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Abstract
We calibrate and test a division-of-focal-plane red–green–blue (RGB) full-Stokes imaging polarimeter in a variety of indoor and outdoor environments. The polarimeter, acting as a polarization camera, utilizes a low dispersion microretarder array on top of a sensor with Bayer filters and wire-grid linear polarizers. We also present the design and fabrication of the microretarder array and the assembly of the camera and validate the performance of the camera by taking multiple RGB full-Stokes images and videos. Our camera has a small form factor due to its single-sensor design and the unique capability to measure the intensity, color, and polarization of an optical field in a single shot.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Polarization cameras have a variety of applications in remote sensing [1–3], biomedical imaging [1,4–6], and interferometry [7–9]. Measuring the polarization state of light requires using polarization filters such as linear, circular, or elliptical analyzers that are incorporated onto a sensor array. Most existing polarization cameras use wire-grid linear polarizers to measure linear polarization [10–12]. Some polarization cameras extend their measurement capability to full-Stokes measurement, i.e., measuring all components of the Stokes parameters using circular/elliptical analyzers made of birefringent material [13–16]. However, since most birefringent material is wavelength-dependent, these full-Stokes cameras are limited to operating in a narrow wavelength band. There exist achromatic broadband full-Stokes cameras that use achromatic wave plates based on the division-of-amplitude [17] or the division-of-aperture [18] configurations. To the best of our knowledge, no broadband polarization camera currently exists that is based on the division-of-focal-plane configuration. The main reason is the difficulty of making achromatic wave plates and elliptical polarizers in the micro scale.
In this paper, a compact division-of-focal-plane red–green–blue (RGB) full-Stokes camera is assembled and tested. This camera utilizes a single layer of micropixelated linear retarder based on low-dispersive birefringent reactive mesogen. This instrument can measure the full-Stokes parameters in the RGB channels in a single shot.
2. SENSOR DESIGN
Our division-of-focal-plane RGB full-Stokes camera is based on the color polarization sensor IMX250MYR recently developed by Sony Corporation [19,20]. Figure 1 shows its sensor layout. The sensor has a micro wire-grid polarizer array on top of the traditional Bayer color filter array, resulting in a color polarizer array that enables simultaneous color and linear polarization measurements. Notably, this micropolarizer layer is formed under the on-chip microlens array, making the distance between polarizers and photodiodes extremely short. This integration reduces the incident angle dependence that exists in traditional linear polarization cameras, where the polarizer array is aligned and packaged on top of the sensor [13,14]. The pixel size of this sensor is 3.45 µm.
Fig. 1. Sensor layout of the Sony color polarization sensor IMX250MYR shows the locations of the RGGB Bayer filters and the wire-grid linear polarizers.
A customized microretarder layer is fabricated and placed on top of the sensor to extend its capability to measure all four Stokes parameters. Figure 2 shows the cross-sectional view of the focal plane array, the ideal microretarder design, and the corresponding measurement tetrahedron on the Poincaré sphere. The retarder design is a periodic two-strip structure that has a uniform linear retardance of 45° but orthogonal fast-axis orientations between the two microstrips. The strip width is twice the pixel size of the sensor. The fast-axis orientation is chosen to be the middle point of micropolarizer angles, which are 22.5° and 112.5°, in order to minimize the equally weighted variance (EWV) of the four measurements [21,22]. EWV provides a sense of how noise propagates through the measurement process. The EWV for these four measurements is 11, while the optimized case is 10. Ideally, the optimized tetrahedron can be achieved with a pixelated retarder whose pixel size is equal to the pixel size of the color polarization sensor. However, such a small retarder pixel will be difficult to fabricate due to material and process constraints.
Fig. 2. (Left) Customized microretarder array is put on top of the Sony color polarization sensor. (Middle) The ideal design of the micro-retarder layer is shown overlaying the RGGB Bayer and wire-grid polarizer filters. (Right) The corresponding four polarization measurements form a tetrahedron on the Poincaré sphere.
