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Abstract
A compressive space-dimensional dual-coded hyperspectral polarimeter (CSDHP) and interactive design method are introduced. A digital micromirror device (DMD), a micro polarizer array detector (MPA), and a prism grating prism (PGP) are combined to achieve single-shot hyperspectral polarization imaging. The longitudinal chromatic aberration (LCA) and spectral smile of the system are both eliminated to guarantee the matching accuracy of DMD and MPA pixels. A 4D data cube with 100 channels and 3 Stocks parameters is reconstructed in the experiment. The feasibility and fidelity are verified from the image and spectral reconstruction evaluations. It is demonstrated that the target material can be distinguished by CSDHP.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the continuous development of emerging fields such as remote sensing, resource detection, anti-terrorism, and chemical defense in complex environments. Higher spectral resolution and contrast are needed as traditional spectral detection methods no longer meet application needs. Therefore, an imaging system that can simultaneously acquire hyperspectral $(\lambda )$, polarization, $(P)$ and spatial information $(x,y)$ about the target is needed to form four- dimension 4D data cubes of the target $(x,y,\lambda ,P)$. Spectral polarization imaging (SPI) systems are divided into time-division imaging systems and snapshot imaging systems. Time- division spectral polarization imaging systems are scanned chronologically in the spatial or spectral domain. The spectral polarization information of static targets is obtained through multiple snapshots such as rotary type [1–5], liquid crystal tunable filter type (LCTF) [6–8], acousto-optic tunable filter (AOTF) [9–11], and dual optical elastic modulator type [12]. These kinds of systems can achieve spectral polarization image of static targets. However, using time-division imaging method for moving targets detecting leads to stitching misalignment, interferometric beam drift, polarizer switching, or mechanical motion of the system. Incorrect intensity data obtained by detector will course the reconstruction data cube unavailable. It is significant to research snapshot hyperspectral polarimeter for moving targets detection.
The snapshot imaging method does not need a scanning mechanism. The images of moving target can be obtained by single-exposure or multiple-exposure. Various methods include split amplitude [13–15], Fourier [16–19], split-focus planar [20–27], polarized grating [28–30], and computed tomography (CTIS) [31]. With the maturity of compressive sensing techniques and coded aperture snapshot spectral imaging (CASSI) [32,33], more and more scholars have adopted coding techniques to recover spatial, spectral, and polarization data in sparse signals. In 2013, Tsung Han Tsai et al. proposed a compressive linear polarization spectroscopic imager based on the CASSI of uniaxial birefringent crystals [34]. The operating band is between 400 to 680 nm and contains 19 spectral channels as well as two Stokes parameters. A uniaxial birefringent crystal was used to disperse the target data cube, and an algorithm was subsequently used to reconstruct the spectrum and polarization. In 2015, Fu et al. proposed a compressive spectral and polarization imager consisting of a rotating prism, a pixelated polarizer, and a colored detector [35]. The combined form of the pixelated polarizer and color detector is similar to the structure function of the micro-polarizer detector, but the whole system requires sampling multiple times through the rotating prism, which reduces its effectiveness. In 2019, Ren proposed a channeled compressive imaging spectropolarimeter [36] which consisting of high-order retarders, a double amici prism (DAP), and a polarizer filter wheel (PFW) to acquire full Stocks parameters for 450-700 nm and 12 spectral channels. However, due to the form of the PFW, five measurements are required to acquire the data cube. In 2021, Ning used a combination of a DAP and Wollaston prisms for compressive circular polarization snapshot spectral imaging [37]. The system uses Wollaston prisms to obtain the target dual Stocks polarization information containing 25 spectral channels with circular polarization. However, objects in nature contain few circular polarization information. In 2022, Chen demonstrated a coded aperture full-stokes imaging spectropolarimeter with a rotatable retarder, a polarizer and a digital micromirror device (DMD) [38]. Chen’s method can obtain full polarization data of 15 spectral channels from 420-700 nm. Although full polarization data can be obtained, there is still a rotating mechanism in the system and the advantages of snapshot spectral imaging in data acquisition speed are completely lost.
Compressive hyperspectral polarization imaging has the advantages of acquiring moving target muti-spectral data instantly. This method provides more basic data to moving targets identification and inversion. However, in existing compressive spectral polarization imaging, the matching and unmixing technologies are independent of the optical system, which simply combines the polarization and spectral devices. There does not form effective cooperation for the optical system, matching, and unmixing. Results in difficulty to play the real effect of computational optics and achieve compressive hyperspectral polarization.
