Miniature computational spectral detection technology based on correlation value selection

Yang Gang; Guo Yinghui; Pu Mingbo; Li Xiong; Luo Xiangang

doi:10.12086/oee.2022.220130

Abstract

Benefiting from the advantages of small size, compact structure, and easy integration, miniature spectral detection technologies based on metasurfaces have been widely studied in recent years. However, the existing designs of the metasurfaces-based miniature spectral detection system usually lack the quantitative analysis of the relationship between the average correlation values of the metasurfaces transmission spectra and the reconstruction quality. The random selection method used in the existing design process cannot guarantee the optimal reconstruction quality. This paper quantitatively analyzes the relationship between the average correlation value of the metasurfaces transmission spectra and reconstruction quality, and proposes a design methodology for miniature spectral detection based on metasurfaces. In addition, this paper also verifies the spectral properties of the metasurfaces-based miniature spectral detection technology. Compared with the random selection design methodology, the proposed methodology can improve the reconstruction fidelity of broadband spectral and image signals.

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1. 引　言

针对上述问题，来自滨州学院的Li等人已提出一种利用极大线性无关准则对传统宽带滤光片进行选择设计的方法^[38-41]。不同于上述方法，本文定量分析了超构表面透射光谱相关性均值与重建保真度的关系，提出了一种用于微型光谱探测的超构表面设计方法。为验证所提出方法的优势，本文从众多光谱选择了10条宽带光谱及图像光谱进行展示。相较于随机选择设计方法，本文所提出方法能对选定10条宽带光谱及图像光谱信号的重建质量进行优化，宽带光谱重建保真度的增幅可达 13.17%，图像光谱信号的重建保真度也得到了一定的提升。此外，本文还仿真验证了基于超构表面的微型光谱探测系统的光谱特性，该系统对宽带、窄带光谱和图像光谱信号都具有较好的重建效果，具有结构紧凑、体积小的优势。

光谱成像探测技术，是一门通过获取目标的空间信息和光谱信息，以实现目标探测和识别的技术。因具有精准、非接触检测等多项优点，光谱成像技术已广泛应用于遥感^[1-3]、医学诊断^[4-5]、食品安全检测^[6]、环境监测^[7]等领域。然而，传统的光谱成像技术通常存在采样时间长、能量效率低、难以同时获得高光谱和空间分辨率等问题。针对这些问题，来自杜克大学Bardy团队的研究人员提出了一种利用编码孔径及色散结构对空间及光谱信息进行先编码再重建的计算型快照式光谱成像技术^[8-11]，该技术可以在快照模式下同时捕获目标的空间和光谱信息，并以较少的滤波通道获取更多的光谱波段。然而，传统的计算型快照式光谱成像系统仍存在结构复杂、体积庞大等问题。

超构表面是一种可对电磁波光谱、振幅和相位进行灵活调控的人工结构功能材料，因具有结构紧凑、对电磁波灵活调控等多项优点^[12-14]，超构表面已被广泛应用于三维全息^[15-17]、光谱检测^[18-20]、超构透镜^[21-26]、超分辨率成像^[27-29]等领域。为解决传统光谱成像系统存在的结构复杂、难以小型化的问题，来自清华大学Cui 团队、威斯康辛大学Yu团队及其它团队的研究人员已提出了一些基于超构表面的计算型快照式光谱成像系统^[30-37]，这些系统通常利用超构表面的宽带光谱特性，并结合压缩感知算法实现轻量化的计算型光谱成像探测。然而，现有工作中超构表面微纳结构设计，通常采用先设计大量超构表面再随机进行选择的方法，这种方法缺乏对超构表面透射谱相关性均值与重建质量的定量分析，无法保证重建质量最优。

