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Abstract
Broadband polarimetric imaging consists of forming an image under spectrally wide illumination after having optimized the polarization state analyzer (PSA) to maximize the target/background discriminability. In previous works, the image sensor was monochrome, and only the intensity contrast was optimized. However, due to its spectrally varying response, the PSA not only changes the light’s intensity, but also its color. This color information can serve as a further parameter to improve discrimination. In this paper, we employ a color camera in a broadband Stokes (passive) polarimetric imaging system and take into color difference’s contribution to discrimination ability in optimizing the PSA setting. We show through experiments that a significant improvement of discrimination ability over monochrome imaging is obtained, especially when there are multiple objects in the scene.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarimetric imagers can reveal information that is not visible in classical intensity images. Therefore, they have many applications in target detection, remote sensing, and biomedical imaging [1–9]. In target detection applications, the target/background contrast (discrimination ability) can be significantly improved by matching the polarization state analyzer (PSA) of the imager to the observed scene [1,4,9]. To perform this optimization in an adaptive way, liquid-crystal variable retarders (LCVRs) that rapidly modulate the polarization state of PSA can be used [10]. For the sake of polarization accuracy of the PSA, a narrowband spectral filter is often inserted in the system, since the polarization response of LCVR is highly wavelength-dependent. However, spectral filters decrease the amount of light entering the system and thus the signal-to-noise ratio. In fact, in target detection applications, the main interest is contrast optimization instead of polarimetric accuracy. For that purpose, reducing the spectral range may not be the best choice. In previous works, it has been found that contrast can be increased by broadening the spectrum of the light entering the system, and in addition, contrast can be further improved by optimizing the PSA with respect to its own spectral response and to the spectral response of the scene [10–12].
In these previous works, the scene is illuminated with a spectrally wide light source [10–15], and the image is formed on a monochrome camera. The state of the PSA is thus optimized in order to maximize the gray level contrast between the background and a target of interest in this monochrome image. However, due to its spectrally varying response, the PSA not only changes the intensity of the light but also its color. This color variation can serve as a further parameter in addition to polarization in order to improve discrimination. Since previous works on broadband polarimetric imaging employed a monochrome camera [10,11], they did not exploit this valuable information, although it can be acquired at virtually no extra cost by using a color camera.
In this paper, we employ a color camera as the detector in a broadband Stokes (passive) polarimetric imaging system, in order to collect both polarization and color information about the scene under broadband illumination. Moreover, we take into account the contribution of color difference to discrimination ability in the optimization of the PSA setting. We show through experiments that a significant improvement of discrimination ability over monochrome imaging can be obtained, especially when there are multiple objects with different polarization properties in the scene.
2. Contrast optimization for broadband passive polarimetric imaging
In this section, we first briefly review the principle of classical broadband polarimetric imaging. We then describe the basics of color broadband polarimetric imaging, that forms the object of this article.
2.1. Broadband passive polarimetric imaging with monochrome camera
In monochrome broadband passive polarimetric imaging, contrast optimization is typically performed with a polarization state analyzer (PSA) composed of a linear polarizer and two liquid-crystal variable retarders (LCVR) [10,16]. In this case, the eigenstate T of the PSA is a function of the control voltages V1 and V2 of the two LCVRs. Let us denotethe Stokes vector of a polarized light. Our goal is to discriminate two regions a and b in the scene that scatter lights with different polarization states of Stokes vectors Sa and Sb. In the polarimetric image, these two regions will have intensities (graylevels) equal to:
where the superscript T denotes transposition. Optimization of the contrast between the two regions a and b is performed by determining the optimal eigenstate of PSA Topt that maximizes the intensity difference between the two regions in the image [4]. Therefore, the optimal state of PSA Topt is given by:Usually, the polarimetric properties of the objects in the scene and of the polarization analysis devices in the polarimetric imaging system depend on the wavelength λ. Hence the Stokes vectors of the two regions depend on wavelength and will be denoted and . Moreover, the eigenstate of the PSA, , also depends on wavelength. The monochrome camera integrates these wavelength-dependent contributions, and the measured intensity should be considered as the summation of the intensities over the entire spectrum:Therefore, Eq. (2) should be changed into an integral form as [10]:In practice, an exhaustive search is employed to find the optimal eigenstate of the PSA by testing every combination (V1, V2) [10,11].2.2. Broadband passive polarimetric imaging with color camera
The contrast optimization method described in the previous section can improve the contrast of the image by maximizing the intensity difference between the two regions of interest. However, it ignores an important characteristic of broadband imaging systems, which is color information. Indeed, in broadband polarimetric imaging systems, changing the state of the PSA not only changes the intensity of the transmitted light, but also its color. Hence in a broadband polarimetric image, different regions can be discriminated not only by their intensity difference but also by their color difference. Color can thus be used as a further degree of freedom to enhance discriminability. This valuable information can be easily collected by employing a color camera. In this section, we assume that a color camera is used instead of the monochrome camera, and describe contrast optimization of such broadband polarimetric color imaging in RGB color space.
