Download New methodology for optical sensing and analysis Jimmy Bakker

Linköping Studies in Science and Technology
Licentiate Thesis No. 1090
LiU-TEK-LIC-2004-19
New methodology
for optical sensing and analysis
Jimmy Bakker
Laboratory of Applied Optics
Department of Physics and Measurement Technology
Linköping University
SE-581 83 Linköping, Sweden
Linköping, 2004
Preface
This thesis describes the research I have done, and partly will do, during my time as
a PhD student in the laboratory of Applied Optics at Linköping University. Due to
circumstances beyond the scope of this book, this incorporates three quite different
projects. The first two, involving gas sensing and measuring on paper with
ellipsometry, have been discontinued, whereas the third one, measuring fluorescence
with a computer screen and web camera, is in full progress and will be until I complete
my studies.
Thus the purpose of this work also has several aspects. Partly, it describes
performed research and its results, as well as theoretical background. On the other
hand, it provides practical and theoretical background necessary for future work.
While the three projects are truly quite different, each of them has certain things in
common with each of the other. This is certainly also true for the necessary theory.
Two of them involve spectroscopic ellipsometry, for example, while another pair
needs knowledge of color theory, etc. This makes it impossible to separate the
projects, despite of their differences. Hopefully, these links between the different
projects, connecting the different chapters, will make this work whole and consistent
in its own way.
Finally, I need to thank several people that were important for the completion of
this work. First my supervisors for the different projects, Kenneth Järrendahl, Hans
Arwin, Daniel Filippini and Ingemar Lundström. Without them, none of this would
ever have existed. My colleagues at Applied Optics, especially my fellow PhD
students and friends, Michal, Alexander and Linda, for making my time at IFM more
enjoyable. The many friends I have made here in Linköping in my korridor, among
exchange students and their peer students, in Chorus Lin and probably some more, for
making my life in Linköping such a great pleasure. Finally my family, for being so
close to me while so far away and for undying support, especially at times when it was
a little harder.
Jimmy Bakker, March 2004
I
Preface
II
Included papers
Paper 1
Improvement of porous silicon based gas sensors by polymer modification
J.W.P. Bakker, H. Arwin, G. Wang and K. Järrendahl
Published: phys. stat. sol. (A) 197, 378-381 (2003)
Abstract
Gas sensing was performed using spectroscopic ellipsometry and porous silicon
films. Modification of the porous layer by polymer deposition showed an increase in
sensitivity to organic solvent vapor of up to 135%. The increase in sensitivity is
strongly dependent on polymer concentration. At high concentrations, too much
polymer is deposited, presumably blocking the pores, causing a decrease in sensitivity.
At sufficiently low concentrations, the polymer causes a strong increase in sensitivity.
This is assumed to be caused by the polymer being deposited inside the pores, where
its interaction with the vapor influences the sensitivity. At very low concentration, the
sensitivity approaches values obtained without polymer modification. The sensitivity
increase is different for different vapors, pointing to possible selectivity enhancement.
Author’s contribution:
All experimental work, analysis and writing.
Paper 2
Determination of refractive index of printed and unprinted paper using
spectroscopic ellipsometry
J.W.P. Bakker, G. Bryntse and H. Arwin
In press: Thin Solid Films
Abstract
An attempt is made to address the basic physical properties of printed and
unprinted paper surfaces by using spectroscopic ellipsometry in the range 300 - 900
nm to determine the effective complex-valued refractive index <N>. Some
simulations to address the effect of structural properties have also been done and a
qualitative comparison with some other methods, in particular Brewster angle
measurements, has been made.
Unprinted paper and paper printed in different colors have been studied. The
measured absorption properties matched the colors of the used inks well. The effects
of roughness on the determined spectra of <N> are discussed. Simulations show that
compared to other methods, like Brewster-angle reflectometry, spectroscopic
ellipsometry provides a more accurate value of <N> especially in wavelength regions
were the color pigments show absorption.
Author’s contribution:
Most experimental work and all analysis. Writing in cooperation with co-authors.
III
Included papers
Paper 3
Computer screen photo-assisted spectroscopic fluorimetry
J.W.P. Bakker, D. Filippini and I. Lundström
In manuscript
Abstract
Fluorescence measurements are demonstrated using a computer screen as a
programmable light source and a web camera as detector; resulting data shows clear
correlation with traditional spectroscopic fluorimetry, enabling the evaluation of
fluorescence based assays in a platform for home based diagnostics and other low cost
applications.
Author’s contribution:
All experimental work, analysis and writing.
IV
Table of contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Elementary Optics . . . . . . . . . . . . . . . . . . .
2.1 Interaction of electromagnetic waves with matter .
2.2 Reflection from layered structures . . . . . . . . .
2.3 Effective medium approximation . . . . . . . . .
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3
3
5
6
3 Ellipsometry . . .
3.1 Principles. . .
3.2 Measurement .
3.3 Analysis . . .
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7
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9
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4 Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.1 Excitation and emission . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Fluorescence in practice . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5 Color theory and color reproduction
5.1 The eye . . . . . . . . . . . . . .
5.2 Color vision. . . . . . . . . . . .
5.3 Color reproduction . . . . . . . .
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13
13
14
16
6 Computer screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.1 CRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.2 LCD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7 CCD . . . . . . . . . .
