spectrum of the resin with the
fluorophore, in order to retain only emission light intensity. The curves are shown in
figure 3.2.3.
Figure 3.2.1: 3D map of the fluorescence spectrum scanning for all excitation wavelengths
between 450 nm to 600 nm in 1 nm steps and a 5 nm slit. For each one of the steps the
spectrometer conducts a scan of the emission spectrum from 510 nm to 630 nm. The map
shows a peak of the fluorescence emission around 352 nm for excitation and 550 nm for
emission. These wavelengths were chosen to conduct the experiment in. In the map there is
also a linear line of higher light intensity. This line relates directly to scattering of the
excitation (initial) light. It is clear to see that is the line where excitation and emission are
equal.
20. 20
iv. Projection intensity measurement.
Since the halogen light source does not emit the same light intensity for all wavelengths,
the need to have the ratio between the intensity of projection in the excitation and
emission wavelengths was needed to determine the ratio of camera sensitivity. To take
this measurement, I used the UDT model S370 optometer. The measurement was taken
while uniform illumination was projected. I took ten measurements at the center of the
camera field of view and took the average for my calculations.
v. Spectralon reference for excitation and emission wavelengths.
Spectralon is a commercially available reflectance standard with well-defined reflectance
values. We make use of a Spectralon with 98.9% reflection. The Spectralon image allows
the normalization of intensities for the images and therefore absolute quantification of
the optical properties of the sample. In the Spectralon image, the factors of the projection
intensity and exposure time, camera sensitivity, solid angle of detection and filter
transmission are taken into consideration. One highly important factor the Spectralon
quantifies and allows for correction is the fact that the projection intensity differs over
the picture as it is affected by the oblique angle of projection. The angle of projection is
necessary to avoid direct reflection of the projected light from the sample to the camera.
By using the Spectralon it is possible to avoid the reflected light and correct for the
intensity difference. The Spectralon image can be mathematically described by:
I!DE = PG,I ∙ SG ∙ Ω ∙ K! ∙ e (3.2.1)
Where Pλ,t is the projection energy as a function of wavelength and exposure time, Sλ is
the sensitivity of the camera as a function of wavelength, Ω is the ratio of light captured
by the solid detection angle, Ks is the reflection of the Spectralon and e is unknown
proportional influences. Since the projection energy depends on time, it is necessary to
take images of the sample with the same exposure time of the Spectralon reference.
vi. Spectralon reference for time interpolation.
The Spectralon image depends on the exposure time and therefore when possible the
preference is to take the image of the sample with the same exposure time of the
Spectralon, though this is not always possible. In the case of the fluorescence
measurement, it is not. The exposure time needed to get good information for the
fluorescence emission is 30 seconds in this setup, but a Spectralon image of 30 seconds
will be in the range of overexposure. Therefore we need to interpolate and predict the
energy of the projection light over the exposure time of the sample. Other solutions were
considered such as taking the fluorescence image for a time shorter than 1 second, for
which it is then possible to take the Spectralon image at the same exposure time. This
solution proved possible but significantly increased the ratio of noise to signal. One more
solution that was considered is the use of a Spectralon with a lower reflection coefficient.
This was not tried, since the available Spectralons with lower coefficients are smaller in
diameter and then a large part of the image would be unusable. The extrapolation of the
energy for the images of the Spectralon leads to good experimental results, but has the
disadvantage of the added calculations and measurements that insert more error
possibilities into the system. From the possible solutions this is the one being used.
In order to make these calculations, I take images of the Spectralon from 0.2 s to 0.8 s, 7
images overall. The minimum time is 0.2 s, since the camera shows a different slope for
the curve under 0.2 s and above. The maximum time is in order to avoid overexposure.
Every image is coupled to a dark image with the same exposure time.
21. 21
vii. Dark reference.
The camera produces small currents even when exposed to darkness. This is of course
not a real signal but a systematic error in the camera’s electronic detection and reading.
This should be subtracted from the signal and for that purpose I take dark images for all
images and make this subtraction. The dark image is taken by turning the filter wheel in
front of the source to the shutter position and taking the image for the same exposure
time as the image for which the correction is intended.
viii. Optical properties for excitation and emission wavelength.
This measurement is the imaging of the sample with different spatial frequencies. For
every frequency, 3 images are taken in three phases (0, 2π/3, 4π/3). These three images
can be mathematically described by:
I!NO = PG,I ∙ SG ∙ Ω ∙ D ∙ e (3.2.2)
Where Pλ,t is the projection energy as a function of wavelength and exposure time, Sλ is
the sensitivity of the camera as a function of wavelength, Ω is the light captured by the
solid detection angle, D is the data of the reflectance signal and e is unknown
proportional influences. From the three phase images, MAC, MDC can be obtained using
the eq. (2.4.2) and eq. (2.4.3).
These images taken using one filter for the incoming light to determine the wavelength
and a filter of the same band are used in front of the camera lens. The use of a filter on
the incoming light is to determine the illumination light. The use of a filter in front of the
detector is to make sure that only the initial light is being detected. If no filter is in front
of the detector, absorption events in the bulk for this wavelength are detected as
scattering events due to fluorescence. Fluorescence affects absorption of the photon at
the excitation wavelength and its re-emission at a longer wavelength. Detection of the re-
emitted photons causes an error in the absorption and scattering coefficients.
ix. Fluorescence intensity measurement.
Taking of the fluorescence images is done while setting the filter wheel to the excitation
wavelength (532 ± 10 nm) for the incoming illumination and another filter in front of the
camera with transmission for the emission wavelength peak (550 ± 10 nm). The offset
between the filters is the "stokes shift" that was obtained in the fluorescence spectrum.