To address these issues, we proposed a compressive space-dimensional dual-coded hyperspectral polarimeter method in our patent [39]. In order to meet the exposure time requirement for detecting moving targets, we propose a compressive space-dimensional dual-coded imaging method with the micro polarizer array (MPA) detector and DMD. The prism grating prism (PGP)is used to improve the dispersion capability and spectral uniformity. In order to separate the aliasing data generated by the combination of DMD, PGP and MPA, the micro-mirror and super-pixel matching method, super-pixel separation and unmixing method are proposed, respectively. The accuracy of pixel matching and unmixing will affect the reconstruction performance of system. The requirements for optical design are pointed out by using interactive design method. The optical system is optimized to control such as pixel matching, spectral smile, longitudinal chromatic aberration (LCA) and system coaxial. Finally, a 4D data cube containing hyperspectral images and linear polarization images are obtained with just only one single-shot. The interactive design method can improve the correlation between computational imaging and optical design.
2. Principle
2.1 Framework
The process of compressive space-dimensional dual-coded hyperspectral polarimeter is divided into four steps. Firstly, we adopted a snapshot, single-detector detection format for moving target hyperspectral polarization imaging. Secondly, the aliasing data of spectrum and polarization is obtained by using DMD and MPA. The PGP is selected to achieve the required dispersion capability, spectral uniformity, and coaxiality of the system. Thirdly, the imaging form of dual-encoded requires high image element matching accuracy, the micro-mirror and super-pixel matching method and super-pixel separation and unmixing method are proposed to put forward requirements for optical system. Fourthly, the spectral signal is reconstructed by the TwIST algorithm, the polarization signal is reconstructed by the super-pixel partition domain. Finally, the field-of-view error is bilinearly interpolated to obtain the final 4D data cube.
As shown in Fig. 1, the CSDHP consists of DMD, PGP, MPA detector, objective, relay and imaging lens. The 4D data cube is imaged through the objective at the primary image plane, as shown in A1; the DMD is placed at the primary image plane of the objective to encode and modulate the data cube, and the encoded data cube is obtained, as shown in A2. The rays pass through the relay lens to emit parallel rays. Then the parallel rays incident to the PGP to generate dispersion. Eventually the dispersive rays converge to the MPA detector by imaging lens. Adjacent spectrum is evenly distributed on the focal plane at regular distances, as shown in A3. Finally, the coded and dispersive data cube containing degree of linear polarization (DOLP) is obtained by the MPA detector, as shown in A4. The four adjacent pixels on the MPA detector are arranged counterclockwise as a super-pixel, and each super-pixel is formed by the four polarization-direction micro-polarizers which corresponds to 0°, 45°, 90° and 135°.
Fig. 1. Structure of CSDHP (A1 is the data cube of the target, A2 is the data cube after DMD coding, A3 is the data cube after PGP dispersion, and A4 is the data cube acquired by the detector surface).
2.2 Micro-mirror and super-pixel matching method and discretization analysis
In Fig. 1A3, the imaging lens focal length and the dispersion capability of the PGP determine the aliasing state of multi-dimensional date together. Based on the compressive space-dimensional dual-coded hyperspectral polarimeter scheme, the center of the Airy spot of the ${\lambda _\textrm{n}}$ spectrum coincides with the first-level dark ring of the Airy spot of the ${\lambda _{\textrm{n + 1}}}$ spectrum at the $2\gamma ( \gamma \in N\ast )$ pixels. After coding and dispersion, the data cube reaches the discretized representation of the MPA's confounding information as shown in Fig. 2. So according to the Rayleigh criterion,
where the dispersion $dl$ between two spectral lines with wavelength difference of $d\lambda$ on the imaging focal plane denotes the line dispersion.${p_{MPA}}$ is the size of the MPA detector pixels, and the $\gamma$ denotes the number of detector pixels.From Eq. (1), the distance between adjacent spectral channels on the MPA after passing through the imaging lens is exactly an even multiple of super-pixels. This allows aliasing data unseparated causing by the instantaneous field-of-view error.
