Traditional imaging systems capture and replicate the imaged environment in terms of color and intensity. One important property of light, which the human eye is blind to and is ignored by traditional imaging systems, is polarization. In this paper we present a novel, low power imaging sensor capable of recording the optical properties of partially linearly polarized light in real-time. The imaging sensor combines polymer polarization filters with a CMOS image sensor in order to compute the first three Stokes parameters at the focal plane. The imaging array contains 100 x 100 pixels and consumes 48mW at 30 fps.
©2010 Optical Society of America
Traditional imaging systems have focused on capturing and replicating the imaged environment in terms of color and intensity . One important property of light, which is mostly ignored by traditional imaging systems and human eye cannot see either, is polarization . Polarization of light caused by reflection from materials contains information about the surface roughness , geometry  and other intrinsic properties of the imaged object. Polarization contrast techniques have proven to be very useful in gaining additional visual information in optically scattered environments, such as target contrast enhancement in hazy/foggy conditions [5,6], depth map of the scene in underwater imaging , and in normal environment conditions, such as classifications of chemical isomers , classifications of pollutants in the atmosphere , non-contact fingerprint detection , and seeing in the shadow  among others. Polarization contrast techniques are readily employed by many species in nature, such as cuttlefish, honeybees, desert ants, and others which are of a vital survival mechanism in optically scattering media [12,13]. Moreover, polarization contrast techniques facilitate these species in navigation and enhancement of target contrast in scattering media.
The current state-of-the-art polarization imaging sensors can be divided into division of time [14,15], division of amplitude [16,17], division of aperture  and division of focal plane polarimeters . A comprehensive review of the state-of-the-art passive polarization imaging sensor can be found in . One of the first approaches toward polarization imaging includes standard CMOS or CCD imaging sensors coupled with electrically or mechanically controlled polarization filters and a processing unit . These imaging systems, known as division of time polarimeters, sample the imaged environment with a minimum of three polarization filters offset by either 45 or 60 degrees and polarization information, i.e. degree and angle of polarization, is computed off-chip by a processing unit. Shortcomings of these systems are reduction of frame rate by factor of 3, high power consumption associated with both the processing unit, and the electronically/mechanically controllable polarization filters and polarization information errors due to motion in the scene during the sampling of the three polarization filtered images.
Division of focal plane polarimeters includes imaging elements and micropolarization filters on the same substrate [19,21–24]. The sampling of the imaged environment is achieved with spatially distributed polarization filters pixel-pitch-matched over a neighborhood of pixels. Incorporating pixel-pitch-matched polarization filters at the focal plane has been first reported by Andreou et al. where birefringent materials and thin film polarization filters have been explored . The pixel pitch for the birefringent and thin film micro-polarizer arrays was 50μm and 25μm, respectively. An 8 x 5 birefringent micro-polarization element array with pixel-pitch size of 128μm was reported in . The large pixel pitch in these polarimetric imaging systems limits the fidelity of the imaged environment, which is a major shortcoming for high resolution polarimetric imaging applications. Although these sensory systems are directly inspired from biological systems and compute polarization difference images, they present limited polarization information in scattered media, such as fog, under water imaging and others. In contrast, complete polarization information tends to be far more complex and requires more complex micropolarization array designs.
Division of focal plane sensors capable of extracting the complete set of polarimetric properties for partially linearly polarized light has been reported in the literature [22,23]. The polarization image sensor reported in  has an extinction ratio of 5, an image array of 10 x 10 pixels and pixel pitch of 30μm. Zhao et al. reported a polarization image sensor with extinction ratios of 7 and imaging array of 25 x 25 pixels and used this image sensor to discriminate various sugar molecules . The small imaging arrays in these sensors limit the precision of the extracted polarization information.
In this paper, we present an integrated imaging system capable of extracting partially linearly polarized information from the imaged environment in real time. This sensory system integrates an array of imaging elements, a micropolarization array and analog processing circuitry for polarimetric computation at the focal plane in order to achieve a compact, low power polarization sensitive system. We have fabricated a micropolarization filter array using commercially available polymer thin films and deposited the filter array on top of the CMOS imaging array composed of 100 x 100 current mode imaging elements. Furthermore, we have developed a custom CMOS imaging sensor using a reduced transistor pixel paradigm in order to improve the spatial and temporal noise performance of the sensor. Polarization information is computed in real time using low power digitally programmable analog circuits. The image sensor is used to determine the Brewster angle for a group of selected materials.
