Examples
M.Theiss Hard- and Software for Optical Spectroscopy
Dr.-Bernhard-Klein-Str. 110, D-52078 Aachen
Phone: (49) 241 5661390
Fax: (49) 241 9529100
E-mail: [email protected]
Web: www.mtheiss.com
© 2001 Wolfgang Theiss
SPRAY
Spectral ray-tracing simulations
by Wolfgang Theiss
All rights reserved. No parts of this work may be reproduced in any form or by any means - graphic, electronic, or
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While every precaution has been taken in the preparation of this document, the publisher and the author assume no
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the author be liable for any loss of profit or any other commercial damage caused or alleged to have been caused
directly or indirectly by this document.
Printed: 01.12.2009, 22:52 in Aachen, Germany
SPRAY examples
Contents
I
Table of Contents
Foreword
0
Part I Introduction
3
1 About
...................................................................................................................................
this document
3
2 Overview
................................................................................................................................... 3
Part II Lenses
5
1 Chromatic
...................................................................................................................................
error
5
2 Edge
...................................................................................................................................
effects
7
Part III IR reflectance unit
12
1 Overview
................................................................................................................................... 12
2 Spot
...................................................................................................................................
size vs. angle of incidence
13
3 Alignment
...................................................................................................................................
sensitivity
16
4 ATR
...................................................................................................................................
experiment
19
Part IV Light scattering
23
1 Dipole
...................................................................................................................................
scattering - blue skies and red sunsets
23
2 Paints
................................................................................................................................... 27
Paints: Beyond
.........................................................................................................................................................
Kubelka-Munk
27
Scatterers......................................................................................................................................................... 28
Large TiO2..................................................................................................................................................
spheres
28
Small TiO2..................................................................................................................................................
spheres
30
CdS clusters
.................................................................................................................................................. 31
The test system
......................................................................................................................................................... 33
Test the test
.........................................................................................................................................................
system
35
Large TiO2.........................................................................................................................................................
particles in resin
37
Sm all TiO2.........................................................................................................................................................
particles in resin
39
Color by CdS
.........................................................................................................................................................
clusters
40
Index
0
Part
I
SPRAY examples
Introduction
1
Introduction
1.1
About this document
3
Spectral Ray Tracing
Examples
ã W.Theiss
M. Theiss – Hard- and Software
Dr.-Bernhard-Klein-Str. 110, D-52078 Aachen, Germany
Phone: + 49 241 5661390 Fax: + 49 241 9529100
e-mail: [email protected] web: www.mtheiss.com
September 2001
1.2
Overview
This document describes introductory examples demonstrating important SPRAY features. The
SPRAY manual should be consulted for details of the individual objects.
Chromatic error of a collecting lens
Collecting lens: edge effects
An IR reflectance unit for variable angle of incidence
Dipole scattering - blue skies and red sunsets
Paints: Beyond Kubelka-Munk
© 2001 Wolfgang Theiss
Part
II
SPRAY examples
2
Lenses
2.1
Chromatic error
Lenses
5
SPRAY is used to investigate the shift of the focal plane of a collecting lens with wavelength.
A circular light source (left) creates a parallel beam which is focussed by a collecting lens (right):
Sending some test rays the function of the lens is demonstrated:
In the focal plane of the lens an array detector (length: 3 mm, 30 pixels) is placed which records
position-dependent spectra along the symmetry axis of the system:
© 2001 Wolfgang Theiss
SPRAY examples
Lenses
6
If the optical constants of BK7 glass are used for the lens the following intensity distribution is
observed:
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
500
Wavelength
[nm]
1.0
0.8
0.6
0.4
0.2
0.0
600
700
5
800
25
20
15
10
Pixel #
0
Clearly blue light (400 nm) is focussed closer to the lens than red light (700 nm) which is due to
the dispersion of the glass. The refractive index of BK7 has the following spectral dependence:
© 2001 Wolfgang Theiss
SPRAY examples
Lenses
7
BK7
Refractive index
1.56
1.55
1.54
1.53
1.52
1.51
1.50
2.2
300
400
500
600
700
Wavelength [nm]
800
Edge effects
The imaging quality of a simple lens decreases with the distance of incoming rays from the center
of the lens. The configuration previously used to demonstrate chromatic errors is used here to
show how the size of the focus depends on the diameter of the incoming beam.
