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In imaging spectrometers, area array detectors are usually used as photoelectric conversion devices, but the inconsistency of the spectral response among pixels can distort the collected target spectra. To improve the spectral radiometric accuracy of imaging spectrometers, calibrating and correcting the inconsistency of the spectral response among pixels is essential. The signal received by each pixel of area array detector of the indirect imaging spectrometer is usually the superposition of the target multi-spectral radiation signals or full-spectral radiation signals. Therefore, its relative spectral radiometric calibration requires measuring the spectral response of each pixel at different wavelengths on the array detector. Under the ideal conditions, the response values of each pixel in the area array detector are different, so the indirect imaging spectrometer cannot simply calibrate the relative spectral response (RSR) function between pixels by using the method of “monochromator + integrating sphere”. In this work, taking the interferometric imaging spectrometer for example, we analyze the influence of the inconsistency of the RSR among pixels on the target spectral radiation measurement accuracy, and propose a system-level RSR function measurement method for the indirect imaging spectrometer based on the Fourier transform modulation calibration source. In addition, we establish a mathematical model for calibrating the RSR function,and provide guidelines for selecting calibration system parameters such as light source, spectral resolution, and OPD sampling interval. The simulation results show that under the ideal noise-free condition, the 1% spectral response inconsistency among pixels results in a relative error of 1.02% to the recovered spectra. After RSR correction, the relative error of the recovered spectra of different rows decreases to 0.08%. Furthermore, in this work we simulate and analyse the influence of spectral signal-to-noise ratio on the calibration accuracy of the RSR function, and point out that increasing the brightness of the calibration light source, extending exposure time, and combining multi-frame interferograms can enhance RSR function calibration accuracy in practical applications. The research result can provide a theoretical basis for realizing the relative spectral radiometric calibration of indirect imaging spectrometer, which is of great significance in promoting quantitative spectral remote sensing.
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Keywords:
- indirect imaging spectrometer /
- Fourier transform spectrometer /
- relative spectral response /
- calibration
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图 2 像元间光谱响应不一致对复原光谱的影响 (a) 像元间的光谱响应曲线; (b) 不同行光谱响应不一致对复原光谱的影响
Figure 2. Effect of the spectral response inconsistency among pixels on the recovered spectrum: (a) Spectral response curves among pixels; (b) the effect of different spectral responses on the recovered spectrum.
图 3 干涉光谱成像仪相对光谱响应函数测试系统
Figure 3. Relative spectral response (RSR) function test system of interferometric imaging spectrometer.
图 4 理想无噪声情况下, 像元间光谱响应不一致对复原光谱的影响 (a) A点对应的相对光谱响应函数; (b) B 点对应的相对光谱响应函数; (c) A和B点误差光谱及其相对误差
Figure 4. Influence of the spectral response inconsistency among pixels on the recovered spectrum under ideal noise-free conditions: (a) RSR function corresponding to point A; (b) RSR function corresponding to point B; (c) error spectrum for points A and B and their relative error.
图 5 干涉光谱成像仪相对光谱响应函数测量及标定流程图
Figure 5. Flowchart of measurement and calibration of RSR function of interferometric imaging spectrometer.
图 6 理想无噪声情况下, 干涉光谱成像仪像面第256个像元的干涉图及复原光谱图(以目标点A点为例) (a)干涉图; (b)复原光谱
Figure 6. Under ideal noiseless condition, interferograms and recovered spectrum of the 256th pixel of the interferometric imaging spectrometer (take the point A for example): (a) Interferogram; (b) spectrum.