To match the pixel size of DMD and MPA, the micromirror size of DMD is an integer time the pixel size of MPA after correction by relay and imaging lens
where $\eta$ is a positive integer, ${p_{DMD}}$ is the DMD micromirror size, ${f_{relay}}$ is the focal length of the relay lens, and ${f_{imaging}}$ is the focal length of the imaging lens.As $\eta$ increases, the spatial resolution of the system decreases, and the DMD micromirror size corresponds to MPA pixels of $\eta \times \eta$. The spatial resolution of the system is determined by the DMD, the resolution of the MPA, and the focal length of the relay lens together. The spectral resolution is determined by the dispersion capability of the PGP together with the focal length of the imaging lens. Therefore, we model the discrete energy transport of the system with the spectral density of each polarization Stocks parameter before entering the system expressed as
The spectral density after the coded aperture is
$T({x_{DMD}},{y_{DMD}})$ denotes the spectral polarization density corresponding to the DMD spatial coordinates. After optical design alignment, the spatial coordinates of space, DMD, and detector target surface correspond to each other and so they areAfter PGP dispersion along the y-axis, the spectral density currently is
Since a one-dimensional grating is used, the spectral density in the detector plane is dispersed on the axis. Finally, the encoded data cube is projected onto the sensor of the MPA detector. The final continuous image on the detector plane can be described as
where $\omega (\lambda )$ is the spectral response coefficient corresponding to the wavelength.Finally, each pixel of the detector measures the integrated intensity of the spectral density at a specific polarization angle. Detector surfaces are pixelated in space at the size of image elements ${p_{MPA}}$, so that the spatial domain at the detector plane $g^{\prime}({x_3},{y_3})$ is sampled as
From Eq. (8), the correspondence of the micro-mirrors and pixels can be derived. Each pixel contains a discrete spectral data and three parameters of polarization data. In the polarization array, each polarization parameter is encoded and filtered to form the spectral and polarization aliasing data. For a single exposure, the sensing matrix of the system is
2.3 Super-pixel separation unmixing and reconstruction method
As shown in Fig. 3 A5, the aliasing data received by MPA detector, from each of the four pixels (0°, 45°, 90°, and 135°) composed of one super-pixel, is relatively independent and in different directions. According to the result of the polarization encoded, the super-pixels are separated, as shown in Fig. A6. The groups of pixels with the same polarization angle are grouped to form four groups of images with different polarization directions. To ensure the aliasing state, the adjacent spectral interval is changed from $2\gamma ( \gamma \in N\ast )$ to $\gamma$ pixels. At this time, the sensing matrices are still known and conform to the original RIP criterion. Convex optimization algorithms can be used to reconstruct the information.
The TwIST algorithm used in this study is denoted as
As shown in A7, the spectral images of the four polarization angles are obtained separately after reconstruction. The pixels are then reconstructed into a spectral polarization image with an instantaneous field-of-view error according to the corresponding positions of the polarization code, as shown in A8. Subsequently, using the bilinear difference method, the polarization super-pixels are complemented to resolve the instantaneous field-of-view error. Finally, the spectral data cubes of the Stocks are obtained separately, as shown in A9. The 4D data cube is deconstructed by the CSDHP with a single shot The complex Fourier transform is reduced, and the unmixing and reconstruction efficiency of the CSDHP improves.
3. Interactive design
3.1 Analysis and optimization of spectral smile
The CSDHP reconstructs the spectral polarization data cube by using the unmixing 2D spectral polarization aliased data. However, the spectral smile of the optical system will cause the spectral lines deviating along the dispersion direction, which will introduce errors in pixel extraction during reconstruction.
The shape of PGP is optimized to control the system spectral smile. Then the system is optimized by ZEMAX to keep system coaxial. The original prism top angles are ${\theta _1}\textrm{ = }{\theta _2}\textrm{ = 14}\textrm{.}{\textrm{5}^ \circ }$. The material of prisms is both SF14, and the grating material is B270. By changing the top angle ${\theta _1}$ of prism 1(${\Pr _1}$), the relation among ${\theta _1}$, spectral smile, and Peak Signal to Noise Ratio (PSNR) of reconstructed image which contaminated by spectral smile can be obtained. Concurrently, the relationship between the top angle ${\theta _2}$ of prism 2(${\Pr _2}$)and the spectral smile, obtained is shown in Fig. 4.
As we can see from Fig. 4, changing the ${\theta _1}$ can correct the spectral smile of the system. With the decrease of the ${\theta _1}$, the spectral smile decreases from 21.198 µm to 4.313 µm with a decrease of 79.65%. As the spectral smile decreases, the PSNR of the reconstructed image also begins to gain. The ${\theta _2}$ does not change the system spectral smile by a significant amount compared to ${\theta _1}$. However, in the PGP, the ${\theta _1}$ cannot be 0. Therefore, we try to reduce the spectral smile by rotating the angle ${\theta _3}$ of the PGP which maintains the grating Bragg diffraction angle. Concurrently, ${\theta _2}$ is optimized to keep the system coaxial.
According to the dispersion principle of PGP, as shown in Fig. 5(a), we analysis and improve the traditional PGP elements. When the rays reach the grating at Bragg angle,
Fig. 5. Spectral smile analysis. (a) Schematic diagram of the PGP principle. (b) Relationship between ${\theta _1}$, ${\theta _2}$ and PSNR.