The microretarder layer is fabricated by the conventional photoalignment technique [23,24], in which a layer of birefringent reactive mesogen or liquid crystal polymer (LCP) is coated on a photoalignment layer that is pre-exposed by patterned linear-polarized ultraviolet (UV) light. The orientation of the linear polarization defines the director orientation of the coated LCP. At the boundary of the microstrip, there will be a transitional region allowing the LCP director to switch its orientation continuously from the fast-axis angle of one strip to the fast-axis angle of another strip, i.e., from ${-}{22.5}^\circ$ to 67.5°.
When the two strips have orthogonal fast-axis angles, degeneracy of the transitional region can occur. Considering the ideal design in Fig. 2 as an example, at the strip boundary, the director of LCP can rotate in two ways, either switch from ${-}{22.5}^\circ$ to 22.5° to 67.5°, or it can switch from ${-}{22.5}^\circ$ to ${-}{67.5^\circ}$ to 67.5°. Both cases have the same elastic energy and same likelihood of occurring [25]. In the actual fabricated filter array, this degeneracy causes the formation of a singularity of LCP orientation at the strip boundary, resulting in alignment defects. These defects can be eliminated by removing this degeneracy. Figure 3 shows the microscopic images of three two-strip microretarder arrays. Magnified images with arrows indicating the director orientations are shown below. The degeneracy causes two possible director orientations at the boundary, leading to alignment defects. As the fast-axis angle difference between two strips decreases, the elastic energy difference between the two angular configurations increases. Since the liquid crystal tends to align itself to minimize the elastic energy, the larger energy difference helps the liquid crystal to distinguish between the two configurations and reduces the probability of defect occurrence. When the fast-axis angles are 70° apart, the probability of defect occurrence decreases to the stage that we cannot see any defects on the sample.
Fig. 3. (Top) Images of microretarders are taken by a polarization microscope. (Bottom) Magnified regions with alignment defects are shown for different fast-axis angles. Dashed arrows represent the LCP director orientation. From left to right, the fast-axis angle difference between two strips are 90°, 80°, and 70°, respectively.
Based on this observation, the microretarder design is modified to the one shown in Fig. 4. The fast-axis angle is rotated by 10° for both strips, resulting in a 70° angle difference between the adjacent fast axis angles. The revised design improves the quality of LCP alignment and reduces the defect density at the cost of slightly increased EWV from 11 to 11.18. The revised design is used in the actual fabrication.
Fig. 4. (Left) Revised design of the microretarder layer is shown overlaying the RGGB Bayer and wire-grid polarizer filters. (Right) The corresponding four polarization measurements of the revised design form a tetrahedron on the Poincaré sphere.
Another important design parameter is the chromaticity of the microretarder. The dispersion of the retarder leads to a wavelength-dependent analyzer vector (the first row of the Mueller matrix) for each pixel. Since the Sony color polarization sensor is responsive over the entire visible band, a chromatic analyzer vector will cause a major error in the measurement of the broadband Stokes parameters.
A negative dispersive LCP material, RMM1705, manufactured by EMD Chemicals, is chosen for microretarder fabrication to reduce this error. Figure 5 shows the retardance curve of RMM1705 along with the spectrum sensitivity of the Sony color polarization sensor IMX250MYR. The chromaticity of RMM1705 can lead to 14.9% maximal analyzer vector variation for two vertices in the measurement tetrahedron and to 7.0% maximal analyzer vector variation in the other two vertices. This variation over the spectral band of 400 to 700 nm is then distributed across the RGB wavelength bands, leading to an approximate 5% variation within each color band. The influence of analyzer vector variation is discussed in Appendix A.
Fig. 5. (Solid line) Measured linear retardance curve of RMM1705 is shown. (Dashed line) The quantum efficiencies of Sony color polarization sensor IMX250MYR are shown for RGB pixels.