2. 工作原理

其中： ${f}{(}{ \lambda }{)}$ 为原始入射光谱， ${{t}}_{{i}}{(}{ \lambda }{)}$ 为第i个超构表面的透射光谱， ${ \eta }{(}{ \lambda }{)}$ 为光电探测器的响应光谱， ${ \lambda }={{ \lambda }}_{{1}}, {{ \lambda }}_{{2}},{{ \lambda }}_{{3}},\cdots \cdots ,{{ \lambda }}_{{N}}$ 为波长采样点。为简化公式，将光电探测器的响应光谱与超构表面的透射光谱进行整合， ${{{\boldsymbol{T}}}}_{{i}}{(}{ \lambda }{)}{=}{{t}}_{{i}}{(}{ \lambda }{)}{\eta }{(}{ \lambda }{)}$ ，最终式(1)变换为 ${{Y}}_{{i}}{(}{ \lambda }{)=} {f}{(}{ \lambda }{)}{{{\boldsymbol{T}}}}_{{i}}{(}{ \lambda }{)}$ 。当超构表面的结构数量为M时，M个超构表面下的光电探测器可以一次性接收到M个不同的信号 ${{Y}}_{{M}}$ ，相应地式(1)变换为 ${{{\boldsymbol{Y}}}}_{{1 \times }{M}}{=}{{{\boldsymbol{f}}}}_{{1 \times }{N}}{{{\boldsymbol{T}}}}_{{N}{ \times M}}$ ，而原始光谱 ${f}{(}{ \lambda }{)}$ 可以通过求解上述方程来重建。

Figure 1. Miniature spectral detection. (a) Schematic diagram of the working principle; (b) Schematic diagram of numerous micro-spectrometers; (c) Schematic diagram of a single micro-spectrometer and transmission spectrum of a metasurface

Figure 1. Full-Size Img PowerPoint

Miniature spectral detection. (a) Schematic diagram of the working principle; (b) Schematic diagram of numerous micro-spectrometers; (c) Schematic diagram of a single micro-spectrometer and transmission spectrum of a metasurface

原始光谱信号 ${f}{(}{ \lambda }{)}$ 需具备稀疏性才能被高光谱探测压缩感知采集，而自然界中的大多数光谱 ${f}{(}{ \lambda }{)}$ 并不具备稀疏性，因此，需要将光谱信号映射到其他稀疏域以获得稀疏表示，使得 ${f}{=}{{\boldsymbol{P}}_{{{\rm{si}}}}}{\times }{{\boldsymbol{x}}}{}$ ，其中P_si为稀疏变换矩阵， ${{\boldsymbol{x}}}$ 为稀疏向量，则式(1)可转化为 ${{\boldsymbol{Y}}}= {{\boldsymbol{T}}} \times {{\boldsymbol{f}}}={{\boldsymbol{T}}}\times{}{{\boldsymbol{P}}_{{\rm{si}}}}\times{{\boldsymbol{x}}}$ ^[42]。重建过程的原理可以用以下公式进行表示^[43-45]：

其中：范数l₁定义为 ${||}{{\boldsymbol{x}}}{|}{{|}}_{{1}}{=}{\displaystyle\sum }_{{j}{=1}}^{{n}}{|}{x}{(}{{ \lambda }}_{{j}}{)|}$ ，残差δ为极小的正常数。当残差接近0时，可以通过预先得到稀疏解 ${{\boldsymbol{x}}}$ ，求解得到重建光谱 ${f}{(}{ \lambda }{)}$ 。作为压缩感知算法的其中一类，本文采用了基于贪婪算法的正交匹配追踪算法进行光谱重构，该算法能在每次迭代中，保证残差与已选传感矩阵的基正交，减少算法的迭代次数，从而保证较高的实时性。该算法对单一光谱的重建计算耗时约为2 s。

Y_{i} = \int_{λ_{1}}^{λ_{N}} f (λ) t_{i} (λ) η (λ) d λ = {\boldsymbol f}_{1 \times N} {\boldsymbol T}_{N \times 1},

\begin{matrix} min_{x} | | \boldsymbol x | |_{1} \\ s . t . | | \boldsymbol T \times P_{s i} \times \boldsymbol x - \boldsymbol Y ‖_{2} ⩽ δ, \end{matrix}