According to the geometric relationship, the angle of incidence $\alpha _{{\lambda _{Bragg}}}^G$ is related to the ${\theta _1}$ as follows
When the Bragg diffraction condition is satisfied, the relation between ${\theta _1}$ and ${\theta _3}$ is
In ${\Pr _2}$, the relationship between the refraction angle $\beta _{{\lambda _C}}^{{{\Pr }_2}}$ and the grating diffraction angle $\beta _{{\lambda _C}}^G$ can be derived from the law of refraction and geometric relations.
To keep the system coaxial, the refraction angle $\beta _{{\lambda _C}}^{{{\Pr }_2}}$ of the light at the central wavelength ${\lambda _C}$ in the ${\Pr _2}$ should be
Therefore, by associating the above equations, we can obtain the relations between ${\theta _1}$, ${\theta _2}$ and ${\theta _3}$,
The relation between the PSNR and the reconstructed image is shown in Fig. 5(b).
Figure 5(b) shows the PSNR relationship between ${\theta _1}$, ${\theta _2}$ and the optimized images, the image PSNR is greater than 30 dB. According to Eq. (18), the system can be solved to meet the coaxial conditions of ${\theta _1}$, ${\theta _2}$ for the curve in the figure. As we know, a PSNR of greater than 35 is known to be of good quality [40]. At point Z in the figure, we choose a top angle ${\theta _1}$ of 10.3° for ${\Pr _1}$, 10.8° for ${\Pr _2}$, and a rotation angle of 2.1°, giving a PSNR of 35.0084 dB. The prism material was SF14 (model crystock-DSP-SF14) and the grating material is B270. The maximum value of the spectral smile is about 1.68µm, accounting for 48.9% of a pixel size. The results of spectral smile meet the system requirements for a spectral smile.
3.2 Analysis and optimization of longitudinal chromatic aberration
The LCA is formed by the rays of different wavelengths arranged on the optical axis through the lens. The optical path difference will be formed after dispersion. Traditional methods to correct LCA is to rotate detector. But the rotating MPA detector cause the pixel mismatch. Therefore, it is necessary to keep the detector perpendicular to the optical axis while correcting the LCA It is known that the power of a single lens is [41]
where $D(\lambda ) = \sum\limits_1^{m - 1} {\frac{{v \times ( {n_\lambda } - {n_{{\lambda _C}}}) }}{{{{({n_{{\lambda _C}}} - 1)}^2}}}}$ is the dispersive power, ${n_{{\lambda _C}}}$ is the refractive index of the center wavelength in the lens, ${n_\lambda }$ is the refractive index of the corresponding wavelength $\lambda$, and $v$ represents the Abbe number of the material.If there are $m$ kinds of glass materials constituting the objective lens, the total focal power of the objective lens can be expressed as
When the system has no LCA, we observe that
For the convenience of calculation, we simplify the above equation into matrix form as $\varphi (\lambda )\cdot D = 0$.
Then its augmentation matrix is
Since the rank of the augmented matrix is less than $n$, the original system of equations has infinitely many solutions. The LCA cannot be 0, so the equation also becomes to find the minimum value of the last column of the augmented matrix. So according to Eqs. (21) and (23), the final equation is reduced to
Combining the above equations, we get
Three-hundred kinds of materials in the working band of 400-650 nm from the CDGM glass library are selected and analyzed them with Eq. (25). The final magnitude of ${\Phi _{\min }}\textrm{(}\lambda \textrm{)}$ is proportional to the Abbe number $v$ of the material and proportional to ${n_{{\lambda _1}}} - {n_{{\lambda _n}}}$ in the equation, as shown in Fig. 6(a). The horizontal coordinate is the code of the glass, the vertical coordinate is the coefficient $v^{\prime}$, $v^{\prime} = \frac{{({{n_{{\lambda_1}}} - {n_{{\lambda_n}}}} )}}{{{{({n_{{\lambda _C}}} - 1)}^2}}}$. Finally, the Coronet glass and Flint glass with the lowest $\varphi (\lambda )$ is H-ZLaF89L and H-LaK53B, respectively. The initial structure of inclined PGP, imaging lens, and the LCA are shown in Fig. 6(b),(c). The maximum LCA is less than 0.109 mm.
Fig. 6. LCA correction results. (a) Relationship between glass code and the coefficient $v^{\prime}$. (b) Longitudinal chromatic aberration. (c) Structure of imaging lens and PGP.