In typical color sensors, due to the cross-talk effect of quantum efficiency, light intensity at a certain wavelength is always split into three individual intensities by certain percentages corresponding to R, G and B channels. Let us consider the sensor of the AVT Stingray F-033C camera that will be employed in our experiment as an example to illustrate the cross-talk effect. The quantum efficiency of RGB channels of the sensor at different wavelengths is shown in Fig. 1. It can be seen that the quantum efficiencies of the R, G and B channels have considerable spectral overlap. Let us denote the quantum efficiencies of R, G and B channels at a certain wavelength λ as QR(λ), QG(λ) and QB(λ) respectively. If a light with wavelength λ and intensity i illuminates the camera, the received intensities of RGB channels will be QR(λ)i, QG(λ)i and QB(λ)i respectively. Because of the cross-talk effect of the quantum efficiency, for a broadband light source, the intensities measured in each RGB channel can be expressed as:
It can be seen from Eq. (5) that the intensities measured in each RGB channel can be considered as the summation of the intensities over the spectrum of each RGB channel, and the intensity at each wavelength depends on the inner product of the eigenstate T of the PSA and the Stokes vector S.As an example, let us consider a scene with two regions a and b with different polarization and color properties. According to Eq. (5), each region has its unique RGB trichromatic coordinates, which can be expressed as:
It can be clearly seen from Eq. (6) that we can change the intensities in RGB channels, and hence the colors of the different regions in the color image, by modulating the control voltages of the PSA. The variation of the colors of a scene with four different regions with the PSA voltages can be seen in Visualization 1.In RGB color space, the Euclidean distance between two sets of trichromatic coordinates describes their color difference. We employ this distance as the contrast criterion for polarimetric color imaging. The optimal eigenstate of the PSA Topt can thus be expressed in the following form, in the sense that it maximizes the contrast defined by the Euclidean distance between two sets of trichromatic coordinates:
In this way, by employing a global search on the voltages of the two LCVRs, we can optimize the contrast of polarimetric color images. In the method of contrast optimization for monochrome polarimetric imaging described in the previous subsection, only the intensity difference contributed to the contrast. Conversely, in the optimization method expressed in Eq. (7), color difference also contributes to the contrast. Monochrome and color broadband polarization imaging will be compared on real images in the next section.3. Experimental validation and discussion
In this section, we perform real-world experiments of optimized broadband polarimetric imaging and compare the discrimination performance obtained with monochrome and color detection.
The experimental setup is shown in Fig. 2(a), which includes a color camera (AVT stingray F-033C) [16], a PSA composed with two LCVRs (Meadowlark Optics) and a linear polarizer [10,17]. A LED light source, whose emission spectrum is shown in Fig. 2(b), is employed to generate the broadband unpolarized illumination of the scene. In particular, the voltages of the two LCVRs (V1 and V2) are controlled by the voltage controller.
The structure of the scene in our experiment is illustrated in Fig. 3. It contains two adjacent regions referred to as a and b respectively. Each region is a superposition of white paper, a linear polarizer with a different orientation in region a and b, and a translucent adhesive tape. Since adhesive tapes are birefringent materials, the light scattered by the scene is modulated by a retarder and a linear polarizer, which gives elliptical polarization states. In our experiment, the difference between the orientations of the two polarizers in regions a and b is around 15°, which implies that the difference between the polarimetric properties of regions a and b is slight. In particular, the Stokes vectors for regions a and b are measured to be and at the wavelength of 632.8 nm, and the corresponding difference of the Stokes vectors between regions a and b is . It can be seen from the Stokes vectors that elliptical polarization states are also involved.
The image of the scene captured by a color camera without the PSA is shown in Fig. 4. In this image, it is hard to discriminate the regions a and b because they have similar color reflectivities.