The rest of paper is organized as follows. In Section 2 we provide a theoretical overview of polarization properties of light and set the theoretical framework for focal plane polarization imaging. In Section 3 we give an overview of the image sensor architecture, followed by measurements and results presented in Section 4. Concluding remarks are presented in Section 5.
2. Overview of polarization properties
Partially polarized light is most common in nature and capturing its properties with sensory devices is one of the primary goals for an integrated polarization sensor. On the other hand, circularly polarized light is less common in natural wave sources and is not considered in the design of the sensor. In order to describe partially polarized light, three parameters are of importance: the intensity of the wave, the angle of polarization (AoP) and the degree of linear polarization (DoLP). For example, in partially polarized light the major axis of the ellipse describes the angle of polarization, while the minor axis of the ellipse affects the degree of polarization. If the minor axis is nonexistent, the ellipse degenerates to a line and the light is linearly polarized. If the light wave is unpolarized, the degree of polarization is zero and there is no major axis of vibration.
There are different ways of computing DoLP and AoP of the electric-field vector, one of which is presented by Eq. (1).
In Eqs. (2) through (4), It is the total intensity; I(0°) is the intensity of the e-vector filtered with a 0 degree polarizer and no phase compensation between the x and y components; and I(45°) is the intensity of the e-vector filtered with a 45 degree polarizer and no phase compensation as above. The first three Stokes parameters can be computed with two linearly polarized intensities and the total intensity of the e-field vector. Therefore, in order to fully describe the polarization state of light in nature, for which the phase information between the components is not available, two linearly polarized projections in combination with the total intensity are needed. The two linear polarization filters are realized via a dual-tier micropolarization filter array and the fabrication steps of the filter array are described in .
The first three Stokes parameters can also be computed via three or more linear polarization filters. For example, Tyo et al. described an optimal configuration for N linear polarization filters such that information recorded by the N filters is uncorrelated . When N is equal to 3, an optimal configuration for the linear polarization filters is 0 o, 60° and 120° orientation. In our imaging sensor architecture, we use two polarization filters offset by 45 degree in order to realize a two-tier patterned thin-film polymer polarization filter array. The overall thickness of the complete filter will be thinner for a two-tier vs. a three-tier filter, which has two main advantages. The first advantage is in minimizing light attenuation through multiple layers and increasing the angle of incidence. The second advantage is in reduction of fabrication steps and minimization of alignment errors. Although this configuration will not yield optimal polarization measurements, the reduced fabrication steps in the design of a two-tier filter array is the main advantage over a three-filter configuration. The impact on signal to noise ratio on the three Stokes parameters for the two different filter array configurations is outside the scope of this paper and will not be considered in the paper.
3. Polarization image sensor overview
A block diagram of the integrated polarization image sensor is presented in Fig. 1 . The image sensor is composed of an array of 100 x 100 photo pixels, difference double sampling circuitry for noise suppression and analog computation circuitry at the focal plane. The photo pixel is based on our switch-less pixel paradigm, which allows for reduced spatial and temporal noise imaging as well as improved linearity of the pixel operation . Each pixel converts the incident photons at the photodiode node into an output current. The difference double sampling circuit is used to eliminate offset mismatches between pixels and improve spatial variations across the imaging array. Hence, the output current from an individual pixel is equal to 0 A for low light intensities (0μW/cm2) and ~3μA for bright light intensities (10μW/cm2 and integration time of 30 msec). Calibration of the pixel’s current output is performed in the analog domain and at the focal plane. The calibration techniques improve matching between the current outputs across all pixels in the imaging array and are described in more details in .
Analog multiplication, addition and subtraction circuits are used to perform arithmetic on individual pixel’s output currents. A block of 2 by 2 pixels is accessed in parallel and the four pixel’s currents are processed in parallel in the analog domain. The final outputs from the imaging chip are the three Stokes parameters, which are computed as described by Eqs. (2) through (4). The linearity of the pixel’s output current is 99.1% over the entire range of operation and the precision of the analog multiplication, summation and subtraction units is 9 bits . The analog electronics and pixel operation circuitry are described elsewhere in more details .
