Compact and robust linear Stokes polarization camera
Nicolas LEFAUDEUX, Nicolas LECHOCINSKI
Sebastien BREUGNOT, Philippe CLEMENCEAU
Bossa Nova Technologies
ABSTRACT
We present a linear Stokes polarization camera working at visible wavelength. The camera is both compact and
robust for use in field experiments and outdoor conditions. It is based on fast polarization modulator. Four polarization
states images are acquired successively. Processing software allows live calculation, visualization and measurement of
polarization images deduced from the acquired images. The architecture of the hardware, calibration results and
sensitivity measurements is presented. Polarization image processing including polarization parameters computed are
proposed. These parameters include linear Stokes parameters (S0, S1 and S2), usual polarization parameters (intensity,
degree of linear polarization, and angle of polarization) and other polarization based parameters (polarized image,
depolarized image, virtual polarizer, polarization difference). Color data fusion and vector overlay algorithms are
presented. Finally experimental results and observations as well as possible applications are discussed.
Keywords: Time division polarimeter, polarization imaging, linear Stokes parameters, visible band, 3D reconstruction,
Target detection/identification
1
INTRODUCTION
Along with intensity and spectrum polarization of light carries abundant information [1-8]. Polarization is by far
the less investigated of these three fundamental properties of light. A lot of different technological approaches of
imaging polarimeters have been studied [9-16]. We present in this paper the experimental results of a compact and robust
polarization camera. We focused on designing both an accurate sensor and powerful software to visualize and measure in
live the polarization parameters of a scene. Having access to live measurement and visualization of acquired data is the
key to successful experiments, especially when these experiments are carried outdoor.
2
POLARIZATION IMAGING
Whereas standard imaging is limited to measuring the intensity of the light (which is the first Stokes parameter),
polarization imaging consists in measuring at least two Stokes parameters. Polarization data contained in the Stokes
parameters give much more information than a simple intensity measurement. Figure 1 (located at the end of the article)
shows a normal intensity image and a linear polarization image where the polarization information is coded with color.
High polarization areas are coded as vivid colors. Orientation of polarization is coded as color hue. The shape of the car
can be inferred from the color hue variations, the asphalt ground (visible as reddish which is partial horizontal
polarization) can be distinguished from natural ground (grey which is unpolarized) with its different polarization
signature. For most of the cases, almost all the polarization information is contained in the three first Stokes parameters.
Circular polarization requires specific conditions to be created (light going through a birefringent medium, light reflected
by a multilayer material), so usually the last Stokes parameter contains mostly noise. Most of the current imaging
systems are so limited to analysis of the three first Stokes parameters which describe linearly polarized light.
3
DIVISION OF TIME POLARIMETERS – FAST POLARIZATION MODULATOR
The first polarization imaging systems have been division of time polarimeters with mechanical rotation of
polarizer and waveplate between frames. These systems are usually quite slow and very sensitive to motion of the scene
between frames. The use of electrically driven polarization elements like liquid crystals or birefringent ceramics reduced
dramatically the time required to acquire the polarization frames, allowing fast division of time polarimeters to be
designed, and so limiting the registration problem caused by the motion of the scene. We developed a fast polarization
modulator. It is composed of two elements. The first element is a 45degree polarization rotator and the second element
90 degree polarization rotator. The 45 degree polarization rotator is composed of a quarter waveplate and a
programmable quarter wave plate. The orientation of the neutral axis of the programmable quarter waveplate is
electrically tilted by 45 degrees between the two states. A ±45 degrees linear polarization is converted to a circular
polarization after the first waveplate and converted again to linear polarization after the second quarter wave plate. The
90 degree polarization rotator is composed of a programmable half wave plate. The orientation of the neutral axis of the
programmable half waveplate is electrically tilted by 45 degree between the two states. Combined together, these
elements give access to 4 states of polarization which are -45°, 0°, 45° and 90°. Although only three images are
necessary to have linear polarization information, we chose to use the 4 images to reduce noise. The principle of the
polarization modulator is explained in Figure 2.