3.3 Optical design
The correspondence between the line dispersion of the system and the MPA pixels is given in Eq. (1)-(2), and the spectral resolution of the system is determined by the PGP and the imaging lens, which results in the following equations
Combining the above equation, the role dispersion of the PGP spectral element is
Then, according to Eq. (1), the focal length of the imaging lens ${f_I}$ is
By optimizing the focal length of the imaging lens ${f_I}$ and relay lens ${f_\textrm{C}}$, the DMD micromirror size can be scaled $\textrm{1}:r$ to align with the detector pixels. Assuming a detector resolution of $\textrm{M} \times \textrm{N}$ and a DMD resolution of $\Delta \textrm{M} \times \Delta \textrm{N}$, the final spectral channel limit ${\lambda _{limit}}$ is given by
According to the interaction design, we give the optimization requirements of the CSDHP using micro-mirror and super-pixel matching method and the super-pixel separation and unmixing method, allowing objective lens, relay lens and imaging lens to be optimized. The DMD provides the primary image of the system with a resolution of 1920 × 1080, pixel size of 7.65 µm, and rotation of 45 degrees. The focal length of objective lens is 100 mm and the aperture is 20 mm.
The rays emitted from the DMD pass through the relay lens. The optical path difference induced by DMD is optimized by the relay lens. The rays emitted are close to parallel. According to Eqs. (2) and (28), the focal length of the relay lens is 50 mm, the focal length of the imaging lens is 22.6 mm and the effective focal length of system is 45.1 mm. The pixel size of the MPA detector is 3.45 µm and the exposure time is 30 fps. The number of spectral channels of the CSDHP is 100.The working wavelength is from 400 nm to 650 nm. The spectral smile is less than 0.5 pixels. The separation distance between adjacent wavelengths on the detector is 13.8 µm. The Modulation Transfer Function (MTF) of the system is better than 0.4 at 144 lp/mm. The total length of the CHDHP is less than 450 mm. The structure, MTF, and footprint diagram of the CSDHP are shown in Fig. 7(a), (b), and (c), respectively.
The moving targets can be imaged in a single shot related to the frame rate ${\varepsilon _{frame}}$ of the system detector, target speed ${V_{target}}$, focal length of system ${f_{system}}$, MPA detector pixel size ${p_{DMD}}$, field angle ${\alpha _{FOV}}$, exposure time of detector ${t_{exposure}}$, and imaging distance ${L_{image}}$. Distance of moving target in the field of view ${L_{fov}}$ is
So, ${V_{target}} = \frac{{{L_{fov}}}}{{{t_{exposure}}}} = \frac{{{p_{MPA}} \times {L_{image}}}}{{{f_{system}} \times {t_{exposure}}}}$. According to the index of CSDHP, the moving target speed is less than 2.45 m/s when the imaging distance at 100 m.
4. Experiments
4.1 Experimental platform construction
To the best of our knowledge, a coded aperture snapshot linear-Stokes imaging spectropolarimeter with a DAP and MPA has been reported in recent years [42]. Using single or multiple shots with direct probe polarization, simulated images have been acquired. However, in this study, a compressive hyperspectral polarization imaging proposed with a DMD, PGP, and MPA. To satisfy the requirements of the unmixing and reconstruction, we proposed a matching and unmixing methods for the CSDHP. Figure 8 depicts the experimental prototype of CSDHP. The coded aperture selected DMD (Texas Instruments DLP6500), which includes 1920 × 1080 elements of random binary pattern with 7.65µm × 7.65 µm mirror pitch. The measured image is taken by a MPA detector (Flir Blackfly BFS-U3-123S6C-C) with pixel size of 3.45 µm and resolution of 4120 × 3000. The abbreviated letters of this institution are chosen for the corresponding target, C for red aluminum, U for white plastic, S for light yellow cardboard, and T for blue rubber.
Fig. 8. System desktop level experiment. (a) Structure of CSDHP; (b) target taken by cell phone; (c) detector image.
4.2 Calibration and results
The CSDHP is aligned and calibrated before acquiring the spectral polarization mixed image. The aligned image uses a cross-fork filament as the reference target, and the imaging lens, PGP, and MPA detector are adjusted to meet the requirements of the micro-mirror and super-pixel matching method. The calibration process uses tungsten and mercury integrating spheres to produce a broadband uniform area source, and four sets of high-performance narrowband filters at 488, 532, 570, and 632.8 nm are placed at the light outlet for the spectral calibration of the system. The reconstructed spectral polarization image is shown in Fig. 9(a)∼(e).
Fig. 9. Spectral polarization images of CUST letters. (a) 0°, (b) 45°, (c) 90°, (d) 135°, (e) DOLP, (f) DOLP@539 nm, (g) 135°@539 nm, (h) ground truth.
A comparison of Fig. 9(a)∼(d) shows that each letter has a reasonable spectral resolution in the four sets of spectral images in the polarization direction, and the letters C and T have obvious peak bands that can be easily distinguished. It is difficult to distinguish the materials of letters U and S with the spectral reconstruction information from Fig. 9(a)∼(d). But in Fig. 9(f) and (g), the letters U and S can be clearly distinguished by the image of DOLP and 135°. It can be concluded that the spectral polarization reconstruction performance is effective. This proves that spectral polarization image can be used to distinguish the target materials.