7.1 Physical principle .
7.2 Readout . . . . . .
7.3 Color . . . . . . .
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21
21
21
22
8 Porous silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
8.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
8.2 Structure and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9 Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.1 Paper science and research . . . . . . . . . . . . . . . . . . . . . . . . . 25
9.2 Gloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
10 Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
12 Improvement of porous silicon based gas sensors
by polymer modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
13 Determination of refractive index of printed and
unprinted paper using spectroscopic ellipsometry . . . . . . . . . . . . . . . 37
14 Computer screen photo-assisted spectroscopic fluorimetry . . . . . . . . 47
V
VI
Chapter 1
Introduction
Three projects are summarized by the papers at the end of this thesis. The first
paper deals with gas sensing with porous silicon using ellipsometry. The second paper
describes spectroscopic ellipsometry measurements on paper and the third and last
fluorescence measurements using a computer screen and web camera.
The following chapters give an overview of the theoretical background for the
scientific work described in the papers. Since all the papers involve optics, it starts
with a brief overview of relevant elementary optics in chapter 2. After that, in chapter
3, theoretical and practical aspects of ellipsometry are described, a technique which is
used for the first two projects. Continuing with optics, chapter 4 describes
fluorescence, which is only relevant for one project: the fluorimetry project described
in paper 3.
After chapter 4, the elementary physics is left behind and some more practical
subjects are treated. Color theory, dealing with analyzing and reproducing color and
human perception of color, is important for the printed paper in the second project and
even more so for the computer screen photo-assisted measurement, where both the
computer screen and the web camera are based on principles described in this chapter.
How the color theory is applied in practice, as well as some physical background, can
be read in the two following chapters about computer screens and CCD photo
detectors. The last two chapters, describing porous silicon and paper, are relevant for
projects 1 and 2, respectively.
Prospects for future work are given in chapter 10, focusing on the last project, since
this is still a work in progress. The papers, finally, show the scientific output produced
so far. The first paper has been published, the second is currently in press, the last one
is in the last stages of manuscript writing.
1
Chapter 1, Introduction
2
Chapter 2
Elementary Optics
2.1 Interaction of electromagnetic waves with matter
The Maxwell equations [1] give a macroscopic description of the propagation of
electromagnetic waves and their interaction with matter:
r
(2.1) Ñ × D = r
r
(2.2) Ñ × B = 0
r r
r
(2.3) Ñ ´ H = J - iwD
r
r
(2.4) Ñ ´ E = iwB
r
r
where D is the dielectric displacement, r the charge density, B the magnetic induction,
r
r
r
H the magnetic field, J the current density and E the electric field.
The behavior of matter when subjected to electromagnetic fields is described by
the constitutive equations,
r
r
(2.5) B = mm 0 H
r
r
(2.6) D = ~
ee 0 E
r ~r
(2.7) J = s
E
~
where m is the relative magnetic permeability, ~
e the relative dielectric function and s
the conductivity.
By inserting (2.6) and (2.7) into (2.3), we obtain:
(2.8)
~
r
r
æ s
ö r
Ñ ´ H = -iwçç i
+~
e ÷÷e 0 E = -iwee 0 E
è we 0
ø
where e now is defined as an effective value, containing both dielectric and conduction
~
effects. In most cases thercontribution of conduction will however be small and e »
r e.
If the displacement field D is not able to follow the oscillations in the electric field E as
described by equation (2.6), damping of the oscillation will occur. This can be
described mathematically by introducing an imaginary part in e:
(2.9) e = e 1 + ie 2
3
Chapter 2, Elementary Optics
Similarly, the concept of refractive index n can be expanded to include absorption
by including an imaginary part in the form of the extinction coefficient k. A capital N is
used for this complex variant:
(2.10) N = n + ik
The Fresnel equations describe the reflection and transmission of a plane
electromagnetic wave incident at an angle j 0 on a planar interface between two
materials with complex refractive indices N0 and N1,
(2.11)
rs =
E rs N 0 cos j 0 - N 1 cos j 1
=
E is N 0 cos j 0 + N 1 cos j 1
(2.12)
ts =
2N 0 cos j 0
E ts
=
E is N 0 cos j 0 + N 1 cos j 1
(2.13)
rp =
(2.14)
tp =
E rp
E ip
E tp
E ip
=
N 1 cos j 0 - N 0 cos j 1
N 1 cos j 0 + N 0 cos j 1
=
2N 0 cos j 0
N 1 cos j 0 + N 0 cos j 1
where rs, rp and ts, tp are the Fresnel reflection and transmission coefficients,
respectively, E is the magnitude of the electric field and j 1 is the angle of refraction.
j 0 , j 1 , N0 and N1 are also related through Snell’s law of refraction,
N 0 sin j 0 = N 1 sin j 1 .
Eis
H
H
f
Material 1
Material 2
0
N0
N1
f
1
H
a
Erp
Eip
Ers
H
H
f
Material 1
Material 2
0
N0
N1
f
1
Etp
Ets
H
b
Figure 1 The (a) s-component and (b) p-component of polarized light incident on a planar
interface
4
Chapter 2, Elementary Optics
The Fresnel equations are split up in reflection and transmission coefficients for
the s- and p-polarized components of the light. For the s-polarized component, the
electric field is normal to the plane of incidence (Fig. 1a) and for the p-polarized
component, the electric field is parallel to the plane of incidence (Fig. 1b). As any
incident wave can be written as a superposition of these two components, these
equations are sufficient for all possible polarization states.