Figure 2 : Polarization modulator principle. The four possible states are the four main linear polarizations, -45°, 0°, 45° and 90°.
4
CALIBRATION AND MEASUREMENTS
4.1
Calibration results
The calibration and results presented are made with a green filter (520-550nm). Test in broad band visible are
currently carried out and show very good results too. The Stokes parameters are linear with intensity, so the link between
each pixel of the images and its Stokes parameters can be expressed with a matrix. If the images are perfectly -45°,
0°,45° and 90° polarization, the Stokes parameters can be easily deduced, and the matrix is obviously deduced from the
definition of the Stokes parameters (Equation 1). However the polarization states are not perfectly -45°,0°,45° and 90°,
so the C matrix is not the exactly the one in Equation 1.
 I 0o 
 S 0  0.5 0.5 0.5 0.5 

S = C*I
S  =  1 −1 0
 *  I 90o 
0
1
  
 I o 
 S 2   0
0
1 − 1  45 
 I − 45o 
Equation 1 : the images acquired and the Stokes parameters are linearly linked by the matrix C. if the polarization states acquired are
perfectly -45°, 0°, 45° and 90°, the C matrix is directly deduced from the Stokes parameters definition
Calibrating the camera consists in determining the calibration matrix C that links the images acquired to the
Stokes parameters. The accuracy of the calibration can be estimated by measuring degree of linear polarization (DOLP)
and angle of polarization (AOP) of a rotating polarizer (Equation 2).
2
. DOLP =
S1 + S 2
S0
2
=
S1 + iS 2
S0
AOP =
1
Arg ( S1 + iS 2 )
2
Equation 2 : Deduction of the DOLP and AOP from the Stokes parameters.
After calibration of the camera, the measurement of DOLP is excellent; the standard deviation around 100% DOLP is
0.45% (Figure 3a). It comes from a bias and from measurement noise. The bias, which is repeatable, can also be
calibrated and removed. It will require the use of a non linear link between the polarizations states acquired and the
Stokes parameters. We are investigated this bias and it is likely to come from slight misalignment of the neutral axis of
the waveplate in the polarization modulator. This leads to an imperfect conversion of the linear polarization to circular to
linear again. Removing this bias leads to a standard deviation of 0.35%. This can be greatly improved by improving the
illumination as will be shown later. The measurement of AOP of the rotating polarizer is also excellent. The standard
deviation of AOP is 0.15° (Figure 3b). There is no obvious bias.
80
1
60
0
40
-1
DOLP theoretical
DOLP measured
20
error on DOLP
-2
bias on DOLP
0
0
15
30
45
60
75
90
1
theoretical angle
160
0.8
angle measured
error on AOP
140
0.6
120
0.4
100
0.2
80
0
60
-0.2
40
-0.4
20
-0.6
0
-3
105 120 135 150 165 180
0
15
30
45
60
75
90
error on AOP (degrees)
2
error on DOLP %
100
DOLP %
180
3
AOP measured (degree)
120
-0.8
105 120 135 150 165 180
Angle of polarizer (degree)
Angle of polarizer (degree)
(a)
(b)
Figure 3 : (a) measurement of the DOLP of a rotating polarizer. A bias of ±0.25% is observed. (b) Measurement of the AOP of a
rotating polarizer. The standard deviation is 0.15°.
4.2
Test at other DOLP
We tested if the camera was able to measure accurately DOLP other than 100%. We designed a simple
experiment on which we manually rotated a dielectric surface to observe if the DOLP was following the Fresnel law. The
dielectric surface was a colored Plexiglas plate. The fact that the Plexiglas plate was colored allows to get rid of the
second internal reflection. The precision of the measurement was limited by the manual rotation of the dielectric surface,
the manual rotation of the illumination, and the accuracy of camera orientation. No large bias is observed and the
experimental data are in excellent agreement with the theoretical prediction. However additional measurements with a
motorized rotation of both the dielectric plate and the illumination would be necessary to confirm this.