本文对一种用于可见光谱范围(400 nm~700 nm)的微型光谱探测系统进行了分析。图1(a)描述了该系统的工作原理：在不同像素点上具备不同光谱信息的图像光谱信号，经透镜组后被CMOS传感器上的多个微型光谱仪所调制，将调制信号经过压缩感知算法进行恢复处理，可获得重建图像光谱信号。图像信号中某一特定像素点所携带的光谱信号，经过置于CMOS图像传感器上的单个微型光谱仪被调制，而重建光谱信号可由调制信号与压缩感知算法重建获得。其中置于CMOS图像传感器上的多个微型光谱仪的示意图如图1(b)所示，而单个微型光谱仪由M = 36个超构表面组成，超构表面在特定的结构参数下有着特定的透射光谱，相应的示意图如图1(c)所示。

对于单个像素点上的光谱信号，当原始光谱入射到具有不同透射光谱的超构表面上时，第i个超构表面下方的光电探测器接收到的调制信号 ${Y}_{i}$ 为

3. 超构表面的数值仿真

ρ (t_{i}, t_{j}) = \frac{c o v (t_{i}, t_{j})}{σ_{t_{i}} \times σ_{t_{j}}} = \frac{\overset{―}{(t_{i} - {\overset{―}{t}}_{i}) \times {(t}_{j} - {\overset{―}{t}}_{j})}}{σ_{t_{i}} \times σ_{t_{j}}},

Figure 2. Design of the metasurfaces. (a) The unit cell of the metasurfaces; (b) Schematic diagram of a single micro-spectrometer; (c) Schematic diagram of the selection of metasurfaces according to different average correlation value intervals; (d) Transmission spectra of different patterns of the metasurfaces

Figure 2. Full-Size Img PowerPoint

Design of the metasurfaces. (a) The unit cell of the metasurfaces; (b) Schematic diagram of a single micro-spectrometer; (c) Schematic diagram of the selection of metasurfaces according to different average correlation value intervals; (d) Transmission spectra of different patterns of the metasurfaces

ρ_{c o l u m n} (i) = \frac{\sum_{j = 1}^{M} | ρ (t_{i}, t_{j}) |}{M - 1} (i \neq j) .

其中： ${{f}}_{{1}}$ 为原始光谱， ${{f}}_{{2}}$ 为重建光谱。不同内孔图案和结构参数的超构表面具备不同的透射光谱，满足了超构表面丰富透射光谱的设计需求，在图2(b)中用不同颜色方框标注的结构所对应的透射光谱如图2(d)所示。

F (f_{1} (i), f_{2} (i)) = (1 - \sqrt{\frac{\sum_{i = 1}^{n} ({f_{1} (i) - f_{2} (i))}^{2}}{\sum_{i = 1}^{n} {f_{1} (i)}^{2}}}) \times 100 %,

\bar{ρ} = \frac{\sum_{i = 1}^{M} | ρ_{c o l u m n} (i) |}{M} .

其中： ${{t}}_{{i}}{,}{}{{t}}_{{j}}$ 分别为第i个和第j个超构表面的透射光谱， ${cov}{(}{{t}}_{{i}}{,}{{t}}_{{j}}{)}$ 为透射光谱 ${{t}}_{{i}}{,}{}{{t}}_{{j}}$ 的协方差， ${\overline{{t}}}_{{i}},{\overline{{t}}}_{{j}}$ 为光谱 ${{t}}_{{i}}{,}{}{{t}}_{{j}}$ 的均值， ${\sigma }_{{t}_{i}},{\sigma }_{{t}_{j}}$ 为光谱 ${{t}}_{{i}}{,}{}{{t}}_{{j}}$ 的标准差。当i = j时，相关性值 ${\rho }{(}{{t}}_{{i}}{,}{{t}}_{{j}}{)}{=}{1}$ ，将此类相关性值去掉后，M = 36个超构表面中第i列的相关性均值被定义为