2.2 Reflection from layered structures
The above described theory only holds for a so-called two-phase system (Fig 2a),
where the interaction takes place at the interface of two materials with different indices
of refraction. For layered structures, all the involved interfaces need to be taken into
account. In a three-phase system (Fig 2b), this would mean summing up light reflected
at interface 01 and light transmitted at interface 01, reflected at interface 12 and
transmitted at interface 10 and so on for higher order reflections. For multilayer
structures, this becomes an impossible task, but a matrix formalism can be used to
solve this problem. This formalism is called the Abelés formalism [2] or scattering
matrix method [3].
Ambient
f
0
N0
f
0
Film
1
N1
Substrate
Ambient
f
N0
f
1
N2
Substrate
a
N1
b
Figure 2 Reflection on a (a) two-phase system and a (b) three-phase system
A matrix equation E( z 1 ) = SE( z 2 ) is defined as follows:
(2.15)
éE + ( z 1 )ù éS 11
ê ú =ê
êëE ( z 1 ) úû ëS 21
S 12 ù éE + ( z 2 )ù
ê
ú
S 22 úû êëE - ( z 2 ) úû
where E + and E - are the complex field vectors of the forward and backwards
traveling waves, respectively, for planes at positions z 1 and z 2 . The scattering matrix S
contains contributions from all the interfaces and layers and thus describes the whole
system. From the scattering matrix, effective reflection coefficients Rp and Rs, can be
calculated, so that:
5
Chapter 2, Elementary Optics
(2.16)
æ E rp
ç
çE
è rs
ö æ Rp
÷ = çç
÷
ø è 0
0 öæ E ip
֍
R s ÷øçè E is
ö
÷
÷
ø
for isotropic media.
2.3 Effective medium approximation
When doing optical analysis, one frequently encounters mixtures of materials with
known optical properties for the constituents. If the local variations of the optical
properties are of a much smaller scale than the wavelength of the light, the mixture can
be modeled as a continuum. The optical properties of the mixture can be calculated
from the optical properties of the constituents. For this purpose, the effective medium
approximation (EMA) method has been developed. Several different EMA models
have been developed, optimized for different microstructures. Only the Bruggeman
EMA model is treated here, since it has been proven fairly successful for the
applications described in this work.
The Bruggeman EMA assumes spherical unit cells for all constituents in the
mixture. For n materials with volume fraction fi, and dielectric function e i the effective
dielectric function e eff can then be defined using the following equation:
e i - e eff
n
(2.17)
åf
i
i=1
e i + 2e eff
=0
and condition
n
(2.18)
åf
i
=1
i=1
This model is frequently used to describe both surface roughness [4] and porosity [5].
In both cases the material is described as a mixture of the substrate material and void.
6
Chapter 3
Ellipsometry
Ellipsometry [3] is an optical technique for determining the optical properties and
microstructure of surfaces and thin films. It is based on measuring the polarization
change that occurs when light is reflected by or transmitted through the surface or film.
Reflection ellipsometry will be considered in the remainder of this text. The technique
has two main advantages. First, it is a non-destructive measurement ‘from a distance’,
which makes it very suitable for in-situ real-time measurements. Second, because the
measured variable is polarization change, it is essentially insensitive to drift in the
intensity of the light source and the spatial resolution for determining film thickness is
not limited by the diffraction limit, enabling changes in layer thickness in the order of
Ångströms to be detectable.
3.1 Principles
Ellipsometry measures the change of polarization of light when it reflects of a
surface. The polarization state of the incident wave can be defined as:
(3.1)
ci =
E ip
E is
and the polarization state of the reflected wave:
(3.2)
cr =
E rp
E rs
The polarization change upon reflection can then be defined as the ratio of these states:
(3.3)
r=
cr
ci
or, expressed with Fresnel reflection coefficients:
(3.4)
r=
Rp
Rs
This is a complex quantity, and is usually expressed as:
(3.5) r = tan Ye iD
With R p = R p e
idrp
and R s = R s e idrs , it follows that
7
Chapter 3, Ellipsometry
(3.6)
Y=
Rp
Rs
and D = d rp - d rs
Thus Y and D are the differential changes upon reflection in phase and amplitude,
respectively, of the components of the electrical field vector parallel and perpendicular
to the plane of incidence. These are the variables that are obtained from an
ellipsometry measurement. Depending on the amount of information needed, they can
be obtained as a function of wavelength, angle of incidence, time, or a combination of
these.
3.2 Measurement
To conduct an ellipsometric measurement, one first needs an incident beam with
known polarization, which is reflected on the sample, after which the change in
polarization needs to be determined. A very common setup is the PCSA system, which
stands for Polarizer Compensator Sample Analyzer. This is the order of the
components between the light source and the detector. The light source is usually a
laser or other monochromatic light source. The polarizer and analyzer are both linear
polarization filters and the compensator is a quarter wave plate, with which an
arbitrary elliptical polarization can be obtained by inducing a phase shift between the
x- and y-components of the polarization vector. When the angles of the polarizer and
analyzer are set in such a way that no light hits the detector (nulling), Y and D can be
calculated from these angles.
