1. 中国科学院计算光学成像技术重点实验室, 中国科学院光电研究院, 北京 100094
2. 中国科学院大学, 北京 100049
3. 武汉大学生物医学分析化学教育部重点实验室, 化学与分子科学学院, 高等研究院, 湖北 武汉 430072
*通讯联系人 e-mail: weilidong@aoe.ac.cn

Reconstruction Simulation with Quantum Dots Spectral Imaging Technology
WANG Ying-jun1,2, ZHOU Jin-song1,2, WEI Li-dong1,*, ZHANG Gui-feng1, ZHU Dong-liang3, GUO San-wei3, TANG Hong-wu3, PANG Dai-wen3
1. Key Laboratory of Computational Optical Imaging Technology, Academy of Opto-Electronics, Chinese Academy of Sciences, Beijing 100094, China
2. University of Chinese Academy of Sciences, Beijing 100049, China
3. Key Laboratory of Analytical Chemistry for Biology and Medicine (Ministry of Education), College of Chemistry and Molecular Sciences, The Institute for Advanced Studies, Wuhan University, Wuhan 430072, China;
Abstract

In order to meet the requirement of compact type and lightweight for spectral imaging system in airborne and satellite platform, and to overcome the limitations of optical splitting system in current spectral imaging technology such as complex structure and high cost, for the first time we present the design of spectral imaging based on quantum dots. In this method, a strip of quantum dots array is placed in front of the focal plane of telescope lens and absorption properties of quantum dots materials is applied to modulate the incident spectrum of the target, then least square method is applied to establish the spectral reconstruction model of the target. Finally, the spectral and spatial information of the target is obtained with the method of push broom and spectral reconstruction. The quantum dots spectral imaging technology has the advantages of high spectral resolution, high energy availability, small size, wide spectral range and low cost. More important, the effects of different spectral intervals and noises on the reconstructed spectral resolution and their impact on the accuracy or distortion of the reconstructed spectra are analyzed. The results show that the spectral resolution increases with the decrease of the spectral interval, and the accuracy and resolution of the reconstructed spectrum are reduced with the increase of the noise level. What's more, the accuracy of reconstruction can be improved by appropriately increasing the spectral interval. With a comparison of the simulation results with the known data cube, the feasibility of the technology is verified, and the results show that the quantum dots spectral imaging possesses higher quality. In conclusion, quantum dots provide a new approach for spectral imaging technology, which has wide applications in the field of aerospace and other miniature spectral remote sensing.

Keyword: Quantum dots; Spectral imaging; Push broom; Least square; Spectral reconstruction

1 量子点光谱成像原理

 Figure Option 图1 量子点透过率曲线Fig.1 Transmission spectra for QDs

 Figure Option 图2 量子点光谱成像系统示意图Fig.2 Schematic diagram of the quantum dots spectral imaging system

$I=∫abT(λ)d(λ)ϕ(λ)dλ(1)$

 Figure Option 图3 数据采集过程Fig.3 The process of data acquisition

2 光谱重建模型及算法分析
2.1 数学模型

 Figure Option 图4 量子点光谱成像系统数学模型Fig.4 Mathematical model of quantum dots spectral imaging system

$Ii=∫abT'i(λ)ϕ(λ)dλ i=1, 2, …, nF(2)$

$Ii=∑jnλT'i(λj)ϕ(λj)Δλj j=1, 2, …, nλ(3)$

$T'(λ)ϕ'(λ)=I(4)$

$T'(λ)ϕ'(λ)+n=I(5)$

2.2 算法分析

$ϕ'(λ)OLS=argminϕ'(λ)‖T'(λ)ϕ'(λ)-I‖22(6)$

$ϕ'(λ)OLS=(T'(λ)TT'(λ))-1T'(λ)TI, ϕ'(λ)OLS≥0(7)$

T'(λ )=UΣ VH是矩阵T'(λ )的奇异值分解, 从而得到普通最小二乘解为[12]

$ϕ'(λ)OLS=VΣ-1UHI, ϕ'(λ)OLS≥0(8)$

$ϕ'(λ)OLSn+1=ϕ'(λ)OLSn+(T'(λ)TT'(λ))-1T'(λ)T×(1-T'(λ)ϕ'(λ)OLSn)(9)$

$ϕ'(λ)OLSn+1=ϕ'(λ)OLSn+VΣ-1UH(1-UΣVHϕ'(λ)OLSn)(10)$

3 仿真分析

3.1 分辨率分析

 Figure Option 图5 光谱谱段间隔3 nm, 双峰间隔分别为5, 4.5 nm和4 nmFig.5 The spectral interval is 3 nm, and the interval between two peaks is 5, 4.5 and 4 nm respectively

 Figure Option 图6 光谱谱段间隔2.5 nm, 双峰间隔分别为4.5, 4和3.5 nmFig.6 The spectral interval is 2.5 nm, and the interval between two peaks is 4.5, 4 and 3.5 nm respectively

 Figure Option 图7 光谱谱段间隔2 nm, 双峰间隔分别为4, 3.5和3 nmFig.7 The spectral interval is 2 nm, and the interval between two peaks is 4, 3.5 and 3 nm respectively

 Figure Option 图8 不同噪声水平的光谱重建Fig.8 Spectral reconstruction at different noise levels

3.2 重建准确性分析

$MSE=1nλ∑j=1nλ(ϕ(λj)-φ(λj))2(11)$

$RQE=∑(ϕ(λ)-φ(λ))2∑φ(λ)(12)$

$MSE=1MN∑j=1M∑i=1N(ϕ(λ)ij-φ(λ)ij)2(13)PSNR=10logL2MSE(14)$

 Figure Option 图9 目标物光谱重建Fig.9 Spectral reconstruction of the target object

 Figure Option 图10 入射光谱和重建谱的彩色合成Fig.10 Color synthesis of the incident and reconstructed spectra

 Figure Option 图11 不同噪声和光谱谱段间隔的MSE值和RQE值的比较Fig.11 The comparison of MSE value and RQE value of different noises and spectral intervals

4 结论

The authors have declared that no competing interests exist.

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