同时，为量化分析重建光谱与原始光谱的吻合程度，本文采用重建保真度F来定义，其公式为

不同超构表面具有不同的内孔图案和结构参数，用橙色方框标注的超构表面的内孔图案与结构参数为十字形，p = 450 nm，l = 330 nm，w = 140 nm，θ = 0°；用黑色方框标注的超构表面的内孔图案与结构参数为十字形，p = 550 nm，l = 395 nm，w = 215 nm，θ = 45°；用蓝色方框标注的超构表面的内孔图案与结构参数为圆形，p = 560 nm，d = 195 nm，如图2(b)及图2(c)顶部所示。图2(c)为依据不同相关性均值对超构表面进行选择设计的示意图，图片顶部为依据相关性均值间隔[0.1~0.3]进行选择，图片底部为依据相关性均值间隔[0~1]进行选择。其中第i、j个超构表面透射光谱的相关性均值被定义为

M=36个超构表面的总相关性均值被定义为

在压缩感知算法中，由超构表面透射光谱和光电探测器响应光谱组成的T_i(λ)被称为测量矩阵，而测量矩阵是实现光谱压缩、重建还原的重要工具，因此超构表面的合理设计至关重要。本文采用有限时域差分法(FDTD)仿真了具有不同内孔图案及结构参数的超构表面，超构表面的单元结构从上到下由190 nm厚的晶体硅膜和蓝宝石衬底组成，190 nm厚的晶体硅膜具有不同周期p和内孔图案，单元结构示意图如图2(a)所示。为满足超构表面在光谱重建中丰富透射光谱的需求，本文将结构周期p、内孔图案、孔结构参数l、w、d和旋向角θ作为其自由度，超构表面的外部周期(p)的变化范围为350 nm~750 nm，内部周期(l, w, d)的变化范围为150 nm~550 nm，占空比(l/p, w/p, d/p)的变化范围为15%~65%，旋向角θ为0°或45°，根据以上结构参数的变换范围，本文仿真出约4200组的超构表面。

4. 相关性均值与重建保真度分析

如表1数据与图4的原始入射光谱所示，不同的原始入射光谱有着不同的光谱重建保真度及增幅，经分析后发现，当原始光谱在较短波长范围内(400 nm~450 nm)有光谱分量时，保真度增幅较低，如光谱1、2、9；当原始光谱在较短波长范围内不包含有光谱分量时，保真度增幅较高，如光谱4、5、8、10。以上结果表明，本方法保真度提升量和原始光谱相关，该方法最适用于在较短波长无光谱分量的原始光谱。

The reconstruction fidelity produced by different metasurfaces selection design methodologies

不同超构表面选择设计方法所产生的重建保真度

光谱	本文提出方法所产生(处于不同相关性均值间隔)的信号重建保真度				传统随机选择方法所产生的信号重建保真度/%	本文方法所产生的信号重建保真度增幅/%
光谱	[0.1~0.3]/%	[0.3~0.5]/%	[0.5~0.7]/%	[0.7~0.9]/%	传统随机选择方法所产生的信号重建保真度/%	本文方法所产生的信号重建保真度增幅/%
光谱1	92.36	91.58	86.99	69.18	89.20	3.50
光谱2	93.83	88.70	87.55	71.95	89.77	4.52
光谱3	97.62	53.01	48.64	50.33	90.84	7.46
光谱4	98.52	77.91	75.09	71.65	90.20	9.22
光谱5	97.07	82.74	79.10	60.06	87.17	11.36
光谱6	96.41	92.29	90.05	85.01	89.32	7.94
光谱7	96.58	94.40	94.48	85.60	91.83	5.17
光谱8	95.75	89.02	90.34	63.26	87.13	9.89
光谱9	98.64	88.05	91.05	83.88	93.96	3.98
光谱10	97.54	94.10	82.70	42.34	86.65	13.17