100%
Experimental data
Theory
90%
80%
DOLP (%)
70%
60%
50%
40%
30%
20%
10%
0%
0
15
30
45
60
75
90
θ (Incidence angle)
(a)
(b)
Figure 4 : (a) Experimental set up for measurement of large variations of DOLP. (b) Experimental results and theoretical prediction.
No large bias is observed for DOLP lower than 100%
4.3
Sensitivity
The standard deviation observed with the rotating polarizer was limited by the noise of the camera. To have a
more realistic idea of the real performances of the camera, we designed a simple experiment on which we are able to
accurately change the DOLP of the light source (Figure 5a). We used a dielectric surface and changed its orientation with
respect to the camera. The Fresnel laws links the angle of incidence of the light to the DOLP of the reflected beam. In
this experiment, we used a powerful light source, so the gain of the camera could be reduced to its lowest value and the
full dynamic of the camera was still used. These are excellent conditions. We tilted the Plexiglas plate by 6mrad
(20arcmin). It leads to a 0.9% change of DOLP (Figure 5b). The sensitivity of the DOLP measurement can be estimated
by looking at the standard deviation of the measurements around the best fit. The standard deviation was measured to be
only 0.017%, which is excellent.
66.6
DOLP (%)
66.4
66.2
66
65.8
65.6
0
1
2
3
4
5
6
θ (mrad)
dθ
(a)
(b)
Figure 5 : (a) experimental set up for measurement of small variations of DOLP. (b) Results of the measurements.
The DOLP standard deviation is 0.017%.
5
LINEAR STOKES POLARIZATION CAMERA
A prototype camera based on this technology has been built. The camera (Figure 6a) is a linear Stokes division
of time imaging polarimeter. It uses standard CCD, standard F mount lenses, and the proprietary patented fast
polarization modulator with 4 states of linear polarization. The power supply for the camera is 15V DC. The switching
time of the modulator is in the order of 100µs. The camera resolution is 782x582 pixels. Its digitalization is 12 bits. It
goes up to 35 frames per seconds in full resolution and up to 111 frames per second in half resolution. The camera is
compact (4”x4”x6”) and robust. The acquisition and image processing software run on a standard computer. The
interface between the camera and the computer is IEEE-1394 connection (FireWire) and USB. The camera presented is
integrated and calibrated with a green filter (520-550nm). Test in broad band visible are currently carried out and show
very good results.
Figure 6 : a) Photo of the Linear Stokes camera. b) Field experiment with the Linear Stokes camera
6
POLARIZATION IMAGE PROCESSING
6.1
Raw images and Stokes parameters
When the camera is calibrated, we can process the Stokes parameters to display and measure in live relevant
polarization parameters. Examples will be given below on a measurement. The scene observed is made of a ball, a CCD
camera, and a polarizer array with all the polarizer with a different orientation. There is no polarizer in the center of the
array. These objects are laid on a glass table. From the raw images acquired (Figure 7) and the calibration matrix, the
three Stokes parameters can be deduced (Figure 8).
(a)
(b)
(c)
(d)
Figure 7 : Raw images acquired. The differences are obvious on the polarizer array on the upper right of each image. (a) Vertically
polarized image, (b) Horizontally polarized image. Obvious differences can be observed on the glass ground and the reflections on the
ball. (c) 45 degree polarization image (d) -45degree polarization image.
(a)
(b)
(c)
Figure 8 : Stokes parameters deduced. (a) S0 parameter = intensity that would be observed by a regular camera. (b) S1 parameter =
how horizontally or vertically polarized the light is. The reflection on the glass plate is high. (c) S2 parameter = how obliquely
polarized the light is.