For spectroscopic ellipsometry, nulling the system for every wavelength would
become very tedious and time consuming. Therefore a Rotating Analyzer
Ellipsometer (RAE) is used in this case (Fig. 3). The analyzer in this system rotates at a
light source
monochromator
detector
polarizer
rotating
analyzer
sample
Figure 3 Measurement setup for a Rotating Analyzer Ellipsometer (RAE) system.
constant speed, while the polarizer is kept in a fixed position. The linearly polarized
incident light (the compensator is often omitted in this system) will generally be
converted to elliptically polarized light, which gives a sinusoidal signal on the detector
due to the rotating analyzer. By a Fourier analysis of the signal, the ellipsometric
angles Y and D can then be determined.
8
Chapter 3, Ellipsometry
3.3 Analysis
Generally, the desired properties of the measured sample cannot be directly
calculated from the measured Y and D. For this reason, ellipsometry is called an
indirect technique. For any sample with known properties, however, the outcome of an
ellipsometry measurement can be predicted using the matrix formalism mentioned in
section 2.2. This calculated result can then be compared to the measured data and if
needed adjusted to better fit the measured data.
The comparison and model tuning is performed as an iterative fitting process by a
computer. In short the procedure is as follows. First, a measurement is performed to
collect information about the sample in the form of ellipsometric angles. In principle
the more information the better, since this gives a better basis for the mathematical fit.
More information can be obtained by measuring at multiple wavelengths or multiple
angles of incidence or both (variable angle spectroscopic ellipsometry). Second, a
model is built up using what is known about the measured sample to define a layered
structure with layer thicknesses and optical properties as close to the real values as
possible. In case of materials with known optical properties, database values from
earlier measurements can be used in the model. Third, some of the parameters (film
thickness, optical properties) in the model are defined as variables, to be changed in
the fitting process. Fourth, the mean square error (MSE) value is calculated, which is
the standard deviation of the values calculated with the model from the measured
values. Fifth, the parameters defined as variables are changed in order to decrease the
MSE value. Step four and five are repeated until a minimum value of the MSE is
reached.
9
Chapter 3, Ellipsometry
10
Chapter 4
Fluorescence
When molecules absorb ultraviolet or visible light, they are elevated to an excited
electronic state. Generally, this excess energy will be dissipated as heat. Under certain
conditions, however, some of the excess energy can be re-emitted as light of a different
wavelength. This process is called photoluminescence [6]: luminescence for the
general effect of molecules emitting light in a deexcitation process, photo- because the
excitation is caused by photons (as opposed to, for example, chemiluminescence).
Fluorescence, which plays an important role in this work, is a form of
photoluminescence. For better understanding, a more detailed look at the process of
excitation and emission is necessary.
4.1 Excitation and emission
What happens to the energy after absorption, can be depicted in a so-called
Jablonski diagram (Fig.4 ). To know what kind of emission is seen, one needs to look
at the molecular multiplicity M:
(4.1) M = 2S + 1
where S is the spin quantum number of the molecule, defined as the sum of the net spin
of all electrons in the molecule. For most organic molecules, S=0, since the number of
electrons is even. The multiplicity is then equal to 1 and the state is referred to as a
singlet state. While in an excited state, it is possible for one electron to change its spin.
Then S = 12 + 12 = 1 and M = 2× 1+ 1 = 3. This is called a triplet state. The states are
numbered by level of excitation: S0, S1, S2, etc. for the singlet states and T1, T2, etc for
the triplet states (there is no T0, since in the ground level all spins are paired).
VR
S2
IC
VR
ISC
S1
VR
T1
S0
Absorption
Absorption Fluorescence
Phosphorescence
Figure 4 Jablonski diagram
11
Chapter 4, Fluorescence
When a photon is absorbed by the molecule, it is excited to a higher singlet state
(see Fig. 4). Let us assume the molecule is excited to S2. It will immediately dissipate
excess vibrational energy in the form of heat by collision with surrounding molecules.
This process is called vibrational relaxation (VR). At the same time, a transition can
occur from a low vibrational level in S2 to a higher vibrational level with the same
energy in S1. This is called internal conversion (IC). After this, the molecule can
further relax to the lowest vibrational level in S1. These processes occur on a short time
scale (~10-12 sec). Further vibrational relaxation to the S0 level is however usually
relatively slow. This enables relaxation by emission of a photon. This process,
deexcitation from S1 to S0 by emission of a photon is called fluorescence. If a further
transition occurs from S1 to T1 by a process called intersystem crossing (ISC), the
relaxation from T1 to S0 by photon emission is called phosphorescence
4.2 Fluorescence in practice
Quenching
Some practical considerations should be noted when dealing with fluorescence
spectroscopy. It is important to know that fluorescence can be inhibited by a
deactivation process known as quenching. Several mechanisms are known to cause
quenching [10], but all involve radiationless deexcitation by interaction with other
(quencher) molecules. This can be used to ones advantage to turn fluorescence on or
off at will, but should of course be noted when designing experiments, to make sure no
accidental unwanted quenching occurs.
Polarization
When polarized light is used to excite fluorescent molecules, absorption will be
most likely to occur for molecules which have their absorption transition vectors
aligned parallel to the polarization of the exciting light. Depending on the mobility of
the molecules and the lifetime of the excited state, the polarization of the emitted light
may vary. The degree of polarization of the emitted light can be defined as
(3.2)
p=
I f || - I f^
I f || + I f^
Where I f || and I f^ are components of the polarization of the emitted light parallel and
perpendicular, respectively, to the polarization axis of the exciting light. This value
can vary from -0.33 to +0.5 [10]. The degree of polarization will be higher for higher
molecular weight of the fluorophore, higher solvent viscosity and longer excited state
lifetime. This effect can be utilized for a fluorescent polarization (FP) measurement,
which gives information about molecular orientation and mobility. This can be of
value in studies of interaction of organic molecules, for example. It may also prove to
be useful to filter out computer screen light in the CSPT setup (see paper 3), by using
crossed polarizers.