Setting the beam diameter to 0.2 cm (i.e. the radius of the circular light source to 0.1 cm) a very
sharp focus is achieved. As shown before, the position of the focal plane depends on wavelength
due to the dispersion of the optical constants of the glass:
© 2001 Wolfgang Theiss
SPRAY examples
Lenses
8
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
1.0
0.8
0.6
0.4
0.2
0.0
25
20
500
Wavelength
[nm]
15
600
10
700
5
800
Pixel no.
0
Increasing the beam diameter to 0.6 cm a much larger portion of the lens is used to collect light:
© 2001 Wolfgang Theiss
SPRAY examples
Lenses
9
However, now the focus is much broader:
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
1.0
0.8
0.6
0.4
0.2
0.0
25
20
500
Wavelength
[nm]
15
600
10
700
5
800
Pixel no.
0
Blocking the rays in the center of the beam with a circular stop of 0.4 cm diameter
© 2001 Wolfgang Theiss
SPRAY examples
Lenses
10
makes clear that the rays at the outer regions of the lens are focussed in a different plane as those
that hit the lens in the center (see figure above):
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
1.0
0.8
0.6
0.4
0.2
0.0
25
20
500
Wavelength
[nm]
15
600
10
700
5
800
Pixel no.
0
© 2001 Wolfgang Theiss
Part
III
SPRAY examples
3
IR reflectance unit
3.1
Overview
IR reflectance unit
12
This section demonstrates the simulation of an almost realistic reflectance unit. Devices like this
are often used in the sample compartment of infrared spectrometers in order to record
reflectance spectra of samples at various angles of incidence and different polarizations.
The SPRAY setup includes the following items: A circular light source emits divergent radiation
directed towards a parabolic mirror. The light source is placed in the focus of the paraboloid hence a parallel beam is created by the mirror. A second parabolic mirror creates a focus on a
rotatable plane mirror.
In real spectrometers a Michelson interferometer - consisting of a beam splitter and a fixed and
movable plane mirror - is usually placed between the two paraboloids. The interferometer is
skipped in this setup because the performance of the reflectance unit is of interest here.
The plane mirror directs the radiation upwards onto an elliptical mirror. The center of the
rotatable mirror as well as the sample position are the focal points of the ellipsoid. A second
ellipsoid directs the beam reflected by the sample (here a perfect plane mirror is taken as
sample) towards a second rotatable mirror. Finally the beam is focussed by another ellipsoidal
mirror to the detector element which records the spectrum.
Here is a side view of the setup (with and without some test rays sent to visualize the function of
the elements):
© 2001 Wolfgang Theiss
SPRAY examples
IR reflectance unit
13
Viewed from the top the scenery looks like this:
3.2
Spot size vs. angle of incidence
In some analytical problems the size of available samples is limited and you have to know how
large the illuminated sample spot is. Placing a screen slightly above the sample position is the
easiest way to visualize the illuminated sample area.
The following pictures show the intensity distribution on a quadratic screen (10 mm by 10 mm)
© 2001 Wolfgang Theiss
SPRAY examples
IR reflectance unit
14
for different rotation angles of the rotatable mirrors. First almost normal incidence of light is
taken:
An almost circular spot of about 2 mm diameter is found:
For larger angles of incidence the spot broadens:
© 2001 Wolfgang Theiss
SPRAY examples
IR reflectance unit
15
For extremely large angles of incidence the spot gets even larger than the screen:
© 2001 Wolfgang Theiss
SPRAY examples
3.3
IR reflectance unit
16
Alignment sensitivity
Optical setups are not always perfectly aligned, and it may be of interest how variations of some
geometrical parameters influence the performance of a device. SPRAY simulations can help to
investigate misalignment effects. This is shown in the following simple example.