The micropolarizer array is deposited on the CMOS imaging sensor with the pattern shown in Fig. 1. The patterning of the thin film polarizer is similar to the Bayer pattern used in color imaging. In the imaging sensor presented in Fig. 1, a neighborhood of 2 x 2 pixels is addressed and accessed simultaneously. In the pixels’ neighborhood of interest, one pixel records the 0 degree projected polarized image (I(0°)), another records the 45 degree projected polarized image (I(45°)) and two pixels record the unfiltered intensity image (It). The polarimetric parameters are estimated by reading out all four pixels in parallel and scaling them individually at the periphery, i.e. away from the imaging array, with programmable analog scaling circuitry in accordance to the first three Stokes parameter equations (Eqs. (2) through (4)). An alternative scheme for computing Stokes parameters has been proposed in , which reduces edge artifacts in the image by modifying the convolution kernel.
The CMOS image sensor is fabricated in a standard 0.5μm, 3 metal, 2 polysilicon layer process. The post processing of the CMOS image sensor was performed as described in  and the final integrated image sensor is tested using series of electro-optical experiments. The electro-optical performance characteristics of the image sensor without polarization filters are described in .
3. Results and measurements
The polarization characteristics of the imaging sensor are presented in Fig. 2 through Fig. 5 . For this set of experiments the incident light to the polarization sensor is uniform, narrowband, collimated and linearly polarized. This is achieved by using a 4” integrating sphere with two input ports and one output port. Two custom made PCB boards equipped with 10 ultra bright narrowband LEDs each are used as inputs to the integrating sphere and the total optical power entering the integrating sphere is about 0.6W/cm2. The output port of the integrating sphere provides uniform light intensity with reduced optical power due to the multiple internal reflections in the sphere. A 100 micron pinhole is placed in front of the output port of the integrating sphere, followed by an aspheric lens with a diameter of 44 mm and focal length of 32mm. The aspheric lens is placed on a three axis micromanipulator in order to align the center of the lens with the pinhole and place the pinhole in the focal point of the lens. The light coming out of the aspheric lens is uniform, narrowband, unpolarized and collimated. A calibrated photodiode and a linear polarization filter are used to verify the incident polarized light beam. The angle of polarization of the incident light is swept from 0 to 180 degrees in increments of 5 degrees via computer controlled rotational stage and the incident light is sampled with a calibrated photodiode and linear polarization filters at 0°, 45°, 90° and 135°. The degree of polarization of the incident light wave is computed to be 0.99 ± 0.0015 for angles of polarization between 0° and 180°.
A linear polarization filter is attached to a computer controlled rotating stage and placed between the aspheric lens and the imaging sensor under test. The angle of polarization of the incident light is swept from 0 to 180 degrees in increments of 5 degrees via the rotational stage and the integration time of the image sensor is swept from 10msec to 30msec in increments of 3msec for each angle of incident polarization. Figure 2 presents the optical response of three neighboring pixels with respect to different angles of polarization.
In Fig. 2, the pixel without a polarization filter records a constant light intensity with respect to the different angles of the linearly polarized incident light. The two pixels with polarization filters offset by 45 degrees follow Malus law of polarization, with maximum transmission of 68% (69.2%) when excited with 0 degree (45 degree) polarized light, i.e. parallel polarized light, and minimum transmission of 9.45% (8.15%) when excited with 90 degree (135 degree) polarized light, i.e. cross polarized light. The integration time of the image sensor is set to 10 msec and the incident light intensity is 0.8 μW/cm2.
From Fig. 2, we can conclude that the unfiltered pixel will receive more photons than the two pixels with linear polarization filters. Hence, the unfiltered pixel is prone to saturate faster than the other two pixels. Since the pixels are implemented in CMOS technology, the saturation of this pixel does not interfere with the operation of neighboring pixels i.e. the charges from the saturation pixels do not spill over to neighboring pixels . Furthermore, the two pixels with linear polarization filters have different optical responses i.e. different extinction ratios. These variations mandate implementation of calibration techniques on per pixel base in order to account for these differences. Our current imaging architecture limits the implementation of such calibration scheme and will be explored in future designs. Similar calibration scheme has been proposed for long wave infrared polarization imaging sensors [27,28].
The extinction ratios for the 0 degree and 45 degree pixels are evaluated as a function of integration time and the results are presented in Fig. 3 . For an integration time of 10 msec and light intensity of 0.8 μW/cm2, the extinction ratios are 13.7 and 12 for 0 degree and 45 degree pixels, respectively. The extinction ratios for both pixels decrease as the integration time of the sensor is increased. For example, for integration time of 30 msec the extinction ratios are 12.7 and 11.4 for 0 degree and 45 degree pixels respectively.