CSV Show Table

Figure 4. The reconstruction fidelity produced by different metasurfaces selection design methodologies in Table 1. (a) Spectrum 1~5 in Table 1; (b) Spectrum 6~10 in Table 1; (c) The reconstruction fidelity produced by different metasurfaces selection design methodologies under spectrum5; (d) The reconstruction fidelity produced by different metasurfaces selection design methodologies under spectrum10

Figure 4. Full-Size Img PowerPoint

The reconstruction fidelity produced by different metasurfaces selection design methodologies in Table 1. (a) Spectrum 1~5 in Table 1; (b) Spectrum 6~10 in Table 1; (c) The reconstruction fidelity produced by different metasurfaces selection design methodologies under spectrum5; (d) The reconstruction fidelity produced by different metasurfaces selection design methodologies under spectrum10

本文从众多光谱选择了10条宽带光谱用于验证所提出方法的优势，采用上述两种选择设计方法对10条选定的原始入射光谱进行重建，可得到如表1所示的重建保真度数据。如表1数据所示，相关性均值间隔[0.1~0.3]内的超构表面所产生的光谱重建保真度均高于随机选择的超构表面所产生的光谱重建保真度，对于10条选定的原始光谱，光谱重建保真度的增幅可达13.17%，对于其他未知原始光谱，本文所提出方法可能存在更高的重建保真度增幅。这些结果表明，相较于传统随机选择方法，本文所提出方法能在一定程度上优化光谱重建质量。此外，相关性均值间隔[0.1~0.3]的超构表面所得到的光谱重建保真度，通常优于相关性均值间隔[0.3~0.5]、[0.5~0.7]、[0.7~0.9]的超构表面所得到的重建保真度。因此在微型光谱探测技术中，低相关性均值的超构表面结构能带来更高的光谱重建保真度。

测量矩阵 ${{{\boldsymbol{T}}}}_{{i}}{(}{ \lambda }{)}$ 由超构表面透射光谱导入，因此对超构表面的设计方法，本质是一种对测量矩阵构建优化的方法。为完成对测量矩阵的构建优化，本文定量分析了超构表面透射光谱相关性均值与重建保真度的关系，并提出一种用于微型光谱探测的超构表面设计方法。该方法的流程图如图3左侧所示，该方法包含以下几个步骤：首先，给出一条具有特定带宽和中心波长的原始入射光谱；随后，给出多组超构表面结构透射光谱；接下来，在本文所提出的方法中，采用式(3)得到两种超构表面透射光谱的相关性值，并采用式(4)，式(5)得到M (M=36、49或64)组超构表面的相关性均值；然后，依据不同相关性均值间隔[0.1~0.3]、[0.3~0.5]、[0.5~0.7]和[0.7~0.9]选择出M组超构表面的透射光谱；接下来，采用压缩感知算法重建原始入射光谱，

并通过式(6)计算原始光谱与重建光谱之间的重建保真度F；最后，当所有原始入射光谱计算完成后，可以得到不同原始入射光谱下的重建保真度F，以及超构表面透射谱相关性均值与重建保真度F的量化关系。相比之下，传统结构设计方法通常采用随机方式进行选择，图3右侧为传统方法的流程图。本文完成了超构表面透射光谱相关性均值所有范围0~1的计算，但计算所得的相关性均值处于0.1~0.9区间内，没有处于相关性均值0~0.1的区间，为保证计算及分析的准确性，本文舍弃掉了0~0.1这段。

图4展示了表1中不同超构表面选择设计方法所产生的重建保真度。图4(a)和4(b)为汇总了表1中的原始入射光谱1~5及光谱6~10的示意图。图4(c)和4(d)重点描述了在入射光谱5、光谱10下，不同超构表面选择设计方法产生的重建保真度。如图4(c)和4(d)所示，相较于传统随机选择方法，选择相关性均值间隔[0.1~0.3]内的超构表面所产生的重建保真度均有不同程度的增幅，这表明本文所提出方法能在一定程度上提高压缩感知算法的光谱重建保真度。