Ideal alignment leads to a throughput of the reflectance unit of 100% (ideal mirrors are assumed):
© 2001 Wolfgang Theiss
SPRAY examples
IR reflectance unit
17
If the sample is moved up from its ideal position by 5 mm no rays reach the detector any more:
In order to investigate how the detector signal decreases with sample position many SPRAY
simulations have to be performed. Using OLE automation the sample height can be automatically
varied by an Excel macro, the detector signal is recorded and the following display of the
detected fraction of rays vs. the z coordinate of the sample is generated:
© 2001 Wolfgang Theiss
SPRAY examples
IR reflectance unit
18
For almost normal incidence of light
the z-alignment of the sample is significantly less critical:
© 2001 Wolfgang Theiss
SPRAY examples
3.4
IR reflectance unit
19
ATR experiment
Reflectance units like the one discussed here are often used in combination with ATR (attenuated
total reflection). If a multiple reflection ATR crystal made of silicon is placed at the sample
position the situation is this:
Here is a side view of the setup:
© 2001 Wolfgang Theiss
SPRAY examples
IR reflectance unit
20
Obviously the ATR crystal has to be moved up in order to work properly because the radiation
has to enter the crystal from the 45° edges. In order to find the best position we can let SPRAY
do the work, controlled by OLE automation commands from Excel's VisualBasic in this case.
Varying the height of the ATR element and recording the detector signals one gets the following
results:
Trying a z-value of 0.33 seems to be promising. In fact, the light throughput is much better now:
© 2001 Wolfgang Theiss
SPRAY examples
IR reflectance unit
21
There are 5 total reflections at the bottom side of the ATR element on the average:
© 2001 Wolfgang Theiss
Part
IV
SPRAY examples
Light scattering
4
Light scattering
4.1
Dipole scattering - blue skies and red sunsets
23
This is a simple example of light scattering effects studied with SPRAY. A parallel light beam
(sun light) is directed into a region with very small particles - these particles represent density
fluctuations in the earth's atmosphere which lead to dipole scattering. SPRAY determines how
much light is received behind the scatterers and the fraction of rays scattered to the side. In both
cases not only the spectra but also the corresponding colors are computed.
The required scattering properties are computed using an external small program that performs
Mie computations (light scattering by spheres). Although water spheres have been used to
generate the data, the results are quite universal since the spheres are so small that they have
almost only dipole properties. The scattering characteristics (viewed with the tool view_rt.exe)
are the following:
Intensity [10 -19 ]
30
30
25
25
20
20
15
15
10
10
5
5
0
0
25000
20000
15000
020
4060
80100
120140
160
180
Scattering angle
[°]
10000
Wavenumber
[1/cm]
Setting the volume fraction of the scattering particles to 0.0001 one gets the following
probabilities for scattering (red curve) and absorption (blue) per cm distance:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
24
Absorption and scattering data
Probability [1/cm]
0.30
0.25
0.20
0.15
0.10
0.05
0.00
12000
16000
20000
24000
Wavenumber [1/cm]
Clearly blue light (wavenumber 25000 1/cm, or 400 nm wavelength) is scattered more efficiently
than red light (700 nm wavelength, corresponding to about 14000 1/cm). The consequences for
the propagation of light through a volume filled with dipoles are investigated in a simple SPRAY
configuration described in the following.
The parallel light beam created by a circular light source (left object in the picture below) is
directed to a large sphere filled with the scattering dipoles (volume fraction: 0.0001). The rays
transmitted straightahead through the scattering volume are recorded by the rectangular detector
displayed to the right. The large detector in front is used to detect the radiation scattered
sideways:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
25
Testing the configuration with some rays (at 500 nm wavelength) gives a qualitative view of the
effects:
A certain fraction of the rays remains unscattered and reaches the 'throughput' detector, whereas
the scattered fraction is distributed in all directions.