4.3 Discussions
Normally, the reconstructed performance of image processing is estimated by the image quality and spectral profile. In this part of image quality, the Structural Similarity (SSIM) and Peak Signal-to-Noise Ratio are both adopted to measure the reconstruction performance.
To analyze the robustness against noise, Gaussian Noise is induced in the standard image to generate contaminated images within 5 dB to 45 dB SNR with an interval of 5 dB. The relationships among the SNR, Wavelength and SSIM in different polarization angles are shown in Fig. 10.
Fig. 10. Relationship among SNR, wavelength, and SSIM in different polarization angles. (a) 0°, (b) 45°, (c) 90°, (d) 135°.
When the SNR of contaminated images is greater than 30 dB, the SSIM values are greater than 0.8 dB. When the reconstructed images SNRs of four polarization angles are up to 45 dB, the SSIM are all close to 1 dB. These results indicate that the image could be reconstructed effectively when the SNR is greater than 15 dB.
The relationships among the SNR, Wavelength and PSNR in different polarization angles are shown in Fig. 11. It can be found that the PSNRs are greater than 20 dB when the SNR is greater than 20 dB. The PSNR with individual wavelength will decrease slightly when the SNR is approximately equal to 30 dB. Therefore, the reconstruction performances could achieve the optimal result while the SNR is greater than 30 dB. Furthermore, the reconstructed performance of 0°image and 90°image (or 45°image and 135°image) are big different which consists Malus’s Law.
Fig. 11. Relationship among SNR, wavelength, and PSNR in different polarization angles: (a) 0°, (b) 45°, (c) 90°, (d) 135°.
In terms of spectral profile, four sampling points on four target letters in Fig. 9(h) are selected to analyze the reconstructed performance. The reconstructed spectral profile is compared with the measurement results from micro-spectrometer (Ocean Optics STS-VIS). The comparison results are shown in Fig. 12. The intensity of sampling point is normalized to the range 0 to 1.
Fig. 12. The spectral profiles of different spatial points. (a) point 1, (b) point 2, (c) point 3, (d) point 4.
It can be found that the reconstructed spectral profile of CSDHP is similar to that of STS-VIS. The spectral reconstructed performance satisfies the using requirement. The spectral profile can be quantified by using root mean square error (RMSE) and spectral angle mapper (SAM). The smaller value of RMSE and SAM prove the higher reconstructed performance. The RMSE and SAM of the spectral profile are listed in Table 1 and Table 2, respectively.
Table 1. RMSE of the spectral profile (a.u.)
Table 2. SAM of the spectral profile (°)
It shows that the RMSE and the SAM will approach to 0 while the SNR is 45 dB. According to the correspondence between SNR and RMSE, the SNR of reconstruction in four polarization angles images are greater than 30 dB but lower than 35 dB. The spectral profile of 90° and 135° polarization angle is better than that of 0°and 45°. Therefore, the identical conclusions taken based on each evaluation criteria are consistent. Therefore, the reconstruction is effective while the image is not contaminated seriously.
5. Conclusion
In conclusion, we have proposed a compressive space-dimensional dual-coded hyperspectral polarimeter (CSDHP) based on DMD, PGP, MPA detector and an interactive design method. The DMD and MPA detector modulate the spectral polarization data cube by pixel matching. The requirements of unmixing and reconstruction have been validated according to the interactive design method. The relations among the spectral smile and LCA, PGP top angle and rotating angle, and lens material are studied. The simulation shows that interactive design can improve the accuracy of computational optics. The optical system is optimized at good state by interaction design. The aliasing rays is controllable in condition of meeting the imaging requirements.
Finally, a 4D data cube with 100 spectral channels and 3 Stocks vectors in the spectral range of 400 to 650 nm was acquired by a CSDHP with a single shot. According to the simulation of the robustness against noise of the system, the reconstruction performance could achieve the optimal result while the SNR is greater than 30 dB. Space-dimensional dual-coded scheme is valid in promoting the reconstruction quality of the system.The reconstruction performance of the CSDHP is similar to that of the STS-VIS. The results show that the moving targets with speed of 2.45 m/s can be identified by the CSDHP. Additionally, this paper provides a theoretical foundation for the interactive design and optimization of matching, unmixing, and imaging systems used in computational optics.