This way the excitation wavelength is screened out of the fluorescence image. For this
measurement three images are taken at the three phases (0, 2π/3, 4Q/3) and again eq.
(2.4.3) and eq. (2.4.2) are used to extract MAC and MDC.
The analysis of these measurements can be described through three procedures:
a) Determination of the optical coefficients (µa,ex, µs',ex, µa,em, µs',em).
b) Evaluation of quantum efficiency of the bulk (Ct/e).
c) Mathematical calculation of the fluorophore concentration.
a) Determination of the optical coefficients (µa,ex, µs',ex, µa,em, µs',em).
For this part of the analysis the measurements of the AC reference, Spectralon reference
for excitation and emission wavelength, and dark reference (i, v, vii, viii).
The images that were captured by the camera are part signal and part dark, that is the
dark noise coming from the electronic system and the residue light in the dark box in
which the experiment was conducted. Therefore the images of the Spectralon and all
three phase images of the sample and the AC reference need to be cleaned from that part.
This is done by subtracting from every pixel of the signal the pixel with the same matrix
coordinates in the dark references.
22. 22
After the dark reference was subtracted from the images, the three phase images of the
AC reference and of the sample were used to produce two matrices, one of the DCAl or
MDC or component, and the other of the ACAl or MAC component, respectively. DCAl and
ACAl are calculated pixel by pixel with eq. (2.4.2) and eq. (2.4.3). At the end of this
calculation we have the offset and the amplitude of the sine function for the images of
aluminum.
The ratio DCAl/ACAl will be used later to correct MAC. As mentioned in the ideal
projection optics, the projection should be the offset (DCAl) plus the sine-function with
amplitude (ACAl), where amplitude equals to the offset. In that case, the ratio DCAl to
ACAl equals one. In the current setup, the projection is DCAl value plus minus ACAl, but
DCAl is not equal to ACAl. The correction could be done simply by the ratio in the
following way:
MR64 ∙
34ST
64ST
= M64 (3.2.3)
Where MAC is the AC value after the correction. The next step of the procedure is to
normalize the values by considering the geometry of the setup, the initial light intensity,
filter transmission and camera sensitivity. All of these are taken into account in the
Spectralon image that we took as a reference. Normalizing is done by dividing the DC
and AC values by the intensity value from the Spectralon image. To explain why it is
valid, it is more intuitive to start by performing the normalization on the image and not
on the values extracted from it (MDC, MAC). Therefore I will show the mathematical
effect of the normalization on the image and then prove that it is mathematically equal to
normalization of the extracted values.
Dividing the sample image eq. (3.2.2) by the Spectralon image eq. (3.2.1):
UVWX
UVYZ[
∙ K! =
],^∙_]∙`∙3∙E
],^∙_]∙`∙aV∙E
∙ K! = D (3.2.4)
where the wavelength (λ) and the exposure time (t) is the same for the two images, all
factors cancelled out and the values are the normalized data from the image. In order to
show that mathematically, it is possible to normalize the values MDC and MAC and it will
be the same as normalizing the image. I will write eq. (2.4.2) and eq. (3.2.4) with all
images normalized and show it is possible to take the normalizing part out of the
brackets. For MAC:
M64 ∙
aV
UVYZ[
=
<%
=
bc
U<
UVYZ[
∙ K! −
U
UVYZ[
∙ K!d + c
U
UVYZ[
∙ K! −
U$
UVYZ[
∙ K!d + c
U$
UVYZ[
∙ K! −
U<
UVYZ[
∙ K!d e
@
A%
(3.2.5)
⇔ M64 ∙
aV
UVYZ[
=
<%
=
bg
aV
UVYZ[
h I − I # + g
aV
UVYZ[
h I − I=# + g
aV
UVYZ[
h I= − I # e
@
A%
(3.2.6)
⇔ M64 ∙
aV
UVYZ[
=
<%
=
bg
aV
UVYZ[
h (I − I ) + (I − I=) + (I= − I ) #e
@
A%
(3.2.7)
⇔ M64 ∙
aV
UVYZ[
=
aV
UVYZ[
∙
<%
=
> I − I # + I − I=# + I= − I # ?
@
A%
(3.2.8)
For MDC:
M34 ∙
aV
UVYZ[
=
=
c
U<
UVYZ[
∙ K! +
U
UVYZ[
∙ K! +
U$
UVYZ[
∙ K!d (3.2.9)
23. 23
⇔ M34 ∙
aV
UVYZ[
=
=
∙
aV
UVYZ[
I + I + I=# (3.2.10)
The entire calculation is done for every pixel of the matrix so the information is
preserved with all the details that the setup allows. If the sample is
homogeneous, all pixels should have the same value. Of course due to errors of
measurement, that will be discussed in a specific section (chapter 3.3), that does
not occur. In order to minimize the effect of the errors but still avoid the
borders, for its errors, an average over the area in the middle of the sample is
taken. In case of a non-homogeneous sample there must be a compromise
between averaging out the noise and errors to resolution that needs to be taken
into account. In this work only homogeneous samples were used.
The extraction of MDC and MAC from the image or images gives the DC value
and AC value for every frequency. The experimental points are drawn on a
graph of SFD reflectance versus spatial frequency. A theoretical curve of the
RTE solution is fitted to the experimental SFD curve and thereby the optical
coefficients (µa and µs') of the sample are extracted.
24. 24
Figure 3.2.2: Summary of the determination process of the optical coefficients (µa,ex, µs',ex, µa,em, µs',em) as a
flowchart. In order to separate measurements from mathematical manipulations, the measurements are
marked in double frame.