For an integration period of 30 msec transmission, the transmission of the micropolarization filters for cross polarized light is increased by ~2% when compared to an integration period of 10msec. Hence, the effective extinction ratio is decreased for both filters. Increasing the height of the polarization filters can reduce this side effect but will introduce crosstalk between neighboring pixels and limit the effective incident angle. The effect on signal to noise ratio for polarization imaging with non-ideal polarization filters have been addressed in .
An ideal polarization filter should have a constant extinction ratio with respect to light intensity i.e. integration time of the sensor. The non-ideal behavior of the extinction ratios is partially due to the electronic cross talk associated with the CMOS imaging sensor. The electronic cross talk is due to the minority charges generated deep into the silicon. As the minatory charges diffuse in the silicon, they can be collected by neighboring photodiodes and contribute to their photon count. It has been reported that as much as 2% of photo generated charges from a N-well/p-substrate photodiode can diffuse to its immediate neighboring photodiode [31,32]. Since the unfiltered pixel will generate high number of photo charges deep into the silicon, some of these charges will diffuse to the neighboring polarization filtered pixels. When larger number of charges is generated by the unfiltered photodiode (such as longer integration time), more charges will diffuse to the pixels with polarization filters and degenerate the extinction ratios. When a pixel with 0 degree polarization filter is illuminated with 90 degree polarized light, the 0 degree pixel records 9.55% of the total incident flux of photons. Most of these charges are due to the cross talk from the neighboring unpolarized pixel and 45 degree polarized pixels .
The angle and degree of polarization for three neighboring pixels as a function of incident angle of polarization is presented in Fig. 4 .
The first three Stokes parameters for these three pixels are computed on chip and the results are presented to a digital processing board for further processing. The degree and angle of polarization are computed using Eq. (1). The computed angle of polarization closely follows the angle of polarization of the incident linearly polarized light and a linear fit yields a 4.68% error. The degree of polarization is 0.96+/−0.01. An ideal linear polarization filter has a degree of polarization of one. The non-ideal behavior of the filter and variations of the degree of polarization as a function of incident angle of polarization are primarily due to the non-zero photo response of the pixels when excited with cross polarized light.
The extinction ratio as a function of the incident angle of light with respect to the surface of the image sensor is evaluated and is presented in Fig. 5.
In Fig. 5, the extinction ratio for the 0 degree pixel is evaluated as the imaging sensor is tilted with respect to the incident light. The imaging sensor is placed on a computer controlled rotating stage and swept from 0 degrees to 50 degrees in increments of 5 degrees. Since the incident light is collimated, the tilting of the imaging sensor allows for increasing the incident angle of light with respect to the imaging sensor surface. The degradations in the extinction ratios are due to multiple effects in the sensor. First, due to the height of the micropolarization filters, the crosstalk between pixels degrades the extinction ratio as a function of the incident angle. Second, the degradation of the extinction ratios is also attributed to the off-normal performance of the polarization filter. For 10 degrees of incident angle the extinction ratios have diminished to 2.2 and above 15 degrees the image sensor does not discriminate polarization due to extinction ratios of one.
Sample images obtained from the image sensor are presented in Fig. 6 and Fig. 7 . A target composed of four linear polarization filters offset by 45 degrees is used for this experiment and a grayscale image of the target recorded with a regular CCD image sensor is presented in Fig. 6a for reference purposes. The raw data from the image sensor is presented in Fig. 6b through Fig. 6d. The raw data from the image sensor is sorted off line such that Fig. 6b presents only the pixels with 0 degree filters, Fig. 6c presents only the pixels with 45 degree filters; and Fig. 6d presents only the pixels without polarization filters. In Fig. 6b, the top left polarization filter in the target is oriented at 0 degrees and exhibits high intensity values since its transmission axis is parallel with the transmission axis of the pixels with 0 degree micropolarization filters. The lower right polarization filter is oriented at 90 degrees and exhibits low intensity values. The transmission axis of this filter is orthogonal to the transmission axis of the 0 degree micropolarization filters. The upper right filter and lower left filter in the target sample are oriented at 45 degrees and 135 degrees respectively. Hence, their intensity values appear around mid level gray value since they will transmit ~1/2 of the total incident intensity. Similar observation can be made for the image in Fig. 6c, where the upper right filter is transparent and has high intensity value. This filter transmission axis is parallel to the transmission axis of the 45 degree pixels. The intensity values of all four filters are equal in brightness in Fig. 6d since this image is recorded with pixels without micropolarization filters.