3. MICRORETARDER FABRICATION AND CAMERA ASSEMBLY
The microretarder array is fabricated using conventional photoalignment techniques [23,24]. RMM1705 is used as the LCP. A linearly photopolymerizable polymer (LPP) solution ROP108, manufactured by Rolic Technologies, is used as the photoalignment material. One important advantage of this fabrication process is its simplicity and compatibility with most existing semiconductor manufacturing. Figure 6 shows a flow diagram of the fabrication process. The process consists of the following steps:
- 1. The LPP solution is spin-coated on a soda lime glass substrate at 2500 rpm for 1 min. The glass substrate is 10.16 cm in diameter and predeposited with aluminum alignment marks using a standard photolithography and lift-off process [13].
- 2. The substrate is hard-baked at 170°C for 5 min.
- 4. The LCP solution is made by adding RMM1705 to chloroform at an 18% weight-to-weight ratio.
- 5. The LCP solution is spin-coated on the LPP layer at 3000 rpm for 30 s.
- 6. The substrate is hard-baked at 56°C for 5 min.
- 7. The substrate is cooled down at room temperature for 20 min.
- 8. The LCP layer on the substrate is cured with UV light in a nitrogen environment. After curing, a solid plastic thin-film microretarder array is formed on the substrate.
In order to characterize the fabrication process, a microretarder array is first fabricated and characterized by an AxoStep, a Mueller matrix imaging polarimeter manufactured by Axometrics Inc. The measurement is done at 550 nm. Figure 7 shows the microscopic image and cross-sectional plot of the measured linear retardance, circular retardance, and retardance orientation. The linear retardance and retardance orientation are as designed. Although there is some unexpected circular retardance due to director twisting [25], this does not increase the chromaticity of the retarder array.
Fig. 7. (From top to bottom) Linear retardance, circular retardance, and retardance orientation of the microretarder sample is measured using a Mueller matrix imaging microscope. The microscopic images are shown on the left. The cross-sectional plot along the dashed line is shown on the right.
After the process is validated, the aforementioned procedures are applied to the fabrication of a microretarder array. The wafer substrate is then diced into rectangular dies by laser dicing techniques at Disco Hi-Tec America, Inc., San Jose, CA. The die with the fewest defects is chosen and bonded to a mounting frame controlled by a six-axis stage. Circular polarized light at 632.8 nm is illuminated through the mounted die to the Sony color polarization sensor. The pixel readout reaches a maximum modulation when the die is aligned properly to the sensor, and UV curing epoxy is then applied to glue the die onto the sensor. Figure 8(a) shows the final assembled camera. Figure 8(b) is a photo of a C-mount fisheye lens connected to the camera. A steel ruler is laid on the side to show the scale, illustrating the compactness of the imaging system.
Fig. 8. (a) Front view of the assembled camera shows the mounted microretarder. (b) A top view is shown for an imaging fisheye lens connected to the camera.
Fig. 9. Histogram plots of the Stokes reconstruction of an LCD screen are shown. Each row represents a different f-number and exposure. RGB curves represent the measurement at the three respective color channels. Histograms of ${f}/{8}$ 200 ms and ${f}/{2}$ 29 ms give about the same near-saturated brightness level. Similarly, histograms of ${f}/{8}$ 20 ms and ${f}/{2}$ 2.9 ms give about the same underexposed brightness level.
4. RESULTS
The calibration process involves measuring the actual analyzer vector for each pixel of the sensor. The analyzer vectors of neighborhood pixels are then integrated to form a measurement matrix, which can be used to convert intensity measurements of individual pixels into Stokes parameters. Details about the calibration and reconstruction algorithm are discussed in a previous work [17] and are not repeated here.
A white LCD screen is used as the target scene in order to estimate the accuracy of the RGB full-Stokes measurement. A Canon ${\rm V6} \times {17}$ TV zoom lens is installed to image the screen onto the sensor. Multiple images are taken with different f-numbers and exposures to evaluate its performance for different lens aperture sizes and signal-to-noise ratios. The LCD screen is linearly polarized at a specific orientation. Consequently, the camera is expected to measure degree of linear polarization (DoLP) as 1, angle of linear polarization (AoLP) as a constant value, and degree of circular polarization (DoCP) as 0, for all three RGB bands. Figure 9 shows the histogram plot of the measured results after measurement matrix reconstruction. Table 1 summarizes the average and standard deviation of the measured DoLP, AoLP, and DoCP across the image, which provides estimates of the camera’s accuracy and precision. Here we define the DoCP as ${S_{3}}/\!{S_0}$, and the sign of DoCP indicates the handedness of the circular polarization. This is different from the definition that only uses the absolute value of ${S_{3}}/\!{S_0}$.