图 7 理想无噪声情况下, $ {S}_{{\mathrm{p}}{\mathrm{e}}{\mathrm{c}}}\left(770\;{\mathrm{n}}{\mathrm{m}}, x\right) $ 及其基线拟合效果 (a) $ {S}_{{\mathrm{p}}{\mathrm{e}}{\mathrm{c}}}\left(770\;{\mathrm{n}}{\mathrm{m}}, x\right) $; (b) 基线拟合效果
Figure 7. Under ideal noiseless condition, $ {S}_{{\mathrm{p}}{\mathrm{e}}{\mathrm{c}}}\left(770\;{\mathrm{n}}{\mathrm{m}}, x\right) $ and its baseline fitting effect: (a) $ {S}_{{\mathrm{p}}{\mathrm{e}}{\mathrm{c}}}\left(770\;{\mathrm{n}}{\mathrm{m}}, x\right) $; (b) baseline fitting effect
图 8 理想无噪声情况下, 相对光谱响应函数的复原效果 (a) A点所对应的行像元间的相对光谱响应函数; (b) B点所对应的行像元间的相对光谱响应函数; (c) A和B点校正后的光谱及其相对误差
Figure 8. Restoration effect of the RSR function under ideal noise-free conditions: (a) RSR function among row pixels corresponding to point A; (b) RSR function among row pixels corresponding to point B; (c) corrected spectrum of points A and B and their relative error.
图 9 SNR = 50时, 相对光谱响应函数的复原效果 (a) A点; (b) B点
Figure 9. Restoration effect of RSR function when spectral SNR is 50: (a) Point A; (b) point B.
图 10 不同信噪比下, A和B点相对光谱响应的校正效果 (a) SNR = 50, 校正前光谱; (b) SNR = 50, 校正后光谱; (c) SNR = 50, 光谱的相对误差; (d) SNR = 100, 校正前光谱; (e) SNR = 100, 校正后光谱; (f) SNR = 100, 光谱的相对误差
Figure 10. Correction effect of RSR of points A and B at different SNR: (a) Uncorrected spectrum at SNR = 50; (b) corrected spectrum at SNR = 50; (c) relative error of spectrum at SNR = 50; (d) uncorrected spectrum at SNR = 100; (e) corrected spectrum at SNR = 100; (f) relative error of spectrum at SNR = 100.
图 11 SNR = 50, 合并50帧干涉图后A和B点相对光谱响应的校正效果 (a) 校正前后的光谱; (b)校正前后的相对误差
Figure 11. Correction effect of RSR of points A and B after combining 50 frames of interferograms at SNR = 50: (a) Spectra before and after correction; (b) relative error before and after correction.
表 1 干涉光谱成像仪相对光谱响应函数测试系统的仿真参数
Table 1. Simulation parameters of the RSR function measuring system for interferometric imaging spectrometer
参数 值 光谱范围/nm 458—956 剪切量 d/mm 0.68 焦距 f/mm 117 像元数 256×512 (光谱维2像元合并) 像元尺寸/μm 18 光源 氙灯 (458—700 nm)
卤钨灯 (700—956 nm)光程差采样间隔/nm 150 步数 10000 光谱分辨率/cm–1 13.33 光程差采样范围/cm –0.075—0.075 
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[1] Luo H Y, Li Z W, Wu Y, Qiu Z W, Shi H L, Wang Q S, Xiong W 2023 Remote Sens. 15 1105
Google Scholar
[2] Lassalle G, Ferreira M P, La Rosa L E C, Scafutto R D P M, de Souza Filho C R 2023 ISPRS J. Photogramm. 195 298
Google Scholar
[3] 刘文龙, 刘学斌, 王爽, 严强强 2022 物理学报 71 094201
Google Scholar
Liu W L, Liu X B, Wang S, Yan Q Q 2022 Acta Phys. Sin. 71 094201
Google Scholar
[4] Calin M A, Calin A C, Nicolae D N 2021 Appl. Spectrosc. Rev. 56 289
Google Scholar
[5] Jia J X, Wang Y M, Chen J S, Guo R, Shu R, Wang J Y 2020 Infrared Phys. Techn. 104 103115
Google Scholar