Funding
National Natural Science Foundation of China (61805027, 61805028, 61890960).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. Yu, T. Liu, H. Huang, H. Hu, and B. Huang, “Multispectral Stokes Imaging Polarimetry Based on Color CCD,” IEEE Photonics J. 8(5), 1–10 (2016). [CrossRef]
2. P. J. Lapray, L. Gendre, A. Foulonneau, and L. Bigué, “Database of polarimetric and multispectral images in the visible and NIR regions,” Proc. SPIE 10677, 1067738 (2018). [CrossRef]
3. A. El-Habashi, J. Bowles, R. Foster, D. Gray, and M. Chami, “Polarized observations for advanced atmosphere-ocean algorithms using an airborne multi-spectral hyper-angular polarimetric imager,” J. Quant. Spectrosc. Radiat. Transfer 262, 1–20 (2021). [CrossRef]
4. M. N. Islam, M. Tahtali, and M. Pickering, “Specular Reflection Detection and Inpainting in Transparent Object through MSPLFI,” Remote Sens. 13(3), 455 (2021). [CrossRef]
5. S. Li, J. Jiao, and C. Wang, “Research on Polarized Multi-Spectral System and Fusion Algorithm for Remote Sensing of Vegetation Status at Night,” Remote Sens. 13(17), 3510 (2021). [CrossRef]
6. H. Kurosaki, H. Koshiishi, T. Suzuki, and K. Tsuchiya, “Development of tunable imaging spectro-polarimeter for remote sensing,” Adv. Space Res. 32(11), 2141–2146 (2003). [CrossRef]
7. K. Homma, H. Shingu, H. Yamamoto, M. Shibayama, K. Sugahara, and S. Itano, “Agro-environment observation using near-infrared LCTF spectropolarimeter,” Proc. SPIE 5655, 407–418 (2005). [CrossRef]
8. J. Qi, C. He, and D. S. Elson, “Real time complete Stokes polarimetric imager based on a linear polarizer array camera for tissue polarimetric imaging,” Biomed. Opt. Express 8(11), 4933–4946 (2017). [CrossRef]
9. N. Gupta, “Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager,” Opt. Eng. 41(5), 1033–1038 (2002). [CrossRef]
10. F. Li, Y. Xu, and Y. Ma, “Design of hyper-spectral and full-polarization imager based on AOTF and LCVR,” Proc. SPIE 9298, 92980U (2014). [CrossRef]
11. R. Abdlaty, S. Sahli, J. Hayward, and Q. Fang, “Hyperspectral imaging: comparison of acousto-optic and liquid crystal tunable filters,” Proc. SPIE 10573, 700–708 (2018). [CrossRef]
12. D. J. Diner, A. Davis, B. Hancock, G. Gutt, R. A. Chipman, and B. Cairns, “Dual-photoelastic-modulator-based polarimetric imaging concept for aerosol remote sensing,” Appl. Opt. 46(35), 8428–8445 (2007). [CrossRef]
13. X. Tu, O. J. Spires, X. Tian, N. Brock, R. Liang, and S. Pau, “Division of amplitude RGB full-Stokes camera using micro-polarizer arrays,” Opt. Express 25(26), 33160–33175 (2017). [CrossRef]
14. T. Mu, S. Pacheco, Z. Chen, C. Zhang, and R. Liang, “Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy,” Sci. Rep. 7(1), 42115 (2017). [CrossRef]
15. J. Rehbinder, J. Vizet, J. Park, R. Ossikovski, J.-C. Vanel, A. Nazac, and A. Pierangelo, “Depolarization imaging for fast and non-invasive monitoring of cervical microstructure remodeling in vivo during pregnancy,” Sci. Rep. 12(1), 12321 (2022). [CrossRef]
16. T. Mu, C. Zhang, C. Jia, and W. Ren, “Static hyperspectral imaging polarimeter for full linear stokes parameters,” Opt. Express 20(16), 18194–18201 (2012). [CrossRef]
17. J. Li, B. Gao, C. Qi, J. Zhu, and X. Hou, “Tests of a compact static Fourier-transform imaging spectropolarimeter,” Opt. Express 22(11), 13014–13021 (2014). [CrossRef]
18. C. Zhang, N. Quan, and T. Mu, “Stokes imaging spectropolarimeter based on channeled polarimetry with full-resolution spectra and aliasing reduction,” Appl. Opt. 57(21), 6128–6134 (2018). [CrossRef]
19. Xiaobo Lv, Yiwei Li, Shuaishuai Zhu, Xinmin Guo, Jianlong Zhang, Jie Lin, and Peng Jin, “Snapshot spectral polarimetric light field imaging using a single detector,” Opt. Lett. 45(23), 6522–6525 (2020). [CrossRef]
20. M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express 20(21), 22997–23012 (2012). [CrossRef]