12
Chapter 5
Color theory and color reproduction
There are different ways to define color. The definition from physics will involve
the wavelength of light within the limits of the visible spectrum (~350-750 nm). When
dealing with spectroscopic measurements, for example spectroscopic fluorimetry,
wavelength is the parameter that is used and color is hardly even mentioned. When
using computer screens, web cameras and other devices optimized for the human eye,
other definitions need to be used. For a better understanding of this, a closer look at the
human eye is necessary.
5.1 The eye
Construction
The eye is built up as a fluid filled sphere, enclosed by three specialized layers [7].
From outermost to innermost, these layers are (see Fig. 5)
1. The sclera/cornea
2. The choroid/ciliary body/iris
3. The retina
The outermost layer consists for the most part of the sclera, a tough layer made of
connective tissue, which is visible as the white part of the eye. At the front, where light
enters the eye, the outer layer is transparent and is called the cornea. The second layer,
the choroid, contains many blood vessels that nourish the retina. This also becomes
specialized towards the front and forms the ciliary body and the iris. The ciliary body
produces nutrients for the cornea and lens, which both lack blood supply. The iris
Figure 5 An overview of the anatomy of the eye.
13
Chapter 5, Color theory and color reproduction
Figure 6 schematic view of the retina
controls the amount of light which enters the eye by changing the size of the opening
(pupil) through which the light enters. The innermost layer is the retina, consisting of a
pigmented layer and a nervous tissue layer.
Retina, rods, cones
The important part of the eye for understanding color vision is of course the retina,
where the actual light detection takes place. There are two kinds of light sensitive cells
in the retina, rods and cones (see Fig. 6). Rods have a much higher sensitivity than
cones, but have no wavelength selectivity in the visible spectrum. They are only used
for vision in dim lighting conditions. The cones however are subdivided in three
different kinds, all with slightly different light receptors, making them sensitive to
different parts of the spectrum.
5.2 Color vision
How the information from the different cones is processed to create a color image
is still not completely understood. Several theories [8], differing in complexity and
explanatory value, have been developed over the years. Three theories are described
below. A schematic overview of the theories is given in Fig. 7.
S
a
b
M
c
L
Figure 7 Schematic view of different color vision theories: a. Young-Helmholtz theory, b.
Hering theory and c. Opponent-process theory.
14
Chapter 5, Color theory and color reproduction
Young-Helmholtz theory
This theory, developed in the nineteenth century, is also called the retinal
approach, component theory or trichromatic theory. It builds on the assumption of the
existence of three kinds of receptors, sensitive to red, green and blue light. These
receptors are then directly coupled to the brain, where the color is reconstructed from
the relative intensities of the different receptors. Note that this theory assumes more or
less unique red, green and blue responses of the receptors, not the broad response that
we now know the receptors in the eye actually have. Though this model may seem to
fit fairly well to what we know about the eye, it cannot give a satisfactory explanation
for several perceptual phenomena, like for example color blindness.
Hering Theory
This theory, developed in the 1870s, is also called opponent theory. It postulates
three different kinds of receptors, which are each sensitive to two opponent colors: one
to red and green, one to blue and yellow and one to black and white. These colors are
called opponent because reddish green or blueish yellow for example are not possible.
By a process described as assimilation or disassimilation, the red-green receptor (for
example) will then emit a signal representing the redness or greennes of the detected
light. The white-black receptors function slightly different, since whitish black (gray)
is actually possible. Here successive contrast plays a role, that is black will be
perceived when a dark area is next to a light area, because the white-black receptors
give an opposite response.
This theory can explain a few phenomena that Young-Helmholtz cannot, but it
lacks both completeness and physiological support. For example, it can explain one
kind of red-green color blindness, but not the existence of two different kinds. Also, no
color sensitive substance that can produce two separate effects by assimilation and
disassimilation has ever been found.
Opponent-process theory
This theory, combining elements of the Young-Helmholtz and the Hering theory,
is also known as zone theory or Hurvich-Jones theory. Like the Young-Helmholtz
theory, it assumes the existence of three different receptors, sensitive to different
wavelengths. The sensitivity maxima lie at 450, 530 and 560 nm. Thus they can be
called red, green and blue receptors. However, since (unlike the receptors in the
Young-Helmholtz theory) they are each sensitive to a very broad wavelength
spectrum, it is better to call them long- (L), medium- (M) and short-wavelength (S)
receptors.
In this theory, the opponent idea is incorporated in the nerve cells. This can be
realized by constantly firing nerve cells, which are either inhibited, causing them to
fire less, or stimulated, causing them to fire more. Each kind of receptor stimulates or
inhibits different nerve cells, as shown in Fig. 7. Black is perceived by lateral
inhibition: stimulation on one part of the retina will cause inhibition on adjacent parts.
The opponent-process theory can accurately explain color blindness as well as several
other perceptual phenomena.