The second and third Stokes parameters, which are computed at the focal plane of the imaging chip, are presented in Fig. 7a and 7b respectively. The first Stokes parameter is not presented since it records the total intensity of the light wave and is identical to the image presented in Fig. 6d. The second Stokes parameter computes the difference between the 0 degree and 90 degree component of the light wave. Therefore, the top left and bottom right filters in Fig. 7a have very high positive and very low negative values respectively.
The reason for these results is that an image filtered with 90 degree polarization filter will have the brightness interchanged of the top left and bottom left filter when compared to an image filtered with 0 degree polarization filter. Hence, the difference between the 0 degree and 90 degree filtered image will accentuate these two regions of the image. The 45 degree and 135 degree filters will have equal response to the 0 degree and 90 degree filtered images and they appear around 0 intensity value in the second Stokes image. Similar results are observed in Fig. 7b, where the 0 and 90 degree polarization filter have intensity values around 0 and 45 degree and 135 degree have high positive and low negative values respectively.
The three Stokes parameters are provided off chip to a digital signal processing unit for further processing in order to compute the degree and angle of polarization. Figure 8 presents the computed degree and angle of polarization of the imaged target.
The four linear polarization filters have bright values in Fig. 8a, which corresponds to high degree of polarization. The paper board base which is used to mount the polarization filters has rough surface and exhibits low degree of polarization. The angle of polarization image presented in Fig. 8b shows the four polarization filters in colors which are offset by 45 degrees.
The degree of polarization of reflected light is a function of the index of refraction and the incident angle. For a given index of refraction, there is an incident angle for which the reflected wave is linearly polarized, i.e. the degree of polarization is one. This angle is known as the Brewster angle. The polarization image sensor is used to determine the Brewster angle of five different materials that have only a positive and real index of refraction. The five materials for this experiment are: fused silica, polymethyl methacrylate, silicon, gallium arsenide and silicon carbide. The samples have smooth flat surface and are mounted on a motorized tilt stage. The stage is tilted between 0 degrees and 180 degrees in increments of 0.1 degrees and the degree of polarization for every angle is recorded. If the degree of polarization exceeds 0.95, the incident angle is identified as the Brewster angle. The results are presented in Table 1 . The deviations of the experimental values form the theoretical values reported in the literature are less than 4 degree. These deviations can be due to the impurities and surface roughness in the test materials which will cause different index of refraction compared to the theoretical value as well as the limited extinction ratios of the micropolarization filters in our imaging sensor. Hence, the polymer polarization image sensor can be used for automatic detection of materials by detecting the Brewster angle of a given target.
We have presented a complete low power integrated polarization image sensor. Table 2 provides a summary of the image sensor performance. The integrated polarization sensor computes the first three Stokes parameters in parallel at the sensory level with an imaging array of 100 x 100 pixels. This imaging system integrated CMOS current mode pixels with polymer polarization filters in order to detect optical properties of partially polarized light. The sensor operates at 30 frames per second and consuming 48mW of power. The polarization extinction ratios of 13 are used to automatically detect the index of refraction of various materials with flat surfaces.
This research is supported by Air Force Office of Scientific Research (AFOSR) grant numbers FA9550-05-1-0052 and FA9550-10-1-0121 and the CMOS chips were fabricated through MOSIS.
References and links
1. E. R. Fossum, “CMOS image sensors: electronic camera-on-a-chip,” IEEE Trans. Electron. Dev. 44(10), 1689–1698 (1997). [CrossRef]
2. D. Goldstein, “Polarized Light,” (Marcel Dekker: New York, NY, 2003).
3. T. Germer and M. Fasolka, “Characterizing surface roughness of thin films by polarized light,” Proc. SPIE 518, 264–275 (2003). [CrossRef]
4. D. Miyazaki, R. Tan, K. Hara, and K. Ikeuchi, “Polarization-based Inverse Rendering from a Single View,” IEEE Inernational Conference on Computer Vision 2, 982–987 (2003).