21. M. Garcia, C. Edmiston, R. Marinov, A. Vail, and V. Gruev, “Bio-inspired color-polarization imager for real-time in situ imaging,” Optica 4(10), 1263–1271 (2017). [CrossRef]
22. K. Shinoda, Y. Ohtera, and M. Hasegawa, “Snapshot multispectral polarization imaging using a photonic crystal filter array,” Opt. Express 26(12), 15948–15961 (2018). [CrossRef]
23. J. Liang, X. Tian, H. Ju, D. Wang, H. Wu, L. Ren, and R. Liang, “Reconfigurable snapshot polarimetric imaging technique through spectral-polarization filtering,” Opt. Lett. 44(18), 4574–4577 (2019). [CrossRef]
24. S. Ono, “Snapshot multispectral imaging using a pixel-wise polarization color image sensor,” Opt. Express 28(23), 34536–34573 (2020). [CrossRef]
25. K. Shinoda and Y. Ohtera, “Alignment-free filter array: Snapshot multispectral polarization imaging based on a Voronoi-like random photonic crystal filter,” Opt. Express 28(26), 38867–38882 (2020). [CrossRef]
26. A. Altaqui, P. Sen, H. Schrickx, J. Rech, and M. Kudenov, “Mantis shrimp–inspired organic photodetector for simultaneous hyperspectral and polarimetric imaging,” Sci. Adv. 7(10), 3196 (2021). [CrossRef]
27. S. Sattar, P. Lapray, L. Aksas, A. Foulonneau, and L. Bigué, “Snapshot spectropolarimetric imaging using a pair of filter array cameras,” Opt. Eng. 61(04), 043104 (2022). [CrossRef]
28. J. Kim and M. J. Escuti, “Snapshot imaging spectropolarimeter utilizing polarization gratings,” Proc. SPIE 7086, 708603 (2008). [CrossRef]
29. M. Alouini, F. Goudail, A. Grisard, J. Bourderionnet, D. Dolfi, A. Beniere, I. Baarstad, T. Loke, P. Kaspersen, X. Normandin, and G. Berginc, “Near-infrared active polarimetric and multispectral laboratory demonstrator for target detection,” Appl. Opt. 48(8), 1610–1618 (2009). [CrossRef]
30. J. Kim and M. J. Escuti, “Demonstration of a polarization grating imaging spectropolarimeter (PGIS),” Proc. SPIE 7672, 767208 (2010). [CrossRef]
31. J. Bo, Y. Gu, W. Xing, X. Ju, C. Yan, and X. Wang, “Spatially modulated snapshot computed tomographic polarization imaging spectrometer,” Appl. Opt. 60(20), 5860–5866 (2021). [CrossRef]
32. M. E. Gehm, R. John, D. J. Brady, R. M. Willett, and T. J. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15(21), 14013–14027 (2007). [CrossRef]
33. Ashwin Wagadarikar, Renu John, Rebecca Willett, and David Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47(10), B44–B51 (2008). [CrossRef]
34. T. H. Tsai and D. J. Brady, “Coded aperture snapshot spectral polarization imaging,” Appl. Opt. 52(10), 2153–2161 (2013). [CrossRef]
35. C. Fu, H. Arguello, B. M. Sadler, and G. R. Arce, “Compressive spectral polarization imaging by a pixelized polarizer and colored patterned detector,” J. Opt. Soc. Am. A 32(11), 2178–2188 (2015). [CrossRef]
36. W. Ren, C. Fu, D. Wu, Y. Xie, and G. R. Arce, “Channeled compressive imaging spectropolarimeter,” Opt. Express 27(3), 2197–2211 (2019). [CrossRef]
37. J. Ning, Z. Xu, D. Wu, R. Zhang, Y. Wang, Y. Xie, W. Zhao, and W. Ren, “Compressive circular polarization snapshot spectral imaging,” Opt. Commun. 491, 1–10 (2021). [CrossRef]
38. Z. Chen, C. Zhang, T. Mu, Y. Wang, Y. He, T. Yan, and Z. Chen, “Coded aperture full-stokes imaging spectropolarimeter,” Opt. Laser Technol. 150, 107946 (2022). [CrossRef]
39. H. Shi, “A spatial dimension encoded spectral polarization integrated imaging system and its design method,” P.R.China, patent application CN115307733A (14 July 2022).
40. Robert O. Green, “Spectral calibration requirement for Earth-looking imaging spectrometers in the solar-reflected spectrum,” Appl. Opt. 37(4), 683–690 (1998). [CrossRef]
41. B. F. de Albuquerque, J. Sasian, F. L. de Sousa, and A. S. Montes, “Method of glass selection for color correction in optical system design,” Opt. Express 20(13), 13592–13611 (2012). [CrossRef]
42. Z. Chen, C. Zhang, T. Mu, T. Yan, D. Bao, Z. Chen, and Y. He, “Coded aperture snapshot linear-Stokes imaging spectropolarimeter,” Opt. Commun. 450, 72–77 (2019). [CrossRef]