15
Chapter 5, Color theory and color reproduction
5.3 Color reproduction
To reproduce a color, it first needs to be sampled by a light sensitive device and
then reconstructed, e.g. on a screen or printed on paper. Generally, an exact
reproduction of the spectral distribution of the original light is however not necessary,
since the purpose of the reproduction is to recreate an image for viewing by humans. It
then suffices if the color looks identical to the human eye. Since the human eye does
not sample with a very high spectral resolution, but only divides the visible spectrum
in three parts by different receptors, recreating the right combination of stimuli for
these receptors will give the desired effect. However, this also means that different
spectral distributions can be identified as the same color. A classical example of this
effect, called metamerism, is the formation of white light, which is possible by
combining monochromatic red, green and blue light as well as by a continuous
distribution of all wavelengths in the visible spectrum. In printing, this same effect can
cause colors that appear the same under certain lighting conditions to be different
when the illumination changes. To avoid misunderstandings, standard lighting
conditions have therefore been defined for color matching. For certain specialized
applications, however, spectral analysis will still be necessary. Especially when colors
need to be recreated independent of lighting conditions, like accurate digitization of art
work or generation of realistic virtual environments, trichromatic analysis does not
suffice. Special techniques have been developed for these purposes, see for example
[9].
Additive vs. subtractive color reproduction
Color reproduction can globally be subdivided in two different processes, additive
and subtractive color reproduction. The additive process uses the primary colors red,
green and blue (hence the abbreviation RGB) and combines them to produce new
Figure 8 Additive (left) and subtractive (right) color reproduction
colors. Secondary colors are produced by combining any two primary colors: red and
green for yellow, green and blue for cyan and red and blue for magenta. Adding all
three colors produces white, absence of all produces black. By varying relative
intensities of the combined colors, other colors and shades can be produced. Any
television, computer screen, digital projector, etc. uses this technique to reproduce
colors. Pigments in printing ink or photographs, however, do not add color but instead
absorb, or subtract, a part of the spectrum of the incident light. In this case subtractive
color reproduction is used. Here one starts with white, i.e. white light reflecting on
16
Chapter 5, Color theory and color reproduction
white paper, and subtracts red, green and blue to produce different colors. This
subtraction is achieved by using the opposite colors of the colors to be subtracted.
Thus to subtract red, a pigment reflecting green and blue and absorbing red is used
(cyan). Likewise, yellow, reflecting red and green, is used to subtract blue and
magenta, reflecting red and blue, to subtract green. Additive and subtractive color
reproduction are illustrated in Fig. 8 Note that not CMY, for Cyan, Magenta and
Yellow, but CMYK is the most frequently used model. Here the K stands for a Key
color, normally black, which is added to enhance contrast, since a mixture of the three
colors produces a grayish black.
Color fusion
Besides spectral resolution, spatial resolution is also an issue for color
reproduction. To reproduce a color out of, say, a combination of colors, one would
have to find a way to combine these colors on one position in space, i.e. a light spot on
a screen or an ink spot on paper. To produce many colors, this would imply the need to
produce light sources with a large variety in colors or a large stack of ink mixtures with
different colors. Fortunately, one can use an effect called color fusion to solve this
problem. Instead of combining the colors in one spatial position, they are now shown
separately as small spots close to each other. If the combination of viewing distance
and the size of the image color elements is such that the human eye cannot distinguish
the separate spots due to lack of spatial resolution, a single color will be seen, which is
a combination of the colors in the separate spots. This effect is known as color fusion
(also known as additive coloration)
17
Chapter 5, Color theory and color reproduction
18
Chapter 6
Computer screens
The most important output peripheral of a computer is certainly the screen. Nearly
everything communicated to the user is displayed as visual information. New
improvements are constantly emerging to make the screens more user friendly, with
higher resolutions and refresh rates, more viewing comfort, etc. Paper 3 describes a
new way of using the computer screen by exploiting it as a light source for optical
measurements, in particular fluorescence spectroscopy, in a technique named
computer screen photo-assisted technology (CSPT). This chapter describes the
technique behind the two leading technologies for computer screens, CRT and LCD.
6.1 CRT
A cathode ray tube (Fig. 9) is
based on an electron beam which is
scanned over a surface covered with
phosphors, which are excited by the
electrons and in turn emit light. Its
core is an evacuated ‘bottle’ with an
electron gun in the narrow end. In
color screens there are three separate
electron beams, one for each color.
These three beams are focused onto
three phosphors with different colors
within one picture element (pixel).
These three phosphors together give
the pixel its color using color fusion Figure 9 Schematic view of a CRT screen
(see section 5.3)
In the electron guns, electrons are released from the cathode by heating and
subsequently focused and accelerated towards the anode, which is located close to the
phosphor screen. The deflection yoke creates a modulated magnetic field, directing
the electron beam towards the desired spot on the screen. The electron beam is scanned
from left to right (as seen from the front) and from top to bottom, lighting up the
phosphor dots in sequence as it goes. The refresh rate (frequency with which the whole
screen is scanned, also called vertical scanning frequency, VSF) is dependent on the
resolution (number of pixels per unit area), and the horizontal scanning frequency
(HSF). For modern CRT computer screens, the refresh rate is usually between 75 and
100 Hz.
19
Chapter 6, Computer screens
6.2 LCD
Liquid Crystal Displays (LCD)
do not emit light in the pixels
themselves, but instead control the
emission of a backlight separately
for each pixel. The backlight emits
white light, color is produced by
using color filters for the separate
color elements in each pixel. Colors
are again produced by color fusion
(section 5.3). The liquid crystals in
the screen consist of rod-like
molecules, which are aligned to a
finely grooved surface on both sides
of the screen (see Fig.10 ). The
grooves are aligned perpendicularly
on either side, causing the molecules
to twist their alignment from one
direction to the other between the Figure 10 The principle of an LCD device. In
two boundaries. Polarized light absence of voltage (left) the molecules (and thus
the light) are twisted, causing it to pass. With a
passing these twisted molecules will voltage, the light keeps its polarization and is
twist its polarization direction blocked.
according to the orientation of the
molecules. Thus, with a polarization filter on each side, the light will pass when the
polarizers are crossed, since the polarization is rotated 90 degrees by the molecules.