Yes
Taking AC
reference images
in 3 phases:
0, 2π/3, 4π/3
Taking Dark
reference images
I!NO = PG,I ∙ SG ∙ Ω ∙ D ∙ e
Taking sample images for optical
properties analysis in 3 phases:
0, 2π/3, 4π/3
I!DE = PG,I ∙ SG ∙ Ω ∙ K! ∙ e
Taking Spectralon reference
Reduction of the dark images from
the other images
Generating MRAC and MRDC from the 3
phase images of the sample, using
eq. (2.4.2) and eq. (2.4.3)
Reduction of the
dark images from
the other images
Reduction of the dark images
from the other images
MR64 ∙
DC6j
AC6j
= M64
Correcting MRAC by using the AC
reference (aluminum)
M64
I!DE
∙ K! ,
M34
I!DE
∙ K!
Normalizing of MAC and MDC using
the Spectralon image for every pixel
Is the sample
homogeneous?
Mlm' , Ml34
Averaging over the
sample pixels
Drawing of SFD curve from the
images of different frequencies
Fitting to theoretical curve of RTE
Extracting µa(λ) and µs'(λ) From the
RTE
Taking Dark
reference images
Taking Dark
reference images
No
25. 25
b) Evaluation of the quantum efficiency of the bulk (Ct/e).
In order to quantify the fluorophore in the bulk there is a need to differentiate
between the absorption coefficient of the fluorophore and of the rest of the bulk
materials. It is possible to do so with the ratio between the amount of light
absorbed to the amount of light emitted as a result of the fluorophore in the
sample. This ratio will be named here the of quantum efficiency of the bulk
(Ct/e).
For this part of the analysis, the measurements of the AC reference, the
collimated transmission spectrum of the filter, fluorescence spectrum of the
target fluorophore, the illumination energy measurement, Spectralon reference
for time interpolation, and the dark reference and fluorescence intensity
measurement are needed (i, ii, iii, iv, vi, vii, ix).
Similarly to the evaluation of the optical coefficients (chapter 3.3 a.), the
measurement images should be corrected to avoid dark noise and the amplitude
(AC value) variances due to electronic noise, residual light and the projection
errors.
Added to these corrections is the need to create a reference image in order to
scale the values of the fluorescence intensity measurement. In the measurement
of the optical parameters, we use for this end the Spectralon image. In this
context, a number of challenges need to be overcome. These challenges arise
from the fact that the initial light and the detected light are at different
wavelengths. Moreover not all intensity and wavelengths of the fluorophore
emission pass through the filter that was installed in the current experimental
setup.
As shown before, the Spectralon image is a combination of the energy of the
projection light, camera sensitivity as a function of wavelength, the solid angle
of the aperture, the Spectralon reflectance coefficient and unknown proportional
influences (see eq. 3.2.1). There is a need to build a reference that will give all of
these parameters respective to the right wavelength. The mathematical
description of the transformation reference is:
IEn,I →EO,Ip
= PEn,Ip
∙ SEO ∙ Ω ∙ K! ∙ e (3.2.11)
Where PEn,Ip
is the energy of the projected light for the exposure time of the
sample and the excitation wavelength Sem is the camera sensitivity for the
emission wavelength, Ω is the light captured by the solid detection angle, Ks is the
Spectralon reflectivity coefficient and e is the factor of other systematic errors.
In order to make this matrix, there is a need for the information that allows the
transformation in time for the energy, and in wavelength for the sensitivity.
The sensitivity is calculated as a ratio. The idea of taking a ratio and not the
absolute value was decided upon in order to have the smallest errors possible.
By division of the two measurements there is a cancellation of systematic
errors. This factor is made out of the Spectralon image of the excitation
wavelength and the Spectralon image of the emission wavelength. I prefer to
take the two images with the same exposure time, but it is possible to take them
with different exposure times, as long as the times are known. In addition to the
Spectralon images, there is a need to know the intensity of light projection for
the two wavelengths. This information is taken from measurement with an
optometer. For that measurement, a uniform projection is used and the detector
is placed in the middle of the camera view. The detector has a 5 mm active
diameter. The intensity measurement is an average over the detector area and
the "uniform" projection has a different intensity because of the oblique angle.
26. 26
The combination of the two leads to the absolute measurement of intensities
being incorrect for every position over the image, but the ratio is assumed to be
correct. Using (eq. 3.2.1) of the Spectralon mathematical description and
intensity and time measurements, the camera sensitivity ratio between the two
wavelengths can be calculated in this way:
UZq
UZX
=
Zq,^∙_Zq∙`∙aV∙E
ZX,^∙_ZX∙`∙aV∙E
=
Zq,^∙_Zq
ZX,^∙_ZX
(3.2.12)
Sr ≡
_Zq
_ZX
=
UZq
UZX
∙
s ZX∙∆IZX
s Zq∙∆IZq
(3.2.13)
Where Sex and Sem are the camera sensitivity for excitation and emission
wavelengths respectively, Iex and Iem are the Spectralon images respectively, Pex
and Pem are the intensity of the excitation and emission wavelengths
respectively, and ∆tex and ∆tem are the exposure times of the Spectralon image
for the excitation and emission wavelengths respectively.
The correction for the energy of the projection light is calculated from a set of
images taken on Spectralon at different exposure times between 0.2 and 0.8
seconds. This time interval was chosen for the measurements in light of two
reasons. The low time limit was set since the camera has a different responsive
slope to exposure times from 0 to 0.1 seconds and exposure time above 0.2
seconds. The high limit was set since the higher exposure time for these
Spectralon images was above the limit of what was defined as overexposure.
Seven images were used to extrapolate the energy expected for the exposure
time of the fluorescence measurement.