Figure 3. Full-Size Img PowerPoint

Flow chart of our proposed methodology and traditional methodology

5. 光谱特性的仿真验证

如表1与图6的保真度数据所示，表1中的保真度增幅高于图6图像光谱的保真度增幅，经分析后发现，图像光谱的重建光谱在400 nm~500 nm范围内有较大杂散波，而与图5(e)~5(f) 类似的表1的宽带重建光谱在此波长范围内并无太大杂散波，这表明微型光谱探测系统对表1宽带光谱的兼容性优于对图6图像光谱的兼容性，兼容性的差异导致了表1中的保真度增幅高于图6图像光谱的保真度增幅。

为获得微型光谱探测系统的完整性能指标，本文对系统的光谱特性进行了仿真验证。仿真验证的流程为：首先，采用有限时域差分(FDTD, finite difference time domain)软件仿真出具有不同结构参数与内孔图案的超构表面透射光谱，将仿真所得的多条超构表面透射光谱导出，用作压缩感知算法的测量矩阵T；随后，采用不同中心波长与带宽的光谱作为原始入射光谱f₁，将原始入射光谱f₁与测量矩阵相乘后得到调制光谱Y；随后，编写好压缩感知重建算法，通过所得的调制光谱Y与测量矩阵T，重建出与原始光谱f₁相近的重建光谱f₂；最后，采用保真度式(6)计算出原始光谱与重建光谱的保真度F。

Figure 5. Spectral characteristic simulation verification. (a) Incident spectrum and the reconstructed spectrum with a central wavelength of 560 nm and a bandwidth of 1.8 nm; (b) Enlarged images around the central wavelength in Fig. 5(a); (c) Spectral resolution simulation verification with a central wavelength interval of 2 nm; (d) Spectral resolution simulation verification with a central wavelength interval of 3 nm; (e) Reconstruction spectrum and reconstruction fidelity of broadband spectrum 1 under different number of structures M; (f) Reconstruction spectrum and reconstruction fidelity of broadband spectrum 2 under different number of structures M

Figure 5. Full-Size Img PowerPoint

Spectral characteristic simulation verification. (a) Incident spectrum and the reconstructed spectrum with a central wavelength of 560 nm and a bandwidth of 1.8 nm; (b) Enlarged images around the central wavelength in Fig. 5(a); (c) Spectral resolution simulation verification with a central wavelength interval of 2 nm; (d) Spectral resolution simulation verification with a central wavelength interval of 3 nm; (e) Reconstruction spectrum and reconstruction fidelity of broadband spectrum 1 under different number of structures M; (f) Reconstruction spectrum and reconstruction fidelity of broadband spectrum 2 under different number of structures M

Figure 6. Image spectral signals perception verification. (a), (b) Original and reconstructed image spectral signals respectively[46]; (c) Reconstruction fidelity of spectral signals generated by different metasurface design methods under different color blocks. The reconstructed spectrum 1 is produced from the metasurface structures selected using the average correlation value interval [0.1~0.3], and the reconstructed spectrum 2 is produced from the randomly selected metasurface structures

Figure 6. Full-Size Img PowerPoint

Image spectral signals perception verification. (a), (b) Original and reconstructed image spectral signals respectively^[46]; (c) Reconstruction fidelity of spectral signals generated by different metasurface design methods under different color blocks. The reconstructed spectrum 1 is produced from the metasurface structures selected using the average correlation value interval [0.1~0.3], and the reconstructed spectrum 2 is produced from the randomly selected metasurface structures