When a voltage is applied between the two boundaries, the molecules will prefer
alignment with the potential, giving them a vertical alignment (Fig. 10, Right). Now
light passes between the polarization filters without changing its polarization, causing
it to be blocked by the second polarization filter. Thus the transmission of light can be
controlled.
LCD screens usually suffice with a lower refresh rate. Since the light is not turned
off for every pixel shortly after setting it, like in a CRT screen, it can operate flicker
free even at low frequencies. Low response time of the liquid crystals used to be a
problem. However, with the current state of the art this does not pose a practical
problem anymore for most applications.
20
Chapter 7
CCD
For recording light, any technique involving light being absorbed and leading to a
detectable physical effect can in principle be used. For traditional photography, light
sensitive chemicals constitute this effect. In digital recording, however, a chemical
conversion does not suffice, since an electric signal is needed. Charged coupled
devices (CCD’s) are the most common choice in this case.
7.1 Physical principle
A CCD [11] photodetector is based on the photoelectric effect [12]. It consists of
an array of metal-insulator-semiconductor (MIS) capacitors, usually of the form
metal-oxide-silicon (MOS). When the silicon is hit by photons, it ‘releases’ electrons
(the electrons are excited to the conduction band). These electrons are collected in the
MOS capacitors and after a certain exposure time, the charge buildup is measured.
Since the number of released electrons is proportional to the intensity of the incident
light, this measurement corresponds to an intensity measurement. Electrons can also
be released by thermal effects, creating the so called dark current. This limits the
exposure time, because the signal is masked by the thermal noise for long exposures.
For low intensities, the amplifier gain can be raised to get a stronger signal.
7.2 Readout
Each MOS capacitor functions as a small well in which the released electrons are
trapped. During the recording phase the wells are isolated from each other, preventing
electrons to move between wells. In the readout phase, however applying an
appropriate voltage to a cell will ‘deepen’ its potential well, causing electrons from an
adjacent cell to be transferred into it. This coupling between the cells gives the CCD its
name. This phenomenon is used to sequentially read all the pixels by moving them in
an ordered fashion (see Fig. 11). The charges are moved in lines towards a readout
register, where the cells are
moved one by one to an amplifier,
which converts the charge into a
voltage, which is in turn
converted by an AD-converter,
enabling it to be processed by a
computer. Moving the charges is
achieved by applying a controlled
series of clock pulses. For a
detailed description, see [11].
Figure 11 Readout of a CCD chip
21
Chapter 7, CCD
7.3 Color
Though CCD image sensors have a certain spectral response curve, they are
essentially insensitive to color. Therefore, filters need to be applied to be able to detect
colors. Usually filters are applied to each cell on the chip separately, creating an array
of (usually) red, green and blue cells. Thus, two colors are never recorded at exactly
the same position. For closely spaced cells, this poses no problem in practice, since
color fusion (see section 5.3) will ensure that this is not detectable to the human eye.
Another technique, which can provide better quality (resolution), but is much more
costly, is to use a separate detector for each color, using a beam splitter to separate the
incoming light. Triplets of color values are usually combined as individual picture
elements (pixels), each pixel containing three values varying from 0-255, giving the
intensity of red, green and blue light for that pixel.
22
Chapter 8
Porous silicon
Porous silicon was discovered in the mid fifties [13]. Since then it has had an
undying attention in scientific literature. Much work has been done to better
understand this complex material. The attention became even greater after reports of
room-temperature photoluminescence [14] and electroluminescence [15].
Exploitation of the material as a gas sensor, as described in this work, is only one of
many applications currently under investigation. Both its versatility and its relative
ease of fabrication make it applicable in many different fields. One of these fields, gas
sensing (see also [16]), is explored in paper 1. This chapter gives additional
background information concerning fabrication, structure and analysis of the material.
8.1 Fabrication
The most common fabrication method for porous silicon is electrochemical
etching or anodization. This method is fast and simple and provides a large control
over the etching process. A schematic overview of the etching setup is shown in Fig.
12. The silicon sample is submerged in a solution
containing hydrofluoric acid (HF), ethanol and
water. The ethanol is used because it is assumed
Galvanostat
to facilitate the removal of hydrogen, which is a
byproduct of the etching process. This should
result in more uniform porous layers [17]. A
galvanostat is used to maintain a constant current
during the etching. A constant voltage would not
be advantageous, since the resistivity of the
sample changes during the etching process,
because porous silicon has a higher resistivity
than crystalline silicon. Silicon is connected to
the positive pole of the galvanostat (hence the
name anodization) and a gold wire is used as
counter electrode. A reaction pathway for the
formation of porous silicon has been suggested
by Lehmann and Gösele [18]. According to this
model, holes are required to initiate the etching Figure 12 overview of the setup for
process. For this reason, p-doped silicon needs to etching porous silicon
be used or holes need to be formed in another
way, for example by ultraviolet radiation.