The dark reference was subtracted from every image and a linear fit was made
to find the relation between energy for every pixel in relation to the time of
exposure. The fit produced the slope and the offset of the closest linear line
possible for the measurement. The offset was then subtracted from the
Spectralon images. This manipulation gives a proportionality relation as the
time-dependence reference. This allows for the use of similar triangles ratio to
determine the extrapolation of the line to the exposure time for the fluorophore
intensity measurement. It can be justified for two reasons. First the energy that
the camera detected for an exposure time of zero should of course be zero.
Second that when taking the offset we interpolate a parallel line to the original
linear line. The longer the integration time, the more negligible is the offset. In
this case it will be 0.1% of the size of the signal.
The last part of the transformation reference that needs to be calculated is the
transmission factor for the fluorescence emission through the filter. In order to
calculate this factor, the area under the curve of the fluorescence spectrum of
the target fluorophore is divided by the area of the same curve multiplied by the
transmission curve of the filter that was obtained with the collimated light
spectrometer (figure 3.2.3).
27. 27
As shown before, the spectrometer curve of the sample with the fluorophore
contains a part related to the scattering of the initial wavelength. This effect is
cleaned out using a spectrum measurement of a resin without the fluorophore.
The curve of the resin is scaled to the same level of the fluorescence curve at
the excitation wavelength (532 nm), and subtracted from the fluorescence curve.
This curve is multiplied by the curve of the transmission percentage through the
filter as a function of the wavelength. Both curves are discrete and therefore the
area of the curves is calculated using the Riemann summation. These three
components come together to fabricate a correction matrix that takes into
account the filter, the time change and the different sensitivity of the camera to
the different wavelengths. A mathematical description of the process can be
written as follows:
From the proportionality between time and energy of projected light detected,
we obtain:
Ip
Iu
=
Zq,^p
Zq,^u
⇒ PEn,Ip
=
Ip
Iu
PEn,Iu
(3.2.14)
Taking a Spectralon image of ti and at excitation wavelength (in order to have a
shorter notation, all non-wavelength or time-dependent factors will be included
in B),
Figure 3.2.3: Area comparison of the fluorescence spectrum of the area under the
curve of the convolution between the filter transmission and the fluorescence
spectrum. The area is taken only for a wavelength bigger than the initial wavelength
(532 nm). The intensity before the initial wavelength is assumed to be reverse stokes
shift from interaction with electrons during aromatic transition. The comparison
shows that only 13.2% of the emitted light pass the filter.
28. 28
IEn,Iu
= PEn,Iu
∙ SEn ∙ B (3.2.15)
Then both sides of the equation are multiplied by the time proportion,
Ip
Iu
IEn,Iu
=
Ip
Iu
PEn,Iu
∙ SEn ∙ B (3.2.16)
⇔
Ip
Iu
IEn,Iu
= PEn,Ip
∙ SEn ∙ B (3.2.17)
In order to have a more accurate interpolation, an average of all time-reference
pictures is taken,
x
tz
t{
IEn,Iu
= x PlEn,Ip
∙ SEn ∙ C
|
{}
|
{}
= W ∙ PlEn,Ip
∙ SEn ∙ B
(3.2.18)
⇔
tz
W
x
1
t{
IEn,Iu
=
|
{}
PlEn,Ip
∙ SEn ∙ B
(3.2.19)
This process allows for the time correction. In the next phase, division of both
equation sides by the ratio Sr is done to correct for the sensitivity change:
tz
Sr ∙ W
x
1
t{
IEn,Iu
=
|
{}
PlEn,Ip
∙
1
Sr
SEn ∙ B = PlEn,Ip
∙ SEO ∙ B
(3.2.20)
The last phase takes into account the transmission factor of the filter,
fEO ∙ tz
Sr ∙ W
x
1
t{
IEn,Iu
=
|
{}
PlEn,Ip
∙ SEO ∙ fEO ∙ B
(3.2.21)
Therefore the transformation reference is:
IEn,I →EO,Ip
=
fEO ∙ tz
Sr ∙ W
x
1
t{
IEn,Iu
|
{}
(3.2.22)
Now after the reference image is available, the next phase is to take the three
phase images of the fluorescence emission of the samples. Taking of the images
is done with the filter wheel for the incoming light set for the chosen excitation
wavelength (532 nm) and a filter is put in front of the camera lens (550 nm).
The dark images are reduced from all the sample images and for every
frequency MRDC and MRAC are extracted with (eq. 2.4.2) and (eq. 2.4.3), as it was
done for the evaluation of the optical coefficients. The ratio DCAl/ACAl is used
to correct MR64. Normalization of MR34 and MR64 is done with the transformation
reference that was calculated before (eq. 3.2.22). Normalization is done by
dividing the image by the transformation reference and multiplying it by the
reflection factor of the Spectralon Ks, as follows:
29. 29
MR34 ∙
aV
Iex,t0→em,tN
= M34 (3.2.23)
MR64 ∙
aV
Iex,t0→em,tN
= M64 (3.2.24)
All of the calculations are done for every pixel of the matrix so the information
is preserved with all the details that the setup allows. If the sample is
homogeneous all pixels should have the same value. Of course due to errors of
measurement that will be discussed in a specific section (chapter 3.3), this does
not occur. In order to minimize the effect of the errors, but still avoid the
borders for their errors, the average over the area in the middle of the sample is
taken. In case of a non-homogeneous sample, there must be a compromise
between averaging out the noise and errors and resolution that needs to be taken
into account. In this work only homogeneous samples were used.