6.2
DOLP and AOP
Whereas all the polarization information is contained in the Stokes parameters, it is very difficult to interpret it.
This is why more relevant parameters are computed. The most used parameters are DOLP and AOP. Figure 9 shows the
DOLP image. The DOLP of all the polarizers is very high, as well as the reflections on the ball and on the glass surface.
The different orientations of the polarizers on the arrays are not distinguished.
Figure 9 : (a) DOLP image.
Displaying the AOP can be tricky. On a simple gray scale, an AOP of 0 degree will be displayed as black, and
AOP of 90 degree will be displayed as medium gray, and an angle just below 180 degree as white (Figure 10, located at
the end of the article). This visualization leads to a “jump” as the angle around 0 and 180 degree (which represent the
same AOP) are displayed as black if just above zero degree and white if just below 180degrees. A better way to display
the AOP is to use the color hue. Color hue is a circular scale, exactly as AOP. The hue goes from red to yellow, green,
blue, magenta, and finally red again. This is exactly the case of the AOP, which can be 0°, then 45°, 90°, 135°, and
finally 180° which is also 0°. This way, the jump around 0° and 180° of AOP disappears with this visualization. This
visualization of the AOP is much easier to understand than the display as gray values.
6.3
Vectors overlay
Once the DOLP and AOP are known, the polarization vectors can be overlaid on the intensity image. The
orientation of the vector is the AOP and the length of the vector is proportional to the DOLP (Equation 3). The AOP and
DOLP of each vector are deduced after averaging the Stokes parameters on an 11x11pixels kernel. It is very important to
average the Stokes parameters which are linear in intensity and not directly the DOLP or AOP. If there is a very low
signal to noise ratio, the DOLP will appear to be almost random between 0 and 1. Averaging the DOLP will lead to
about 50% DOLP. Averaging the Stokes parameters and then calculating the DOLP will give the real DOLP value on the
area. The signal to noise ratio on the area is 11 times better than on a single pixel.
π 

cos( AOP)
cos( AOP + 2 )
V = DOLP 
 N = f ( DOLP ) 
π 
 sin( AOP) 
 sin( AOP + ) 
2 

Equation 3 : Left equation: polarization vector. Right equation, normal vectors.
Some interesting effects can be observed on the image with overlaid vectors (Figure 11). For example the vectors of
polarization are rotating along the ball. However on the reflection of the ball, the image is reversed but not the
polarization, so they do not follow the shape of the reflection of the ball. It is also possible to calculate the normal to the
surface from the DOLP and AOP data. The Fresnel equations give the link between DOLP and angle of incidence of
light. Inverting this equation allows to determine the angle of incidence of light on the surface from the DOLP (Equation
3). In this calculation, the first root of the equation is taken (the incidence angle is supposed to be below Brewster’s
angle). This result has to be taken with a certain care. The DOLP depends on the refractive index of the material for a
dielectric material and it does not follow the Fresnel equations if the material is not dielectric and as the calculation
assumes an un-polarized environment. The material is supposed to have a 1.5 refractive index in the calculation. On the
image with normal vectors overlaid, the vectors look like “hairs” on the objects (Figure 11). The effect on the ball is
particularly visible.
(a)
(b)
Figure 11 : (a) polarization and (b) normal to surface vectors overlaid on the intensity image. Normal vectors are proportional to the
projection of the normal to the surface in the observation plan for a dielectric object under unpolarized illumination.
6.4
Color data fusion
The most relevant color data fusion is HSL (Hue, Saturation and Luminance) color data fusion. This is
essentially because hue is a circular parameter like AOP. A possible visualization is to represent AOP as a color hue, and
DOLP as the luminance of the image. Black areas are associated with low DOLP whereas bright areas are associated
with high DOLP. The saturation is kept at its maximum value. This visualization only displays polarization information
of the scene. No information on the intensity of the scene is displayed (Figure 12a located at the end of the article).