HF/Ethanol/H20
-
Gold wire
Silicon
+
23
Chapter 8, Porous silicon
8.2 Structure and analysis
A scanning electron microscopy (SEM) picture of a porous silicon sample is
shown in Fig. 13. The dark spots on the picture are the pores, which are of the order of
about 5-10 nm in size. The properties of the porous material, such as layer thickness,
porosity, pore size and shape, etc, can vary largely depending on etching conditions
such as HF concentration, doping concentration, crystal orientation, current density,
etc [19].
For the experiments described in this work, pore sizes of 10 nm or less are used.
Since these are small compared to the wavelength of the visible light used in the
ellipsometry measurements, the material can be treated as a homogeneous medium
using an effective medium approximation (EMA, see section 2.3). Designing a good
model for a material as complex as porous silicon is however far from trivial. By using
a multilayer model [5] with several EMA layers with varying porosity to incorporate a
porosity gradient normal to the surface, a reasonable fit can be obtained. For gas
sensing purposes, however, extensive modeling is not necessary, since not the
absolute properties of the sample are important, but the relative change which arises
when gas adsorbs to the surface.
Figure 13 SEM image of a porous silicon surface
24
Chapter 9
Paper
9.1 Paper science and research
Even though we are fully submerged in the digital age, paper is still a very
important medium. Most people cannot (yet) imagine a world without printed books,
newspapers, photos, etc. Because of this, much research is being done on different
aspects of paper. The chemistry of paper production [20] comprises a wide range of
specializations. Research is done to improve paper quality, increase production
efficiency, make production more environmentally friendly, etc. Research on the
optical properties of paper is of course an important aspect (see for example [21]).
Paper 2 in this work describes optical analysis of paper using spectroscopic
ellipsometry, with a special focus on gloss.
9.2 Gloss
Obviously, when paper is used for printing text, images or both, the optical
properties of the paper and the ink are of utmost importance, since they determine the
readability and/or image quality to a great extent. One very important property is gloss
[22]. Gloss deals with the ‘shininess’ of the paper and is determined by measuring the
specular reflectance of the paper. Several standards have been developed to measure
gloss (see for example [23], [24]). Depending on the application, different gloss
characteristics of paper are required. For high quality images, a high gloss value is
desirable. Unfortunately, local gloss variations become a critical issue and can have a
negative effect on the quality of the image. Much is still unknown about the influence
of microstructural and chemical properties of paper on its optical properties. New
techniques are therefore constantly explored to gain knowledge in this field.
25
Chapter 9, Paper
26
Chapter 10
Prospects
Two important tasks remain in the near future for the CSPT fluorescence project.
One is to increase sensitivity by filtering out the computer screen light, the other is to
miniaturize the experimental setup, making measurements on smaller volumes
possible and providing a more convenient format. These two goals are to be realized in
a completely new measurement setup. The current plan is to produce small wells using
photolithography (see Fig. 14), which will contain the fluorescent substance to be
measured. For creating the wells, a photoresist called SU8 will be used, with which
layers of up to 2 mm can be obtained within a single processing step. After finishing
the setup, computer screen light will enter from below (as seen in the illustration) and
the detector will be placed facing the top.
This new design will incorporate some of the ideas developed when designing the
old setup, as well as some new ones. The walls of the wells will be coated (by
evaporation) with aluminum (or some other highly reflective material), so that they
will act as mirrors, reflecting the light towards the detector. The aluminum will also
serve as an integrated mask, allowing light to enter only in the wells, where it is
needed. To prevent possible quenching of
the fluorescence by the metal, it should not
Glass substrate
Al deposition
be the inner wall of the well, therefore a
coating of photoresist will be applied
(more standard photoresist than SU8 can
be used here, since no thick layer is
SU8 exposure
SU8 depostition
required). Note that the procedure shown
and developing
in Fig. 14 is just a tentative plan, which has
not been tested yet.
If the developed setup now is placed in
a container, preventing unwanted light
from entering, most aspects of the original
Al deposition
Photoresist deposition
setup (see paper 3) are present. One
important aspect is missing: the mask
which prevents unabsorbed computer
screen light from entering the detector.
The current plan is to solve this in another
Photoresist exposure
Al etching
way. If the exciting light is linearly
and developing
polarized, the emitted light will at most be
partially polarized (see section 4.2). So if a
polarizer is placed under the glass and one,
with the polarization axis perpendicular to
the first one, between the well and the Figure 14 Possible deposition procedure for
detector, then in principle all the computer creating wells for the CSPT measurement.
screen light will be blocked, while nearly Note that the figure is only schematic, not on
half (depending on the degree of scale.
27
Chapter 10, Prospects
polarization) of the emitted light will be able to pass. Note that the first polarizer is not
needed when using an LCD screen, since the light coming from such a screen is
already linearly polarized (see section 6.2). One important consideration when using
this technique is that in the deposited polymers tension can occur, which can cause the
polarization of transmitted light to change. Therefore it is important that the computer
screen light does not pass through the polymer. This is the reason why the
photolithography is designed in such a way that there is no polymer present on the
bottom of the well and is also an additional motivation for the integrated aluminum
mask.
28
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