Comparing the results at different f-numbers and different exposures, we see that the camera’s performance does not change much with the size of the lens aperture. On the other hand, decreasing the integration time increases the standard deviation. At near-saturated brightness level (${f}/{2}$ 29 ms and ${f}/{8}$ 200 ms), the accuracy is within 0.0345 for DoLP and 0.0257 for DoCP, respectively. This offset can be caused by the chromaticity of the microretarder filters. The precision is within 0.0335 for DoLP, 1.90° for AoLP, and 0.0670 for DoCP. The green channel has better precision, since the number of green pixels is twice the number of red or blue pixels. When the camera is underexposed (${f}/{2}$ 2.9 ms and ${f}/{8}$ 20 ms), the accuracy is kept within 4.15%. The precision is within 0.0432 for DoLP, 2.64° for AoLP, and 0.0941 for DoCP.
Table 1. RGB Full-Stokes Measurement of LCD Screena
We take four images and two videos (see Visualization 1 and Visualization 2) of indoor and outdoor using the camera. The data reduction matrix method and a bicubic-spline interpolation algorithm are adopted for the RGB full-Stokes reconstruction [22,26–29]. Other techniques such as Fourier-domain analysis and edge-detection interpolation can be applied to further improve the reconstruction accuracy [30–33]. The different images illustrate the utility of multispectral polarization imaging and are discussed below.
Figure 10 shows a building with windows. The building is surrounded by a clear sky, with the Sun at the center of the picture and blocked by the building. In the Stokes image, the window has a DoLP signal due to the reflection of sky polarization. A ring of peak DoLP is seen at the edge of the picture, and the variation of AoLP around the building indicates the location of the Sun. The observed polarization pattern matches the theoretical polarization pattern of the sky [34]. There is a black border surrounding the fisheye image at the edge of the field. The linear polarization signal at the border is caused by the reflection inside the lens barrel.
Fig. 10. RGB full-Stokes image of a building with large-area window surrounded by sky was taken using a Fujinon DF1.4HB-L1 fisheye lens.
Fig. 11. RGB full-Stokes image of the sky through a stress-birefringence window was taken with a Canon ${\rm V6} \times {17}$ TV zoom lens.
Figure 11 is a view of the sky through a window inside the Meinel building at the James C. Wyant College of Optical Sciences, University of Arizona. The linearly polarized sky is converted into elliptical polarization due to the stress birefringence of the window. Variation of DoCP is seen in the Stokes images, indicating the distribution of stress inside the window. The vertical strip in the color image is the metal frame of the window. It has linear polarization signals from the specular reflection.
Figure 12 shows several small objects including a black cylinder (left), white sphere (upper right), black sphere (middle right), and a beetle (lower right). The cylinder and sphere have some specular reflection and thus show a linear polarization signal. The black objects have larger DoLP than the white one due to the Umov effect, which states that the degree of polarization is inversely proportional to the albedo of an object [35]. The AoLP image maps the surface normal orientation of the object. A large DoCP signal is seen at the beetle because of the chiral microstructures inside the beetle’s exoskeleton; the chiral microstructure acts as a reflective circular polarizer when the chiral pitch multiplying the refractive index is close to the wavelength of incident light.
Fig. 12. RGB full-Stokes image of small objects was taken using a Canon ${\rm V6} \times {17}$ TV zoom lens.
Figure 13 is a chopper wheel covered with circular polarizers in the inner circle and linear polarizers in the outer circle. In the Stokes image, we see that the outer circle has large DoLP and the inner circle has large DoCP. Also, the DoCP is maximum at the red channel and minimum at the blue channel due to the birefringence dispersion of the circular polarizer.