3.1. Polarimetric contrast optimization with a monochrome camera
Let us first consider a broadband polarimetric imager using a monochrome camera. We can improve the contrast between these two regions because they have different polarization properties. The discrimination ability depends on the state of the PSA through the voltages V1 and V2 applied to the two LCVRs. We have represented in Fig. 5(a) the contrast defined in Eq. (2) as a function of the voltages (V1, V2). The maximal contrast is obtained for V1 = 3.8V, V2 = 2.15V. The optimal monochrome polarimetric image obtained with this PSA setting is shown in Fig. 5(b). A significant graylevel difference between the two regions is observed in this image (the graylevels for the two regions are measured to be 0.32 and 0.19, for an image pixel range from 0 to 1), so that the two regions can be easily discriminated.
Fig. 5 Left column: Monochrome polarimetric contrast C, defined in Eq. (8), as a function of (V1, V2) for (a) the scene with 2 regions, (c) the scene with 3 regions, (e) the scene with 4 regions. Contrast values are normalized to 1 in all maps separately. Right column: polarimetric monochrome image with optimal contrast of (b) the scene with 2 regions, (d) the scene with 3 regions, (f) the scene with 4 regions.
Let us now consider scenes with more than two different regions. In the presence of an arbitrary number n of different regions in the scene, we will define the contrast criterion as the product of the intensity differences between all different regions, which is given by:
wheredenotes the intensity difference between region i and region j. By maximizing the contrast criterion C, one can find the state of PSA leading to the optimal contrast of the monochrome polarimetric image.Let us first consider a scene containing three different regions a, b and c. As in the scene represented in Fig. 3, the polarimetric contrast between the different regions is due to slight differences in the angle of the polarizer. The variation of the contrast C, defined in Eq. (8), as a function of voltages (V1, V2) for the scene with three regions is represented in Fig. 5(c). The optimal voltages are found to be V1 = 2.7V, V2 = 3.05V. The monochrome polarimetric image obtained with this optimal PSA setting is shown in Fig. 5(d). It is observed that the graylevels are different in the three regions, however, it is also noticed that discrimination between regions b and c is relatively poor. In particular, the average graylevels for regions b and c in Fig. 5(d) are measured to be 0.04 and 0.11, which corresponds to a small graylevel difference.
As a further example, let us now consider a scene containing four different regions a, b, c and d. The polarimetric contrast between the regions is still due to slight differences in the angle of the polarizer. The variation of the contrast C as a function of voltages (V1, V2) for this scene is represented in Fig. 5(e). The optimal voltages are found to be V1 = 3.10V, V2 = 5.95V. The monochrome polarimetric image of this scene obtained with this optimal PSA setting is shown in Fig. 5(f). It is seen that the differences of gray level are insufficient to correctly discriminate the four regions, especially regions a and b (the average graylevels for regions a and b in Fig. 5(f) are measured to be 0.12 and 0.03).
To summarize, monochrome broadband polarimetric imaging can efficiently improve the graylevel contrast between regions with different polarimetric properties. However, the limited diversity of gray level space makes it difficult to obtain satisfying discrimination performance as the number of regions increases. This is why in the next section, we take into account color information in the imaging device and in the contrast optimization procedure.
3.2. Polarimetric contrast optimization with color camera
Let us now consider that a color camera is used as the image sensor in a broadband polarimetric imaging system. Figure 6(a) represents the variations of the color contrast defined in Eq. (7) with the voltage configuration (V1, V2) of the PSA. Comparing it with the map of monochrome contrast in Fig. 5(a), we can observe that it is quite different. Moreover, the optimal voltages that correspond to the maximum color contrast are found to be V1 = 5.2V, V2 = 3.35V, so they are also different from the monochrome case. The image of the two-region scene with this optimal PSA setting is shown in Fig. 6(b). The average RGB values for regions a and b are calculated to be and . The region a appears blue, the region b green, and this color difference makes them very easy to discriminate. Comparing with the image of the same scene using a monochrome polarimetric imager (Fig. 5(b)), it is obvious that the color image with optimal contrast has a better discrimination ability, because the contrast between the two regions is not only determined by a graylevel difference, but also by a color difference.
Fig. 6 Left column: Color polarimetric contrast as a function of (V1, V2) for (a) the scene with 2 regions, (c) the scene with 3 regions, (e) the scene with 4 regions. Contrast values are normalized to 1 in all maps separately. Right column: color polarimetric image with optimal contrast of (b) the scene with 2 regions, (d) the scene with 3 regions, (f) the scene with 4 regions.
