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Hardmard transfer imaging spectrometer (HTIS) is a novel computationally optical system. Its characteristic of multi-channel multiplexing increases the luminous flux of the optical system without sacrificing spatial resolution, thereby enabling the system’s signal-to-noise ratio to be significantly higher than traditional spectrometer’s. Encoding with digital mirror devices (DMD) in the system causes a serious diffraction effect that gives rise to the apparent degradation of the imaging formation. For improving the image quality and spectral accuracy of the reconstructed data cube, the Hadamard coded spectral imaging data degradation model is established based on the scalar diffraction theory. A data reconstruction algorithm is proposed based on the Lucy Richardson (L-R) algorithm. Through the simulation experiment, the process of image degradation is revealed. On the one hand, it proves that the degradation of system imaging diffraction is the main reason for the distortion of reconstructed data. On the other hand, it verifies the effectiveness of the correction method adopted in this paper. The evaluation result of the spectral angle distance of the restored data cube after L-R correction is 0.1296, and the image similarity evaluation factor is better than 0.85. Compared with the reconstructed data before being corrected, the corrected data is greatly improved in quality. The experimental results show that the algorithm has a good correction effect on the data cube reconstruction of HTIS.
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Keywords:
- Hadamard coding /
- spectral imaging /
- image diffraction degradation /
- data reconstruction /
- spectral correction
[1] Cao J, Yuan Y, Su L, Zhu C, Yan Q 2020 Sensors 20 1195
Google Scholar
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Google Scholar
[3] Tilotta D, Hammaker R, Fateley M 1987 Appl. Opt. 26 4285
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[22] Richardson W 1972 J. Opt. Soc. Am. 62 55
Google Scholar
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Google Scholar
[24] Ge Y, Li Y, Chen J, Sun K, Li D, Han Q 2020 Sensors 1789 1
Google Scholar
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Google Scholar
Liu Y Y, Lu Q B, Zeng X R, Huang M, Xiang L B 2013 Acta Phys. Sin. 62 060203
Google Scholar
[26] Diaz N, Rueda H, Arguello H 2018 Appl. Opt. 57 4890
Google Scholar
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图 1 空间调制型哈达玛编码光谱成像系统光学结构示意图
Figure 1. Schematic diagram of SD-HTIS optic structure
图 2 空间调制型哈达玛光谱成像仪编码原理示意图
Figure 2. Schematic diagram of SD-THIS encoded principle
图 3 AVIRIS数据仿真生成及复原光谱数据 (a)原始输入数据; (b)编码生成的多帧图像数据; (c)复原后的光谱数据立方体
Figure 3. Simulation of AVIRIS data and the restoration spectral data: (a) Original input data; (b) multi-frame image data generated for encoding; (c) restored spectrum data cube.
图 4 归一化的系统点扩散函数分布图 (a)像点的点扩散函数图; (b)归一化的像点强度分布曲线
Figure 4. Normalized system point spread distribution diagram: (a) Point spread function diagram of image spot; (b) distribution curve of normalized image point intensity.
图 5 Hadamard编码单谱段图像 (a)衍射降质图像; (b)复原修正图像
Figure 5. Encoded single-spectrum image: (a) Image with the influence of diffraction; (b) image optimized by the L-R repair algorithm.
图 6 不同谱段光谱图像 (a)原始输入和理想复原图像; (b)经过衍射效应影响复原的多谱段图像; (c)经过L-R修正后复原的多谱段图像
Figure 6. Spectral images of different bands: (a) Original input and ideal restoration image; (b) multi-spectral image restored by diffraction effect; (c) multi-spectral image restored after L-R correction.
图 7 不同坐标处光谱曲线对照图 (a)坐标(10, 10)位置处的光谱曲线; (b)坐标(50, 50)位置处的光谱曲线; (c)坐标(100, 100)位置处的光谱曲线
Figure 7. Spectral curves contrast diagram: (a) Spectral curves at coordinates (10, 10); (b) spectral curves at coordinates (50, 50); (c) spectral curves at coordinates (100, 100).
表 1 哈达玛编码光谱成像系统的参数表
Table 1. Parameters of the Hardmard transfer imaging spectrometer system.
Parameters f1 f2 f3 D1 D2 D3 D4 Value/mm 100 50 50 50 25 25 3.81 
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表 2 单谱段图像相似度因子
Table 2. Similarity evaluation factor (SSIM) of the single-spectrum image.