Fig. 13. RGB full-Stokes image of a chopper wheel with circular polarizers in inner wheel and linear polarizers in outer wheel was taken using a Canon ${\rm V6} \times {17}$ TV zoom lens.
Two videos of moving cars, taken by the camera and included in the supplementary material (see Visualization 1 and Visualization 2), demonstrate the continuous measurement capability of the camera. The car has substantial specular reflection on its surface when illuminated by polarized skylight. In the video, we can see a moving DoLP signal from the cars and a changing AoLP when the car changes its direction.
5. DISCUSSION AND CONCLUSION
In this section, the performance and limitation of the instrument are discussed, and potential solutions to reduce measurement error are presented. The analyzer vector variation with wavelength is limited by the dispersion of the filter material. In this work, the dispersion is reduced by using a single layer of low-dispersive LCP. While this solution simplifies the fabrication process, the performance of the microretarder can be improved further by using multiple layers of the same LCP or a combination of high-dispersive LCP and low-dispersive LCP [36,37].
The polarization measurement result is generally dependent on the angle of the incident light. One source of the angle dependency is the cross talk between neighboring pixels. Ideally, when aligning the microretarder array to the Sony color polarization sensor, every pixel should be precisely aligned on top of each designated retarder. In addition, the gap between the retarder and the sensor should be zero everywhere. However, there is inevitable stress and deformation in the microretarder glass substrate such that a zero gap is difficult to achieve. When the gap between the sensor and the microretarder is comparable to the pixel size, off-axis light rays can pass through a retarder layer of an adjacent pixel before reaching the pixel. This cross talk between neighboring pixels increases as the incident light ray becomes more oblique or as the gap increases. One solution to reduce this cross talk is to use an image space telecentric lens. Another solution is to use a lens with a large f-number. This type of cross talk can also arise from a thick microretarder layer.
After extensive calibration and testing, we observe a relatively small ray angle dependency in our instrument. We believe there are several reasons for this. First, the microretarder is made of a single layer of LCP with a small linear retardance around 45°. The thickness is relatively thin, of the order of 2 µm, compared to the 6.9 µm strip width. Second, the wire-grid polarizer is directly under the on-chip lens array, and there is little cross talk from the polarizer layer.
Another type of angle dependency is the angle-dependent birefringence of the LCP. The LCP used here acts like a patterned A-plate. Its retardance and fast-axis orientation can change under different incident angles, leading to an angle-dependent analyzer vector. This dependency can be reduced by increasing the f-number or by using a wide viewing angle microretarder with a C-plate LCP [38].
The error induced by angle dependency can be estimated by looking at an image taken using a wide-angle fisheye lens, as observed in Fig. 10. The fisheye lens has a relatively short focal length compared to the zoom lens in Figs. 11–13. At the edge of the sensor, the ray angle can be larger, and this larger ray angle can induce substantial error in the polarization measurement. This error is seen in the DoCP image of Fig. 10, where significant DoCP signal, around 0.1 to 0.2, appears at the edge of the picture. We believe this signal is not real, since the clear sky has no circular polarization.
In conclusion, we have demonstrated a compact division-of-focal-plane RGB full-Stokes camera that can capture intensity, color, and polarization of an optical field in one shot. The camera is based on applying a customized microretarder array to the Sony color polarization sensor. The microretarder array is a periodic two-strip structure made of low-dispersive LCP. The filter is fabricated by a conventional photoalignment technique. The camera provides a resolution of ${2056} \times {2464}$ with an 8-bit depth at 70 fps, or 12-bit depth at 30 fps. Several images and videos are captured to validate the camera’s performance. Our camera is able to rapidly detect color polarization signals of various natural scenes and thus can be utilized for a variety of polarimetric applications.