Doing the simulation with 41 spectral points in the range 400 ... 800 nm and 10000 rays per
spectral point, the following results are obtained. The transmitted radiation has the following
spectral distribution and color (which is computed by SPRAY as well):
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
26
'Throughput detector'
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
400
500
600
700
Wavelength [nm]
800
The missing rays in the blue are scattered to the side:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
27
'Side detector'
Detected fraction
0.10
0.08
0.06
0.04
0.02
0.00
400
500
600
700
Wavelength [nm]
800
The conclusions from this simple simulation are the following: Light travelling through a medium
filled with scattering dipoles looses blue light and appears to be red (like sunlight closely before
sunset when it has to travel the largest distance through the earth's atmosphere). Watching light
scattering dipoles from the side (that's what you do looking at the sky) gives a blue appearance.
4.2
Paints
4.2.1
Paints: Beyond Kubelka-Munk
This example shows how SPRAY can be used to predict colors of paints. In most cases paints
consist of a transparent host material (resin) with embedded particles that scatter and absorb
light. For the design of paints it is important to know how the amount of reflected light and its
spectral composition depend on the concentrations and types of inclusions. Problems of this kind
are often approached applying the so-called Kubelka-Munk theory. This rather old concept is a
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
28
two-flux radiation transfer model. In its simplest form it assumes diffuse illumination, isotropic
scattering and perfect interfaces air-resin and resin-substrate. The probabilities per distance for
absorption K(l) and scattering S(l) must be known - these are the input quantities of the model.
The Kubelka-Munk theory returns the diffuse reflection coefficient of the paint for each
wavelength.
Using SPRAY you can do the same - but with less approximations and much more realisitic
results. The required input quantities are the scattering and absorption properties of each particle
species, the optical constants of all materials involved and - of course - the geometry of the setup
like the thickness of the resin or the direction of the incident radiation. You can increase the
complexity of the model as you like - approaching more and more the real paint.
This SPRAY application example investigates a very simple model paint. Spherical inclusions are
embedded in a resin with a constant and real refractive index of 1.5 - the resin itself does not
absorb light. The following inclusions are used:
· Large TiO2 spheres
· Small TiO2 spheres
· Very small CdS spheres
The scattering and absorption properties of the inclusions are summarized in their individual
sections (just double-click the links above).
The SPRAY configuration used to investigate the paint properties is described in the section 'The
test system'. Before the actual work is done some short initial tests confirm the consistency of the
setup.
The TiO2 spheres will be used to create diffuse light scattering almost independent of
wavelength. In a first exercise we will learn how much inclusions we have to take in order to get
a white paint covering a black substrate. The required amount strongly depends on the particle
size. This is demonstrated comparing the case of large and small TiO2 spheres.
In a second step CdS clusters are added. They mainly function as absorbers in the blue and will
be responsible for the color of the paint.
4.2.2
Scatterers
4.2.2.1
Large TiO2 spheres
The scattering properties of TiO2 spheres are computed using the external Mie program. The
optical constants of TiO2 have been taken from the SPRAY database. In order to avoid some
numerical problems of the Mie software, a small imaginary part has been added to the dielectric
function which would be purely real otherwise.
The radius distribution for the Mie computation is this:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
29
Size distribution large TiO2 spheres
Probability
0.5
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
Sphere radius [10-6 m]
The spectral and angular distribution of the scattered intensity is dominated by forward and
backward scattering
Intensity [10 -11 ]
10
8
6
4
2
0
25000
10
8
6
4
2
20000
0
0 20
40 60
80 100
120 140
160 180
Scattering angle
[°]
15000Wavenumber
[1/cm]
10000
If these particles are embedded in the resin with a volume fraction of 1% one gets the following
absorption (blue curve) and scattering probabilities/distance (red):
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
30
Absorption and scattering probability
K(l), S(l) [1/cm]
200
175
150
125
100
75
50
25
0
12000
16000
20000
24000
Wavenumber [1/cm]
In summary: The large TiO2 particles scatter light mainly in the forward direction. There is also
pronounced backward scattering, but no absorption. All these properties are independent of
wavelength.