最后，本文将维度为1392×1083×601的图像光谱信号设定为原始光谱，其中1392×1083为图像纵横比，601为波长采样点的个数，该图像光谱信号数据来源于跨学科计算视觉实验室^[46]，原始图像光谱信号如图6(a)所示。采用图3的方法，在现有的超构表面透射光谱数据库中，依据所提出的方法和随机选择设计方法，分别选择出了两组不同的超构表面。原始图像光谱信号通过两组不同的超构表面后被调制，被调制的信号经压缩感知算法恢复后可得到两组重建的图像光谱信号，其中按照相关性均值[0.1~0.3]选择出的超构表面结构所产生的重建图像光谱信号如图6(b)所示。为表征系统感知图像光谱信号的能力，本文展示了四个色块的重建结果，结果示意图如图6(c)所示，其中重建光谱1为依据相关性均值[0.1~0.3]选择的超构表面所产生的，重建光谱2为随机选择出的超构表面所产生的。如图6(c)所示，在所选择的四个色块，重建光谱1的保真度始终高于重建光谱2的保真度，这表明相较于随机选择设计方法，本文所提出的超构表面设计方法，能在一定程度上提高图像光谱信号的重建质量。

首先，采用窄带光谱验证系统感知自然界中单色光的能力，将原始入射光谱设为中心波长为560 nm、带宽为1.8 nm的窄带光谱，图5(a)为窄带光谱下的重建效果，图5(b)是图5(a)的中心波长附近的放大图像。如图5(a)和5(b)所示，重建后的光谱与原始光谱吻合，系统能准确感知窄带光谱。随后，本文仿真验证了系统的光谱分辨率，将原始入射光谱设为中心波长间隔分别为2 nm 和3 nm、带宽为1.8 nm的双峰光谱，图5(c)和5(d)为双峰光谱下的重建结果。如图5(c)和5(d)所示，系统能较好地分辨中心波长间隔为3 nm的双峰光谱，不能分辨中心波长间隔为2 nm的双峰光谱，这表明系统的光谱分辨率约为3 nm。随后，本文验证了系统感知宽带光谱的能力，将入射光谱设定为不同中心波长和带宽的宽带光谱，图5(e)和5(f)为宽带光谱下的重建结果。如图5(e)和5(f)所示，系统对宽带光谱具有较好的重建效果，这表明系统能对宽带光谱进行感知重建。为测试不同数量的超构表面对重建保真度的影响，图5(e)和5(f)还分别描述了超构表面数量M为36、49和64时宽带光谱的重建效果。如图5(e)和5(f)所示，随着结构数量增加，重建光谱的保真度也相应增加，这是因为随着超构表面的数量增加，其透射光谱的随机性也增加，重建算法对噪声的鲁棒性也相应增强。

6. 结　论

本文完成了超构表面透射光谱的仿真设计，并对一种基于超构表面的微型光谱探测系统进行了分析。针对现有基于超构表面的微型光谱探测系统设计中存在的超构表面设计缺少定量分析、无法保证重建质量最优的问题，本文定义了超构表面透射光谱的相关性均值，定量分析了超构表面透射光谱相关性均值与重建保真度的关系，提出一种用于微型光谱探测的超构表面设计方法。为验证所提出方法的优势，本文从众多光谱选择了10条宽带光谱及图像光谱进行展示。相较于随机选择设计方法，本文所提出方法能提高选定的10条宽带光谱与图像光谱信号的重建质量，宽带光谱重建保真度的增幅可达13.17%，图像光谱信号的重建保真度也得到一定的提升。此外，本文还仿真验证了基于超构表面的微型光谱探测系统的光谱特性，该系统对宽带、窄带光谱和图像光谱信号都具有较好的重建效果，具有结构紧凑、体积小的优势。

利益冲突

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  - State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
  - School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China
- Guo Yinghui On this Site On Google Scholar
  - State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
  - School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China
  - Research Center on Vector Optical Fields, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
- Pu Mingbo On this Site On Google Scholar
  - State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
  - School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China
  - Research Center on Vector Optical Fields, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
- Li Xiong On this Site On Google Scholar
  - State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
  - School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China
- Corresponding author: Luo Xiangang, lxg@ioe.ac.cn On this Site On Google Scholar
  lxg@ioe.ac.cn
  - State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
  - School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.12086/oee.2022.220130