The extraction of MDC and MAC from the image or images gives the DC value
and AC value for every frequency. The experimental points are drawn on a
graph of SFD reflection versus the spatial frequency. The optical coefficients
that were obtained in the first part of the process (chapter 3.2 a.) are used as
parameters in the solution of the diffusion equation for the fluorophore. The
solution assumes a quantum efficiency of one. There is a difference in intensity
between the theoretical SFD curve that is the solution of the diffusion equation
and the curve of the experimental results. A fit is made between the two by
scaling down the theoretical curve to the experimental one. The factor by which
the theoretical curve is multiplied should be equal to the effective quantum
efficiency of the bulk, Ct/e.
30. 30
Figure 3.2.4: Summary of the process to create the transformation matrix (IEn,I →EO,Ip
) for Spectralon
image. It is the first part of the evaluation of quantum efficiency of the bulk (Ct/e). In order to separate
measurements from mathematical manipulations, the measurements are marked in a double frame.
Taking AC
reference images
in 3 phases:
0, 2π/3, 4π/3 I!DE = PsG,I ∙ SG ∙ Ω ∙ K! ∙ Δt ∙ e
Taking Spectralon reference
and dark images from ∆t=0.2
sec to ∆t=0.8 sec
Reduction of the
dark images from
the other Images
Reduction of the dark images
from the other Images
Taking dark
reference images
PsEn , PsEO
Taking illumination intensity
with optometer at the excitation
and emission peak wavelengths
Sr =
SEn
SEO
=
I!DE ,En
I!DE ,EO
∙
PsEO
PsEn
∙
ΔtEO
ΔtEn
Calculating the camera
sensitivity ratio between
excitation and emission
wavelengths:
Fit of a linear line to the
intensity vs. time and
reduction of the offset from
the signal images
Extrapolate from every signal
matrix the expected intensity
in time of the fluorescence
image and average the resultfEO
Finding the transfer
coefficient of the
filter
IEn,I →EO,Ip
=
fEO ∙ tz
Sr ∙ W
x
1
t{
IEn,Iu
|
{}
= PlEn ∙ SEO ∙ fEO ∙ C
Creating the correction matrix for the fluorescence images:
31. 31
Figure 3.2.5: Summary of the process of the evaluation of the quantum efficiency of the bulk (Ct/e). In order
to separate measurements from mathematical manipulations, the measurements are marked in double frame.
Yes
I!NO = PG,I ∙ SG ∙ Ω ∙ D ∙ e
Taking sample images of optical
properties analysis in 3 phases:
0, 2π/3, 4π/3
Reduction of the dark images
from the other images
Generating MAC and MDC from
the 3 phase images of the
sample, using eq. 2.3.2 and
eq. 2.3.4
MR64 ∙
DC6j
AC6j
= M64
Correcting MRAC by using the AC
reference (aluminum)
M64
IEn,I →EO,Ip
∙ K! ,
M34
IEn,I →EO,Ip
∙ K!
Normalizing of MAC and MDC using
the Spectralon image for every pixel
Is the sample
homogeneous?
Mlm' , Ml34
Averaging over the
sample pixels
Drawing of SFD curve from the
images of different frequencies
Scaling the theoretical curve to the experimental curve. The
scaling factor is the effective quantum efficiency of the bulk
(Ct/e).
Plotting theoretical diffusion equation
curve for fluorescence with quantum
efficiency 1, Cq=1, and the optical
coefficients that were obtained in the
first part of the process
(chapter 3.2 a).
Taking dark
reference images
No
IEn,I →EO,Ip
=
fEO ∙ tz
Sr ∙ W
x
1
t{
IEn,Iu
|
{}
= PlEn ∙ SEO ∙ fEO ∙ C
Correction matrix for the fluorescence images:
Figure 3.2.4 shows the way to create this matrix
32. 32
c) Mathematical calculation of the fluorophore concentration.
The measurement produced the quantum efficiency of the bulk and in order to calculate
the amount of the fluorophore material in the bulk, three relations should be used:
The quantum efficiency of the bulk in terms of the absorption coefficients in the bulk and
the quantum efficiency of the fluorophore itself:
CI
E% =
ƒW„∙4…
ƒW„∙4… ƒW†
(3.2.25)
where µaf is the absorption coefficient of the fluorophore, µar is the absorption coefficient
of the rest of the components of the bulk, and Cq is the quantum efficiency of the
fluorophore.
The total absorption coefficient of the bulk of the sum of the different materials in the
bulk:
μNI = μNr + μN‡ (3.2.26)
where µat is the absorption coefficient of the all bulk.
The relation between the absorption coefficient of the fluorescence part and the amount
of fluorophore is:
μN‡ = f ∙ σN‰! (3.2.27)
where f is the concentration of the fluorophore in units of mm-3
, and σabs is the absorption
effective cross-section for the fluorophore absorption in units of mm2
.