[6] 王建威, 李伟艳, 孙建颖, 李兵, 陈鑫雯, 谭政, 赵娜, 刘扬阳, 吕群波 2022 光谱学与光谱分析 42 2013
Google Scholar
Wang J W, Li W Y, Sun J Y, Li B, Chen X W, Tan Z, Zhao N, Liu Y Y, Lü Q B 2022 Spectrosc. Spect. Anal. 42 2013
Google Scholar
[7] 唐远河, 崔进, 郜海阳, 屈欧阳, 段晓东, 李存霞, 刘丽娜 2017 物理学报 66 130601
Google Scholar
Tang Y H, Cui J, Gao H Y, Qu O Y, Duan X D, Li C X, Liu L N 2017 Acta Phys. Sin. 66 130601
Google Scholar
[8] 李志伟, 熊 伟, 施海亮, 王先华, 叶函函, 韦秋叶, 乔延利 2014 红外 34 27
Li Z W, Xiong W, Shi H L, Wang X H, Ye H H, Wei Q Y, Qiao Y L 2014 Acta Opt. Sin. 34 27
[9] 王润昊, 孙影茹, 甘茵露, 吴兴江, 柯俊杰, 王新强, 甘永莹 2022 激光与光电子学进展 59 364
Google Scholar
Wang R H, Sun Y R, Gan Y L, Wu X J, Ke J J, Wang X Q, Gan Y Y 2022 Laser Optoelectronics Prog. 59 364
Google Scholar
[10] 相里斌, 计忠瑛, 黄旻, 王忠厚, 袁艳 2004 光学学报 33 850
Xiangli B, Ji Z Y, Huang M, Wang Z H, Yuan Y 2004 Acta Opt. Sin. 33 850
[11] Zhao B C, Yang J F, Xue B, Qiqo W D, Qiu Y H 2010 Acta Photon. Sin 39 769 [赵葆常, 杨建峰, 薛彬, 乔卫东, 邱跃洪 2010 光子学报 39 769]]
Google Scholar
Zhao B C, Yang J F, Xue B, Qiqo W D, Qiu Y H 2010 Acta Photon. Sin 39 769
Google Scholar
[12] 崔燕 2009 博士学位论文(西安: 中国科学院研究生院西安光学精密机械研究所)
Cui Y 2009 Ph. D. Dissertation (Xi’an: University of Chinese Academy of Sciences, Xi’an Institute of Optics and Precision Mechanics
[13] Barrat C, Lepot T, Ramamonjisoa M, Fradcourt S 2016 Proc. SPIE 9987 307
Google Scholar
[14] Hedelius J K, Squire K J, Peterson J Q, Blagojević B, Gliese U B, Gorman E T, Moser D K, Rhodes Z, Sevilla P, Meister G 2022 Proc. SPIE 12232 283
Google Scholar
[15] Englert C R, Harlander J M, Marr K D, Harding B J, Makela J J, Fae T, Brown C M, Venkat Ratnam M, Vijaya Bhaskara Rao S, Immel T J 2023 Space Sci. Rev. 219 27
Google Scholar
[16] 相里斌, 吕群波, 才啟胜, 方煜, 周锦松, 黄旻 2020 中国科学: 信息科学 50 1462
Google Scholar
Xiang L B, Lv Q B, Cai Q S, Fang Y, Zhou J S, Huang M 2020 Sci. Sin. Inf. 50 1462
Google Scholar
[17] 王爽 2014 博士学位论文(西安: 中国科学院研究生院西安光学精密机械研究所)
Wang S 2014 Ph. D. Dissertation (Xi’an: University of Chinese Academy of Sciences, Xi’an Institute of Optics and Precision Mechanics
[18] Wang F B, Zhou J S, Jing J J, Wu Q S, Cheng W 2015 Proc. SPIE 9811 114
Google Scholar
[19] 相里斌, 王忠厚, 刘学斌, 袁艳, 计忠瑛, 吕群波 2009 航天器工程 24 257
Google Scholar
Xiang L B, Wang Z H, Liu X B, Yuan Y, Ji Z Y, Lü Q B 2009 Spacecraft Engineering 24 257
Google Scholar
[20] 张亚飞 2023 博士学位论文(西安: 中国科学院西安光学精密机械研究所)
Zhang Y F 2023 Ph. D. Dissertatio (Xi'an Institute of Optics and Precision Mechanics of CAS
[21] 王昕, 康哲铭, 刘龙, 范贤光 2020 物理学报 68 200701
Google Scholar
Wang X, Kang Z M, Liu L, Fan X G 2020 Acta Phys. Sin. 68 200701
Google Scholar
[22] 孙晨, 冯玉涛, 傅頔, 张亚飞, 李娟 2020 物理学报 69 084201
Google Scholar
Sun C, Feng Y T, Fu D, Zhang Y F, Li J 2020 Acta Phys. Sin. 69 084201
Google Scholar
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