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Yang Gang, Guo Yinghui, Pu Mingbo, Li Xiong, Luo Xiangang. Miniature computational spectral detection technology based on correlation value selection. Opto-Electronic Engineering 49, 220130 (2022). DOI: 10.12086/oee.2022.220130

Yang Gang, Guo Yinghui, Pu Mingbo, Li Xiong, Luo Xiangang. Miniature computational spectral detection technology based on correlation value selection. Opto-Electronic Engineering 49, 220130 (2022). DOI: 10.12086/oee.2022.220130

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- Received Date June 15, 2022
- Revised Date July 17, 2022
- Accepted Date July 19, 2022
- Available Online September 29, 2022
- Published Date October 24, 2022
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光谱	本文提出方法所产生(处于不同相关性均值间隔)的信号重建保真度				传统随机选择方法所产生的信号重建保真度/%	本文方法所产生的信号重建保真度增幅/%
光谱	[0.1~0.3]/%	[0.3~0.5]/%	[0.5~0.7]/%	[0.7~0.9]/%	传统随机选择方法所产生的信号重建保真度/%	本文方法所产生的信号重建保真度增幅/%
光谱1	92.36	91.58	86.99	69.18	89.20	3.50
光谱2	93.83	88.70	87.55	71.95	89.77	4.52
光谱3	97.62	53.01	48.64	50.33	90.84	7.46
光谱4	98.52	77.91	75.09	71.65	90.20	9.22
光谱5	97.07	82.74	79.10	60.06	87.17	11.36
光谱6	96.41	92.29	90.05	85.01	89.32	7.94
光谱7	96.58	94.40	94.48	85.60	91.83	5.17
光谱8	95.75	89.02	90.34	63.26	87.13	9.89
光谱9	98.64	88.05	91.05	83.88	93.96	3.98
光谱10	97.54	94.10	82.70	42.34	86.65	13.17

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Miniature computational spectral detection technology based on correlation value selection

Abstract

Keywords

1. 引　言

2. 工作原理

3. 超构表面的数值仿真

4. 相关性均值与重建保真度分析

5. 光谱特性的仿真验证

6. 结　论

利益冲突

References

Cited by

Periodical cited type(5)

Other cited types(4)

Author Information

Yang Gang, yanggang19@mails.ucas.ac.cn On this Site On Google Scholar

Guo Yinghui On this Site On Google Scholar

Pu Mingbo On this Site On Google Scholar

Li Xiong On this Site On Google Scholar

Corresponding author: Luo Xiangang, lxg@ioe.ac.cn On this Site On Google Scholar

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Miniature computational spectral detection technology based on correlation value selection

Abstract

Keywords

1. 引 言

2. 工作原理

3. 超构表面的数值仿真

4. 相关性均值与重建保真度分析

5. 光谱特性的仿真验证

6. 结 论

利益冲突

References

Cited by

Periodical cited type(5)

Other cited types(4)

Author Information

Yang Gang, yanggang19@mails.ucas.ac.cn On this SiteOn Google Scholar

Guo Yinghui On this SiteOn Google Scholar

Pu Mingbo On this SiteOn Google Scholar

Li Xiong On this SiteOn Google Scholar

Corresponding author: Luo Xiangang, lxg@ioe.ac.cn On this SiteOn Google Scholar

Copyright

About this Article

Cite this Article

Article History

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Corresponding author: Luo Xiangang, lxg@ioe.ac.cn

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Citation

Format

Content

WeChat Qrcode

1. 引　言

6. 结　论

Yang Gang, yanggang19@mails.ucas.ac.cn On this Site On Google Scholar

Guo Yinghui On this Site On Google Scholar

Pu Mingbo On this Site On Google Scholar

Li Xiong On this Site On Google Scholar

Corresponding author: Luo Xiangang, lxg@ioe.ac.cn On this Site On Google Scholar