In (eq. 3.2.25) and (eq. 3.2.26), all variables are known from the measurement except
for µaf and µar. µaf is the variable that is needed for calculating the amount of fluorophore
in the bulk. The manipulation of these equations in order to extract µaf is, starting with
(eq. 3.2.25):
CI
E% 8μN‡ ∙ CŠ + μNr; = μN‡ ∙ CŠ (3.2.28)
⇔ CI
E% 8μN‡ ∙ CŠ + μNr; − μN‡ ∙ CŠ = 0 (3.2.29)
Exchanging of µar, with μNI − μN‡ using (eq. 3.2.26)
CI
E% 8μN‡ ∙ CŠ + μNI − μN‡; − μN‡ ∙ CŠ = 0 (3.2.30)
CI
E% ‹μN‡8CŠ − 1; + μNIŒ − μN‡ ∙ CŠ = 0 (3.2.31)
⇔ CI
E% ∙ μN‡8CŠ − 1; + CI
E% ∙ μNI − μN‡ ∙ CŠ = 0 (3.2.32)
⇔ CI
E% ∙ μN‡8CŠ − 1; − μN‡ ∙ CŠ = −CI
E% ∙ μNI (3.2.33)
⇔ μN‡ •CI
E% 8CŠ − 1; − CŠŽ = −CI
E% ∙ μNI (3.2.34)
⇔ μN‡ =
4^
Z% ∙ƒW^
4^
Z% 84… ; 4…
(3.2.35)
33. 33
where all variables are material properties of the fluorophore or ones that were obtained
in the measurement. The direct approach is to use µaf in (eq. 3.2.27) to calculate the
concentration of the fluorophore in the bulk:
f =
ƒW„
•W•V
(3.2.36)
but in order to show that the method is working and it is possible to calculate the
fluorophore concentration using the measurement data, it is possible to do the following:
σN‰! =
ƒW„
‡
(3.2.37)
The effective cross-section for the fluorophore absorption is constant. Therefore if by
substituting µaf with the result of the measurement and f with the planned construction of
the sample, (eq. 3.2.31) should reach a constant result.
3.3. Expected measurement error.
In this experiment there are three categories of errors expected. One is errors related
to theoretical assumptions [8]. The second is errors related to the experimental
parameters [8]. The third is errors related to the sample preparation.
The data analysis assumption of the scattering function is being made. The choice
of wrong phase function (p(θ)) can lead to errors, especially in the high frequencies.
Errors related to the analysis assumptions result from the fitting to the diffusion
theory, since this is an approximation to the solution of the RTE and is valid only to
some extent as mentioned in chapter 2.1. Therefore it contains an error, depending
on the µa and µs' values. Graphs connecting the values of these parameters to the
size of the error can be found in "sources of errors in spatial frequency domain
imaging of scattering media" [8] section 2.2.
The second category of errors is the errors that occur due to the experimental setup.
The boundary related to the sample size or the size of the projection area is cause
for error. It was explained in chapter 2.2 that light propagating from one point is
being compensated for by light from the sources around it, but at the boundary the
symmetry of that effect is broken. This is a cause of error when coming closer to a
boundary. The distance from the boundary needed to converge in to 1% error or less
is dependent on the optical coefficients.
The CCD camera that is used outperforms the spatial resolution of the SFD, since it
depends on the official coefficient of the sample. It makes sense to average over a
number of pixels before the computation of the AC value using (Eq. 2.4.2). This
way the size of electronic noises is averaged out. This is a cause for another error
called binning error, which is effective only for frequencies different from zero.
The binning of 8 pixels raises an error of less than 1.4%. That is relatively small
and therefore binning has its benefits, as long as it is kept small. The setting of the
height is also a factor that can bring error into the system. For example, an error
calculation of 1 mm deviation from a 20 cm distance between the sample and the
camera leads to a 1% error for the optical coefficients.
The accuracy of the spatial frequency projection is highly important for the
accuracy of the optical coefficients calculation. The ratio between errors in the
projection to errors in the optical coefficients is linear for calculations made from
one spatial frequency.
The third category of errors is the errors that occur due to the sample preparation.
During the preparation, there is an error in the weight of components, which was
kept under 0.5%. The particles of the fluorophore and of the scatterer may be
creating clusters. If it so in these areas, the assumption of independent interaction is
34. 34
not valid. There is also concern that the hardener of the resin is aggressive to the
fluorophore and some of the fluorophore molecules are destroyed. It may be reason
for a different amount of fluorophore in the sample than the one that was planned.
35. 35
4. Results and Discussion.
In this chapter I will present the results from measurements of 5 resin phantoms with different
weight percentages of rhodamine 6G:
Phantom #1 - 0.02e-3 g/g of rhodamine 6G
Phantom #2 - 0.06e-3 g/g of rhodamine 6G
Phantom #3 - 0.01e-3 g/g of rhodamine 6G
Phantom #4 - 0.18e-3 g/g of rhodamine 6G
Phantom #5 - 0.26e-3 g/g of rhodamine 6G
All phantoms contain the same amount of titanium dioxide as a scatterer and no absorbers except
for the neutral absorption of the resin and the absorption of the rhodamine 6G.
As it was explained in the data analysis method (chapter 3.2), there are three parts to the
measurement and analysis:
a) Determination of the optical coefficients (µa,ex, µ's,ex, µa,em, µ's,em).
b) Evaluation of the quantum efficiency (Ct/e).
c) Mathematical calculation of the fluorophore concentration.
I will present the results in the same order.
a) Determination of the optical coefficients (µa,ex, µ's,ex, µa,em, µ's,em).
In order to evaluate the optical coefficients, the SFD curves are extracted from the images of
532 nm and 550 nm. The curves can be seen in figure 4.0.2 and figure 4.0.3 respectively
Figure 4.0.1: The five phantoms that where measured in
the experiment lowest to highest concentration from
right to left
36. 36
Figure 4.0.3: The graph shows the measurements of five phantoms with SFD for the
emission wavelength where the markers indicate the actual results obtained by (eq. 2.4.2)
and (eq. 2.4.3). The dashed line is only interpolation from the point of measurement and
should be used as help to follow the results related to the same phantom.
Figure 4.0.2: The graph shows the measurements of five phantoms with SFD for the
excitation wavelength where the markers indicate the actual results obtained by (eq. 2.4.2)
and (eq. 2.4.3). The dashed line is only interpolation from the point of measurement and
should be used as help to follow the results related to the same phantom.