波长/μm 3.86 4.01 4.17 4.33 4.49 4.64 4.80 SSIM (10 dB噪声) 0.961 0.961 0.971 0.960 0.963 0.969 0.952
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表 3 受衍射影响的编码图像和经过修正的编码图像的相似度因子评价
Table 3. Similarity factor evaluation of uncorrected coded image and corrected encoded image.
序号 1 2 3 4 5 6 7 无修正编码图像的SSIM 0.860 0.862 0.861 0.862 0.860 0.862 0.861 修正后编码图像的SSIM 0.947 0.948 0.949 0.948 0.948 0.948 0.949
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表 4 未修正SSIM与修正后SSIM的相似度评价
Table 4. Similarity evaluation of uncorrected SSIM and corrected SSIM.
波长/μm 3.86 4.01 4.17 4.33 4.49 4.64 4.80 未修正SSIM 0.583 0.647 0.694 0.654 0.702 0.657 0.598 修正后SSIM 0.832 0.845 0.861 0.872 0.902 0.893 0.859
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[1] Cao J, Yuan Y, Su L, Zhu C, Yan Q 2020 Sensors 20 1195
Google Scholar
[2] Swift R, Wattson R, Decker J, Paganetti R, Harwit M 1976 Appl. Opt. 5 1595
Google Scholar
[3] Tilotta D, Hammaker R, Fateley M 1987 Appl. Opt. 26 4285
Google Scholar
[4] RobichaudJ, Wong W, Van T 1994 Appl. Opt. 33 75
Google Scholar
[5] Duarte M, Davenport M, Takhar D 2008 Signal Processing Mag. 25 83
Google Scholar
[6] Tan J, Ma Y, Rueda H 2013 IEEE J. Sel. Top. Sign. Proces. 10 389
Google Scholar
[7] Smith M W, Smith J L, Torrington G K 2002 Proc. SPIE 4816 372
[8] Kittle D, Choi K, Wagadarikar A, Brady D J 2010 Appl. Opt. 49 6824
Google Scholar
[9] Wagadarikar A, John R, Willett R 2008 Appl. Opt. 47 B44
Google Scholar
[10] Streeter L, Burling G, Cree M, Künnemeyer R 2009 Appl. Opt. 48 2078
Google Scholar
[11] Galvis L, Arguello H, Arce GR 2015 Appl. Opt. 54 9875
Google Scholar
[12] Love S P, Graff D L 2014 J. Micro/Nanolith. MEMS MOEMS 13 011108
Google Scholar
[13] Graff D L, Love S P 2014 Proc. SPIE 9101 910111
Google Scholar
[14] 王峥杰, 杜云飞, 胡炳樑, 刘磊, 孔亮, 闫鹏, 武琪敬 2013 光子学报 42 891
Google Scholar
WangZ J, Du Y F, Hu B L, Liu L, Kong L, Yan P, Wu Q J 2013 Acta Photon. Sin. 42 891
Google Scholar
[15] Liu C, Hu B L, Wei R, Yan P 2013 Spectrosc. Spect. Anal. 5 1427
Google Scholar
[16] Chi M, Hao P, Wu Y, Liu Y, Zhang P 2013 Appl. Opt. 52 6467
Google Scholar
[17] Chi M, Wu Y, Ge D, Zhou W, Hao P, Liu Y 2016 Appl. Opt. 55 1500
Google Scholar
[18] ChiM, Wu Y, Qian F, Hao P, Zhou W, Liu Y 2017 Appl. Opt. 56 7188
Google Scholar
[19] Su L, Yan Q, Yuan Y, Wang S, Liu Y 2018 Chin. Phys. B 27 080702
Google Scholar
[20] Cuadros A, Arce G 2017 Opt. Express 25 23833
Google Scholar
[21] Smith W, Paxman R, Barrett H 198 J. Opt. Soc. Am. A 2 491
Google Scholar
[22] Richardson W 1972 J. Opt. Soc. Am. 62 55
Google Scholar
[23] Woolliams P, Ferguson R, Hart C, Grimwood A, Tomlins P 2010 Appl. Opt. 49 2014
Google Scholar
[24] Ge Y, Li Y, Chen J, Sun K, Li D, Han Q 2020 Sensors 1789 1
Google Scholar
[25] 刘扬阳, 吕群波, 曾晓茹, 黄旻, 相里斌 2013 物理学报 62 060203
Google Scholar
Liu Y Y, Lu Q B, Zeng X R, Huang M, Xiang L B 2013 Acta Phys. Sin. 62 060203
Google Scholar
[26] Diaz N, Rueda H, Arguello H 2018 Appl. Opt. 57 4890
Google Scholar
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