Small TiO2 spheres
Reducing the size of the large TiO2 particles by a factor of 10
Size distribution small TiO2 spheres
0.5
Probability
4.2.2.2
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
Sphere radius [10 -6 m]
changes the angular distribution of the scattered intensity significantly. There is still preferred
forward and backward scattering but now the difference to the other directions is not so large
any more:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
31
Intensity [10 -13 ]
10
8
6
4
2
0
25000
10
8
6
4
2
20000
0
0 20
40 60
80 100
120 140
160 180
Scattering angle
[°]
15000 Wavenumber
[1/cm]
10000
Filling up the resin with these small TiO2 spheres (1% volume fraction) gives these scattering
probabilities:
Absorption and scattering probability
K(l), S( l) [1/cm]
3000
2000
1000
0
12000
16000
20000
24000
Wavenumber [1/cm]
Note the much larger probability for scattering events compared to the large TiO2 spheres which
is the main difference between the two types of TiO2 scatterers discussed here.
4.2.2.3
CdS clusters
The optical constants of the CdS clusters are taken from the SPRAY database. The radius
distribution used in the Mie computation is shown below:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
32
Size distribution CdS clusters
Probability
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.01
0.02
0.03
Sphere radius [10
-6
0.04
m]
Due to the very small sizes the scattering is almost dipole scattering:
Intensity [10-17 ]
6
5
4
3
2
1
0
6
5
4
3
2
1
0
25000
0
40
20000
80
Scattering angle
[°]
120
15000
160
10000
Wavenumber
[1/cm]
The CdS particles in the resin (1% volume fraction) absorb and scatter with the following
probabilities:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
33
Absorption and scattering probability
K(l), S(l) [1/cm]
3000
2000
1000
0
4.2.3
12000
16000
20000
24000
Wavenumber [1/cm]
The test system
The paint test system consists of a circular light source (transparent) sending a parallel beam
towards the air-resin interface (rectangular, 2 mm * 2 mm). Below this interface there is another
one representing the resin-substrate transition. A view of this configuration is given below:
Here is a side view of the arrangement:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
34
The space between top and bottom interface is filled with a composite scatterer (the TiO2 and
CdS particles). The distance between the interfaces, i.e. the thickness of the paint, is 100
microns. The concentration of the TiO2 and CdS particles can be varied in the model, like all
other parameters and dimensions.
Four perfect mirrors enclose the scattering volume in order to avoid radiation leaving the test
volume (reflecting boundary conditions). The next picture shows the four mirrors which are
about to be moved to their final positions:
Finally we show the complete system with some test rays:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
35
Above the light source there is a huge rectangular detector (10 m * 10 m) collecting all rays that
leave the top surface in the upward direction. Since in the views shown above the observer
looks downwards the detector is not visible.
4.2.4
Test the test system
Before the actual work begins we should perform some simple tests of the SPRAY setup. This is
a very important step since there is a good chance that some of the numerous parameters may
be wrong (although we did our best).
No scattering particles, perfect absorber at the bottom interface
Here the rays are partly reflected at the air-resin interface. Since the resin has a constant and real
refractive index of 1.5 the reflectance of the top interface is about 4%. All rays transmitted to the
bottom interface are absorbed if we use a perfect absorber for that interface. Here is a side view
with some test rays:
The detector should have a constant signal of about 4%. Doing the simulation in the spectral
range 300 ... 1000 nm with 20 spectral points and 10000 rays/spectral point one gets the
following detector signal:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
36
Detected fraction
Rectangular Detector
0.048
0.046
0.044
0.042
0.040
0.038
0.036
0.034
0.032
0.030
300
400
500
600
700 800 900 1000
Wavelength [nm]
This is the expected behaviour. The noise level can be estimated the following way: If 10000
rays are processed and 4% reach the detector, the average number of rays is 400. The statistical
variation of the number of detected rays is the square root of 400, i.e. 20. The amplitude of the
noise is then given by (420-380)/10000 = 0.4% which is roughly what you see in the graph
above.