Another possibility is to display the intensity image and to code the polarization information only as color information.
AOP is represented as a color hue, and DOLP as the saturation of the color hue. The luminance is the real intensity of the
image (Figure 12b) which makes this data fusion easy to understand as dark objects remain dark and bright objects
remain bright. Color areas are associated with high DOLP areas and pale colors/grays with low DOLP areas. This
visualization displays intensity and polarization information about the scene. This type of image appears to have only
little noise as the real dark areas (small signal) is kept dark whereas in the previous visualization, dark areas with high
DOLP can appear bright.
7
APPLICATIONS AND EXPERIMENTS
7.1
Target detection, contrast enhancement
It has been showed that DOLP imaging is a powerful tool to detect man made objects [8-11]. Manmade objects
are usually associated with much higher DOLP than natural objects. We tested this property with a miniature car in a
scene made of random natural objects like wood and paper (Figure 13). Whereas not obvious to detect in the intensity
image, the car is the only prominent object in the DOLP image. This quick experiment shows how useful DOLP can be
for automated detection and identification of manmade objects.
(a)
(b)
Figure 13: (a) intensity and (b) DOLP image of a car in a “natural” background.
An interesting property of DOLP and AOP is that they do not depend on the intensity of the light. This makes
polarization data powerful to detect objects hidden in shadows. Objects in shadows should keep a similar polarization
signature, but with a poorer signal to noise ratio. We tested this property by placing two miniature cars in a scene, on in
the light and the other in shadow. We used the first HSL color data fusion, and observed a very similar polarization
signature for the two cars (Figure 14). This confirms the insensitivity of polarization imaging and signatures to intensity
of light.
(a)
(b)
Figure 14: (a) intensity and (b) DOLP image of a car in a “natural” background.
As polarization information does not depend on intensity information, polarization is an excellent way to
increase contrast of object. It can as well increase the contrast of object in shadows as the contrast of white object on a
white background. We tested this on a white mug in a white environment (Figure 15, located at the end of the article).
When mapped as color, the Polarization information greatly enhanced the contrast of the mug on the background.
7.2
Reflection enhancement/removal
Another interesting possibility offered by polarization data is to separate polarized to unpolarized light
(Equation 4). Polarized image is different from the DOLP. For instance, for a same absolute amount of polarized light, a
black area will have a high DOLP whereas a bright area will have a lower DOLP. On usual objects, polarized image will
only show the polarized part of reflections, with absolutely no diffused light. The objects look like metallic mirrors has
they do not show any information on their diffused light. On the other hand, unpolarized image removes all the polarized
part of reflections. It is very useful to remove as much reflections as possible on an object. It is exactly equivalent to
having for each pixel of the image a polarizer with the right orientation to remove the reflections. Unpolarized image
enhances the diffused light from the objects. The sum of the unpolarized and polarized light gives the normal intensity
image.
2
Pol = S1 + S2
2
2
Unpol = S0 − S1 + S2
2
Equation 4 : Deduction of polarized and unpolarized light from the Stokes parameters.
(a)
(b)
Figure 16: (a) Polarized image. The car appears like a metallic mirror. (b) Unpolarized image. The car reflections on the car are
dramatically reduced. The normal intensity image (Figure 1, left) is the sum of the polarized and unpolarized images.
7.3
Transparency of thin clouds/fog
Polarization of the sky has been a subject of much interest [17-20]. Most of the studies were limited to DOLP and
AOP measurements. Parameters like polarized image (Equation 4) have not been studied. During an outdoor field
experiment, we observed an interesting phenomenon. We imaged some thin clouds in polarization. The clouds were way
brighter than the surrounding sky because they were diffusing the bright light of the sun (Figure 17a). They were
decreasing the DOLP of the background sky (Figure 17b). However, we observed that they were almost not visible in the
polarized image (Figure 17c). As the clouds were thin, they were almost transparent. The background polarized sky was
directly visible by transparency. Polarized image, which removes all the diffused light, allows observing polarized light
through diffusing media.