APPENDIX A: IMPACT OF ANALYZER VECTOR VARIATIONS ON STOKES PARAMETERS RECONSTRUCTION
A polarization analyzer is characterized by a four-component analyzer vector, similar to the four-component Stokes parameters [27]. The wavelength-dependent analyzer vector variation is defined as
Fig. 14. (Left) Analyzer vector is a function of wavelength and traces out a curve (color line) on the Poincaré sphere. The curve is shown inside a smallest enclosing circle (dashed circle). The deviation of the analyzer vector from the center of the circle is the analyzer vector variation [Eq. (1)]. (Right) The reconstruction errors of ${S_0}$, DoLP, DoCP, and AoLP are plotted as a function of incoming polarization states. We assume the incoming light is monochromatic at 680 nm. The incoming light is fully polarized with a fixed ${S_0} = {1}$, such that the DoCP and AoLP are sufficient to define all four Stokes parameters.
In order to reconstruct all four Stokes parameters, at least four intensity measurements through different polarization filters are required. The measured intensity $I$ is related to the analyzer vector $A$ of the polarization filter and the Stokes vector $S$ of incoming light,
The equation can be rewritten in matrix form by combining all $N$ measurements,
For our polarimeter, the measurement matrix is calibrated at a specific wavelength. The measurement matrix on the calibration wavelength is used to reconstruct the Stokes vector of incoming light at other wavelengths. This can be described as
Here $S$ and $S^\prime$ represent the actual Stokes vector and reconstructed Stokes vector. ${W_{\text{cal}}}$ is the calibrated measurement matrix. $W$ is the actual measurement matrix and depends on the spectrum of the incoming light, which can be measured separately. To get an accurate reconstruction, we want the ${W_{\text{cal}}^ +} W$ as close to the identity matrix as possible. That is the motivation for minimizing the analyzer vector variation.To illustrate the impact of analyzer vector variation on Stokes parameters reconstruction, we consider the following example. The polarimeter described in Fig. 4 is calibrated at 620 nm and is used to measure monochromatic polarized light at 680 nm. The reason for choosing these two wavelengths is that 620 and 680 nm are the peak and FWHM locations of the red pixel quantum efficiency curve shown in Fig. 5. The calibration is spectrum-dependent due to the chromaticity of the microretarder. We choose the peak of the spectrum responsivity, since no knowledge is provided about the image scene spectrum. However, if we know the image scene in advance, for example, the spectrum is monochromatic or is dominant in certain wavelength range, a calibration can be made at the known wavelength range to improve the accuracy of the camera. Back to this example, the analyzer vector at 620 nm is used to reconstruct the Stokes vector at 680 nm. The measured retardances of the microretarder layer at 620 and 680 nm are 40.37° and 36.71°, respectively, leading to analyzer vector variation of 2.70%, 2.70%, 5.79%, and 5.79% for the measurement tetrahedron’s four vertices. The numerical form of Eq. (5) is computed to be
Figure 14 (right) shows the calculated error of Stokes reconstruction for all possible polarized incoming light. The value of ${S_0}$ is underestimated or overestimated by up to 1.15% when the incoming light is linearly polarized at 22.5° or 112.5°. The largest AoLP reconstruction error is 0.62° when the AoLP of incoming light is at 0°, 45°, 90°, or 135°. The DoLP is overestimated by up to 5.6% when the incoming light is linearly polarized at 22.5°. The DoCP is underestimated or overestimated by up to 7.7% when the incoming light is right or left circularly polarized, respectively. In this example, analyzer vector variation has a smaller impact on the values of ${S_0}$ and AoLP and a larger impact on the values of DoLP and DoCP. In general, the impact of analyzer vector variation depends on the spectrum shape and polarization state of the incoming light.
Funding
National Science Foundation (1607358, 1918260).
Acknowledgment
The authors thank Dr. David Wilkes at Merck KGaA for help on negative dispersive LCP and Barry Seff at EMD Performance Materials for making RMM1705 available. The authors also thank Dr. Lu Lu and Dr. Oleg Yaroshchuk at Facebook Reality Labs for helpful discussions.
Disclosures
All authors declare no conflicts of interest or financial relationships to disclose.
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