5. S. Shwartz, E. Namer, and Y. Schechner, “Blind Haze Seperation,” Proc. IEEE Comp. Vision and Pat. Recog. 2, 1984–1991 (2006).
8. W. Plucknett and R. Dowd, “Refraction and Polarization Properties of Binary Solutions of the Nitrotoluene Isomers with the Xylene Isomers, Chloroform and Cyclohexane,” J. Chem. Eng. Data 8(2), 207–210 (1963). [CrossRef]
9. J. L. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER-ADEOS-1 polarized measurements,” J. Geophys. Res. 106(D5), 4913–4926 (2001). [CrossRef]
10. S. S. Lin, K. M. Yemelyanov, E. N. Pugh Jr, and N. Engheta, “Polarization-based and specular-reflection-based noncontact latent fingerprint imaging and lifting,” J. Opt. Soc. Am. A 23(9), 2137–2153 (2006). [CrossRef]
11. S.-S. Lin, K. M. Yemelyanov, E. N. Pugh Jr, and N. Engheta, “Separation and contrast enhancement of overlapping cast shadow components using polarization,” Opt. Express 14(16), 7099–7108 (2006). [CrossRef] [PubMed]
13. T. Labhart, “Polarization opponent interneurons in the insect visual system,” Nature 331(6155), 435–437 (1988). [CrossRef]
16. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta (Lond.) 29, 685–689 (1982).
17. C. A. Farlow, D. B. Chenault, K. D. Spradley, M. G. Gulley, M. W. Jones, and C. M. Persons, “Imaging polarimeter development and applications,” Proc. SPIE 4481, 118 (2002). [CrossRef]
18. J. S. Tyo, “Hybrid division of aperture/division of a focal-plane polarimeter for real-time polarization imagery without an instantaneous field-of-view error,” Opt. Lett. 31(20), 2984–2986 (2006). [CrossRef] [PubMed]
19. A. Andreou and Z. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2(6), 566–576 (2002). [CrossRef]
22. T. Tokuda, S. Sato, H. Yamada, K. Sasagawa, and J. Ohta, “Polarisation-analysing CMOS photosensor with monolithically embedded wire grid polarizer,” Electron. Lett. 45(4), 228–230 (2009). [CrossRef]
23. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin Photo-Patterned Micropolarizer Array for CMOS Image Sensors,” IEEE Photon. Technol. Lett. 21(12), 805–807 (2009). [CrossRef]
25. J. S. Tyo, “Optimum linear combination strategy for an N-channel polarization-sensitive imaging or vision system,” J. Opt. Soc. Am. A 15(2), 359–366 (1998). [CrossRef]
26. V. Gruev, Z. Yang, J. Van der Spiegel, and R. Etienne-Cummings, “Current Mode Image Sensor with Two Transistors per Pixel,” IEEE Trans. Circuits Syst. I Regul. Pap. 57(6), 1154–1165 (2010). [CrossRef]
27. D. L. Bowers, J. K. Boger, L. D. Wellems, S. E. Ortega, M. P. Fetrow, J. E. Hubbs, W. T. Black, B. M. Ratliff, and J. S. Tyo, “Unpolarized calibration and nonuniformity correction for long-wave infrared microgrid imaging polarimeters,” Opt. Eng. 47(4), 046403 (2008). [CrossRef]
28. J. E. Hubbs, M. E. Gramer, D. Maestas-Jepson, G. A. Dole, M. P. Fetrow, D. L. Bowers, J. K. Boger, and E. Atkins, “Measurement of the radiometric and polarization characteristics of a microgrid polarizer infrared focal plane array,” Proc. SPIE 6295, 62950C (2006). [CrossRef]
29. V. Gruev, J. Van der Spiegel, and N. Engheta, “Image Sensor with Focal Plane Polarization Sensitivity,” Proc. IEEE ISCAS, Seattle, USA, May 2008.
30. J. S. Tyo, C. F. LaCasse, and B. M. Ratliff, “Total elimination of sampling errors in polarization imagery obtained with integrated microgrid polarimeters,” Opt. Lett. 34(20), 3187–3189 (2009). [CrossRef] [PubMed]
31. H. Mutoh, “3-D optical and electrical simulation for CMOS image sensors,” IEEE Trans. Electron. Dev. 50(1), 19–25 (2003). [CrossRef]