No scattering particles, perfect mirror at the bottom interface
In this case all rays are reflected at the bottom interface
and should reach the detector. We get this:
Detected fraction
Rectangular Detector
1.2
1.0
0.8
0.6
0.4
300
400
500
600
700 800 900
Wavelength [nm]
1000
No scattering particles, gold mirror at the bottom interface
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
37
This case is used to test a case with spectral variation. The optical constants of gold are taken
from the SPRAY database. The obtained spectrum (300 ... 1000 nm, 71 points, 1000 rays/
point) and the corresponding color are shown below:
Rectangular Detector
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
500
600
700 800 900
Wavelength [nm]
1000
This looks like gold, and we can continue with more serious investigations.
4.2.5
Large TiO2 particles in resin
Now we can start to look at light scattering. In this first investigation we want to find out how
many of the large TiO2 particles we have to add to the paint to make it optically dense, i.e.
independent of the substrate.
The bottom interface is set to be a perfect absorber again. As shown in the tests before, the
detector signal is 4% (due to the specular reflectance of the air-resin interface) if the volume
fraction of the TiO2 spheres is 0. We now slowly increase the volume fraction, compute spectra
in the range 300 ... 1000 nm with 7 points (we do not need spectral resolution in this case) and
collect the results with the Collect program.
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
38
Starting at a volume fraction f = 0.01 a side view shows what happens:
The rays travel through the whole resin layer. Due to the pronounced forward scattering many of
the rays that get scattered nevertheless reach the absorbing bottom. Consequently the detector
signal is not too high yet:
Rectangular Detector
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
500
600
700 800 900
Wavelength [nm]
1000
At f = 0.2 almost no particles reach the bottom interface:
The diffuse reflectance signal is much higher now:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
39
Rectangular Detector
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
500
600
700 800 900 1000
Wavelength [nm]
The next graph summarizes the results for various volume fractions:
Diffuse reflectance
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
300400
500
600
700
0.3
800
Wavelength
[nm]
4.2.6
0.0
0.4
0.2
900
1000
0.1
Volume fraction f
Small TiO2 particles in resin
To investigate the influence of the TiO2 particle size on the paint performance we repeat the
previous computations for the small TiO2 spheres. Here is side view for f = 0.02:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
40
It turns out that much smaller volume fractions are needed to obtain an optically thick paint:
Diffuse reflectance
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
300400
500
600
700
800
900
1000
Wavelength
[nm]
4.2.7
0.0
0.020
0.015
0.010
0.005
Volume fraction f
Color by CdS clusters
Finally we add some absorbers to the paint to get a real color. As shown above, the small CdS
inclusions absorb in the blue much more than in the red - hence we can expect a color like red,
orange or yellow.
Mixing a paint with f = 0.02 of the small TiO2 particles and f = 0.001 of CdS clusters, the
following spectrum (71 points covering the range 300 ... 1000 nm with 1000 rays/point) is
obtained:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
41
Rectangular Detector
Detected fraction
1.0
0.8
0.6
0.4
0.2
0.0
300
400
500
600
700 800 900 1000
Wavelength [nm]
To visulasize what happens we can compare the fate of some test rays for different wavelengths.
At 400 nm (blue light) most of the rays get absorbed on their way through the paint:
On the other hand, red light (700 nm) can travel much longer through the resin and has a much
larger chance to get to the top again without absorption:
© 2001 Wolfgang Theiss
SPRAY examples
Light scattering
42
The graph below summarizes the results of various simulations:
Variaton of CdS volume fraction
0.00000
0.00005
0.00010
0.00020
0.00050
0.00100
0.00200
Diffuse reflectance
1.0
0.8
0.6
0.4
0.2
0.0
300
400
500
600
700 800 900
Wavelength [nm]
1000
© 2001 Wolfgang Theiss