(a)
(b)
(c)
(d)
Figure 17: (a) Intensity, (b) DOLP, (c) Polarized and (d) AOP image of a thin cloud.
The cloud appears very bright on the intensity image and so is seen as having a lower DOLP. However, the cloud is almost
transparent in polarized image. AOP is almost constant over the whole image.
7.4
3D shape information
Polarization carries information about the 3D shape of objects [21-26]. We tested this property by putting various
objects in a depolarized light environment. Figure 18 shows an experiment carried out with a rubber ball. DOP and AOP
information are coming only from the shape of the object. The increase of DOP on the edge of the ball and the rotation of
AOP along the ball are perfectly observed. Normal vectors follow perfectly the shape of the surface. From the normal to
the surface information, the 3D shape can be reconstructed by integrating the local slopes. Figure 18d shows the 3D
reconstruction of the sphere. The exact shape of the reconstructed object depends on the model chose to link the DOLP
and the angle of incidence (Dielectric material, metal or diffusive surface).
(a)
(b)
(c)
(d)
Figure 18: (a) DOP, (b) AOP, and (c) normal vectors image of a sphere. All the information about the 3D shape of the object is
contained in the polarization data. (d) a 3D model can be reconstructed by integrating the normals to surface
Similar experiment has been carried out with a miniature car (Figure 19).
(a)
(b)
(c)
Figure 19: Intensity (a), DOLP (b) and AOP (c) image of a miniature car.
The 3D reconstruction is more difficult in this case. The miniature car is not made of a single material and has strong
angles on its surface. However, a simple reconstruction algorithm shows acceptable results (screenshots of Video 1
below).
(a)
(b)
(c)
(d)
Video 1: Different views of the 3D model of the car deduced from polarization data acquired. This 3D reconstruction comes only from
polarization data acquired from a single point a view. No stereoscopic or photo-stereoscopic information is used in this
reconstruction. The reconstruction shows some deformations of the shape but the overall shape is very close to the real one as can be
observed from these screenshots of the 3D model video. http://dx.doi.org/xx.xxxx/x.xxxxxxx.x
(a)
(b)
Figure 1 : (a) Normal intensity image of a car. (b) Polarization image of the same scene.
(a)
(b)
Figure 11: (a) Black and white image of AOP.(b) Color hue image of AOP. The jump between black and white which represent the
same AOP does not appear on the color hue image (b). This jump can be seen on the ball and on the polarizer array.
(a)
(b)
Figure 12: (a) Color data fusion of polarization data only. High DOLP areas are bright and with vivid colors whereas low DOLP
areas are dark. (b) Color data fusion of intensity and polarization data. Low DOLP areas are grey while high DOLP areas are
displayed as vivid colors
(a)
(b)
Figure 15: (a) Intensity and (b) Color data fusion of a white mug in a white environment. The color data fusion clearly enhances the
visibility of the mug on the background.
8
CONCLUSION
We have presented a linear Stokes polarization camera. We focused on developing both the sensor and also a
powerful acquisition and processing software to have a live visualization and measurement of all the presented
polarization parameters. This effective polarization camera combines:
• Very good calibration results
• Excellent sensitivity
• Portability and robustness for field experiments
• Powerful software for live polarization measurement, analysis and visualization.
• The experimental results obtained with this camera allowed to (re)demonstrate applications of
polarization imaging like:
o target detection
o contrast enhancement
o reflection enhancement/removal
o 3D reconstruction
We will keep on improving software, acquiring more polarization data and conduct other experiments to find new
applications for this versatile and user friendly sensor.
9
ACKNOWLEDGMENTS
The authors would like to thank Robert Karlsen and Grant Gerhart of the US Army TACOM-TARDEC.
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