Let us now assume that the scene is composed of three different regions a, b and c. We first have to choose a definition of the global color contrast on color polarimetric images. For that purpose, let us consider the triangle formed by three points representing the regions a, b and c, in the RGB trichromatic space, namely, Pa, Pb and Pc. This triangle is represented in Fig. 7(a). We will consider the area of this triangle as the contrast criterion in polarimetric color imaging [18]. In other words, the contrast between different regions will be considered to be optimal when the area of the triangle reaches its maximum value.
The variation of this contrast as a function of the PSA voltages (V1, V2) is represented in Fig. 6(c). The optimal voltages to be V1 = 3.75V, V2 = 2.65V. Comparing with the same map obtained for monochrome imaging (see Fig. 5(c)), we can see it is quite different and that the values of the optimal voltages are also different. The color polarimetric image obtained with the optimal PSA setting is shown in Fig. 6(d). The three regions a, b and c appear to be forestgreen, blue and atrovirens respectively with the average RGB values of , , , and we can clearly distinguish these regions by their distinct color differences. In sharp contrast, the monochrome polarimetric image of this scene represented in Fig. 5(d) shows relatively poorer discrimination performance, since in particular, the regions b and c are difficult to discriminate. They are much more distinct thanks to the addition of color information.
As a final example, let us now consider that the scene is composed of four regions a, b, c and d. The four points corresponding to regions a, b, c and d in the RGB trichromatic space, namely, Pa, Pb, Pc and Pd, form a tetrahedron in RGB color space as shown in Fig. 7(b). In this case, we consider the volume of the tetrahedron as the contrast criterion, and the global contrast between the regions will be considered optimal when the volume of the tetrahedron reaches the maximum value. The variation of this contrast as a function of the PSA voltages (V1, V2) is represented in Fig. 6(e).The optimal voltage configuration is found to be V1 = 2.65V, V2 = 1.20V whereas for monochrome imaging, it was V1 = 3.10V, V2 = 5.95V (see Fig. 5(e)).
Fig. 7 (a) Schematic of the coordinates of three objects and the corresponding triangle in RGB color space. (b) Schematic of the coordinates of four objects and the corresponding tetrahedron in RGB color space.
The color polarimetric image obtained with the optimal PSA setting is shown in Fig. 6(f). The four regions a, b, c and d appear with different colors of blue, forest green, cyan and plum respectively with the average RGB values of ,, , . They can be easily discriminated by their distinct color differences. The increase of discriminability compared to the optimal monochrome image of the same scene (see Fig. 5(f)) is striking: the four regions can now be easily discriminated, whereas in Fig. 5(f), it is obvious that graylevel differences are not sufficient, especially between regions a and b.
Summarizing these results, we can say that introducing color imaging into a broadband polarimetric imaging system improves target discrimination. Moreover, when the number of regions to discriminate increases, the advantage of polarimetric color imaging becomes even more significant. It is due to the fact that diversity in RGB color space is much richer than diversity in graylevel space.
4. Conclusion
In conclusion, we have proposed a method of contrast optimization in broadband passive polarimetric imaging based on color camera, in which the color polarimetric image is captured and the color difference is considered as the contrast criterion. Compared with the previously proposed method of contrast optimization for polarimetric monochrome images, the method proposed in this paper shows a distinct superiority in terms of discrimination performance, which is attributed to the contribution of color difference. In addition, the experimental results also show that in the case of discriminating multiple regions in the scene, the advantage of our method is even more distinct thanks to the richer diversity of color space. The efficiency of broadband polarimetric imaging systems can thus be significantly improved at virtually no extra cost by replacing the monochrome sensor by a color camera.
The method of contrast optimization for broadband polarimetric imaging based on color camera proposed in this paper goes beyond the particular case of Stokes polarimetric imaging, and can be extended to other types of polarimetry, such as Mueller polarimetric imaging [19,20] and orthogonal state contrast (OSC) polarimetric imaging [21].
Funding
National Natural Science Foundation of China (No. 61775163), National Instrumentation Program (No. 2013YQ030915), Young Elite Scientists Sponsorship Program by CAST (2017QNRC001), Director Fund of Qingdao National Laboratory for Marine Science and Technology (QNLM201717), China Postdoctoral Science Foundation (No. 2016M601260).
Acknowledgments
Haofeng Hu acknowledges the Fondation Franco-Chinoise pour la Science et ses Applications (FFCSA) and the China Scholarship Council (CSC).
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