37. 37
Fitting of the MDC and MAC (SFD curve) that were obtained from the images to RTE
solutions produce the following result for the optical coefficients (table 4.0.1):
Number
of
phantom
Concentration
of rhodamine
6G
µa (λ=532 nm) µ's (λ=532nm)
Value Error Error % Value Error Error %
g/g mm-1
mm-1
% mm-1
mm-1
%
1 2.00E-05 0.041 ±0.003 7.83 2.20 ±0.08 3.47
2 6.00E-05 0.124 ±0.008 6.34 2.22 ±0.09 4.19
3 1.00E-04 0.23 ±0.01 6.17 2.3 ±0.1 4.81
4 1.80E-04 0.41 ±0.04 10.30 2.3 ±0.2 8.95
5 2.60E-04 0.55 ±0.07 12.51 2.4 ±0.3 11.34
Number
of
phantom
Concentration
of rhodamine
6G
µa (λ=550 nm) µ's (λ=550 nm)
Value Error Error % Value Error Error %
g/g mm-1
mm-1
% mm-1
mm-1
%
1 2.00E-05 0.024 ±0.002 10.42 2.12 ±0.08 3.64
2 6.00E-05 0.070 ±0.005 6.46 2.10 ±0.07 3.49
3 1.00E-04 0.125 ±0.009 7.59 2.1 ±0.1 4.99
4 1.80E-04 0.22 ±0.01 6.63 2.1 ±0.1 5.10
5 2.60E-04 0.31 ±0.03 9.49 2.3 ±0.2 7.84
The results for the optical coefficients show an increase in absorption coefficients (µa)
for the expiation wavelength (532 nm) and for the emission wavelength (550 nm), this is
predictable for the increase in the fluorophore. It was expected since the screening of
the re-emitted with the filters. In the phantoms of this experiment, except for the
relatively minor absorption of the resin, the fluorophore is the only absorber in the
phantoms. It can be shown that for absorption coefficients that the absorption of the
resin was subtracted from, there is a direct linear correlation between the concentration
of fluorophore and the absorption coefficients. The results can be seen in table 2 and
figure 4.0.4. It is also shown that the scattering coefficient is kept constant under the
error assumed in the measurement. IT is expected since the amount of scattering
particles was constant between all phantoms.
Table 4.0.1: The table gathers the optical coefficients and error assessment for the five
phantoms that were tested for the excitation wavelength (532 nm) and the emission
wavelength (550 nm). The measurement was taking with objective filters 532 nm and 550
nm respectively. It is shown the absorption coefficient is increasing with the rise of the
rhodamine 6G concentrations in the phantom, and that the scattering coefficients stay the
same in the range of the measurement error. The error in the table is the errors that rise
from the fitting process and it is the derivative of the fit function in the axis of a variable.
On top of this error a 10% error is estimated occur from the setup (chapter 3.2)
38. 38
Number
of
phantom
Concentration
of rhodamine
6G
µa 532 nm
Concentration
of Rhodamine
6G normalize
µa 532 nm
Ex.
value
Ex. value
minus
resin
Ratio of
resin asb
for the
total
Ex value
minus
resin
normalize
g/g mm^-1 mm^-1 %
1 2.00E-05 0.008 0.006 27.5% 0.1 0.06
2 6.00E-05 0.024 0.022 9.2% 0.2 0.21
3 1.00E-04 0.04 0.038 5.5% 0.4 0.37
4 1.80E-04 0.07 0.070 3.1% 0.7 0.69
5 2.60E-04 0.10 0.102 2.1% 1.0 1.00
b) Evaluation of the quantum efficiency (Ct/e).
As a proportion to the fluorescence emission, SFD intensity measurement, a correction
matrix was fabricated using the formula shown in chapter 3.2 b (eq. 3.2.21).
y = 1.02x - 0.02
R² = 1.00
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.0 0.2 0.4 0.6 0.8 1.0 1.2
ExperimantalValueminusresin.
(normalize)
Concentrtion of rhodamine 6G normalized
Linear fit to the normalized concentrations
and absorption coefficients
Table 4.0.2: The table shows the ratio between the absorption coefficients of the bulk
and of the resin. Also the normalized values of the absorption coefficient minus
the resin part and the fluorophore concentration.
Figure 4.0.4: Linear fit on the normalized values of the normalized rhodamine 6G
concentration and the normalized values of the absorption coefficient of the bulk minus
the absorption coefficient of the resin. Since the rhodamine 6G is the only absorber added,
it can be assumed that this is the absorption coefficient of the rhodamine. The linear fit
shows very good correlation and it shows strong dependence of the absorption coefficient
on the fluorophore concentration for these phantoms.
39. 39
With this matrix as reference, the flowing SFD curves were obtained for the fluorescence
emission of the five phantoms figure 4.0.5.
The curve that is shown in figure 4.0.5, needs to be fitted to the theoretical curve of the
diffusion equation solution for the fluorescence. The curve is made with the optical
coefficients that were obtained in the previous part of the experiment. The optical
coefficients were used as the parameter for the diffusion equation solution in addition
the optical index of the resin at 532 nm (n=1.5585) and quantum efficiency of the bulk
was considered to be 1.
Figure 4.0.5: The graph shows the measurements of five phantoms with SFD for the
emission intensity of the fluorophore. The markers indicate the actual results obtained by
(eq. 2.4.2) and (eq. 2.4.3). The dashed line is only interpolation from the point of
measurement and should be used as help to follow the results related to the same phantom.
40. 40
The idea of the fitting of the theoretical curves to the curves that were obtained in
the experiment is shown in figure 4.0.5.
Figure 4.0.6: The graph shows the theoretical curves for the fluorescence with the parameters of the
five phantoms as were obtained in the previous part of the experiment.
41. 41
This fitting process was done on every one of the results from the five phantoms and
the results shown in figure 4.0.7 and gathered in table 4.0.3.
Figure 4.0.7: The graph shows the theoretical SFD curve for the fluorescence intensity with the
parameters of the phantom as were obtained in the previous part of the experiment (the solid
line). The marks showing the experimental point that were obtained by measurements. The
dotted line is the fitted line which means: the scaling of the theoretical curve with a factor in
order to have the sum of the distance between the new (fitted) curve and the experimental results
the smallest possible. In this case the factor is 0.668 and this is the quantum efficiency of the
bulk (Ct/e).
42. 42
number
of
Phantom
concentration
of
Rhodamine
6G
Ct/e μaf σabs error
mm
-3
mm
-1
mm
2
%
1 2.9E+13 0.412 0.02 6.26E-16 40.62%
2 8.6E+13 0.659 0.08 9.86E-16 6.41%
3 1.4E+14 0.668 0.16 1.11E-15 5.47%
4 2.6E+14 0.664 0.28 1.10E-15 4.45%
5 3.7E+14 0.661 0.38 1.02E-15 3.50%
The primary objective of this thesis was to quantify the fluorophore in the bulk. In
order to do so, the absorption cross-section of the fluorophore is needed as shown in
eq. 3.2.37. The absorption cross-section is a constant of the material. It may be
changing in different solutions but in the phantoms, where its surrounding is the
Table 4.0.3: Collection of the data summary and calculations of the part c of the analysis.
Where Ct/e is the quantum efficiency of the bulk obtained by the fitting of the theoretical
SFD curve to the experimental measurements. The concentration of rhodamine 6G was
converted from mass ratio to density per volume and µaf was extracted from µat with eq.
3.2.35
Figure 4.0.7: The graph shows the theoretical SFD curves for the fluorescence intensity with the
parameters of the five phantoms as were obtained in the previous part of the experiment and fitted to
the experimental measurement (the dotted line). The marks showing the experimental point that were
obtained by measurements. In the code box, the fitting factors are written, these are the values of the
quantum efficiency of the bulk (Ct/e).
43. 43
same, it is the same. The absorption cross-section was calculated with eq. 3.2.37
and the results are in table 3. With the exception of phantom number 1, the results
have under 7% deviation from the average result (error) of the absorption cross-
section that was found for phantoms two to five. The fact that it has only a small
deviation from the average result shows that this method is working. I am assuming
that phantom number one is with too low fluorophore for our setup to detect
properly and therefore it gives a different result than the other four phantoms.
44. 44
5. Conclusions.
From the results that were shown in chapter 4 I draw the following conclusions:
This method for the quantification of the fluorescence is possible with SFD imaging. The
secondary objectives were only very partially achieved. The lowest level of fluorophore
that can be quantified with the current setup is between the concentration of 0.02 w% to
0.06 w% but no high limitation was found. The objective of the concentration resolution
detectable in this method and the current setup is also very partial. It can detect a change
of 0.04 w% in the concentration but no smaller differences of concentration were tested
and therefore I do not know if higher resolution is possible or not.
This method result is a defined number that can be match to a normal value and be
compared between patients. This is a big advantage over the fluorescence imaging
methods that are is use this days. Since in this methods the evaluation is done by the
ability of the doctor to differ between the shades of the fluorophore and the experience.
45. 45
6. Acknowledgements.
I would like to acknowledge the contribution of the ILM and the members of the
research group that I was working in and these people in particular:
Prof. Dr. Alwin Kienle, my supervisor, for the opportunity given to me to work in the
ILM and write my thesis in it, and for sharing his knowledge and experience.
Nico Bodenschatz, my guide, for his support along the way, the experimental setup and
sharing his knowledge of the SFD.
Andre Liemert, for the working solution Matlab scripts for the RTE for the non-
fluorescence and the diffusion equation for the fluorescence part.
Arnd Brandes, Philipp Krauter, Emanuel Simon for sharing ideas, discussions,
suggestions and general support.
Levi Klempner for language editing of the thesis.
46. 46
7. References.
[1] Alfano, R., & Pu, Y. (2013). Optical biopsy for cancer detection. In H. Jelinkova, Lasers for
medical applications (pp. 325 - 367). Woodhead Publishing Limited.
[2] Cancer Facts & Figures 2014. Atlanta: American Cancer Society.
[3] Georgakoudi, I., Jacobson, B. C., & Mueller, M. G. (2002). NAD(P)H and Collagen as in Vivo
Quantitative Fluorescent Biomarkers of Epithelial Precancerous Changes. Cancer Research , 683-687.
[4] Hecht, E. (2002). OPTICS. Addison Wesley.
[5] Mishchenko, M. I., Travis, L. D., & Lacis, A. A. (2006). Multiple scattering of Light by Particles,
Radiative Transfer and Choherent Backscattering. New York: NASA.
[6] Cuccia, D. J., Bevilacqua, F., Durkin, A. J., Ayers, F. R., & Tromberg, B. J. (2009). Quantitation
and mapping of tissue optical properties using modulated imaging. Journal of Biomedical Optics ,
024012-1 to 13.
[7] Bodenschatz, N., Brandes, A., Liemert, A., & Kienle, A. (2014). Sorurces of errors in spatial
frequency domain imaging of scattering media. Journal of Biomadical Optics , 071405-1 to 8.
[8] Mazhar, A. (2010). Structured illumination enhances resolution and contrast in thick tissue
fluorescence imaging. Journal of Biomedical Optics , 15(1), 010506-1 to 3.
