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Currently, the engineering of miniature spectrometers mainly faces threeproblems: the mismatch between the number of filters at the front end of thedetector and the spectral reconstruction accuracy; the lack of a stablespectral reconstruction algorithm; and the lack of a spectral reconstructionevaluation method suitable for engineering. Therefore, based on 20 sets offilters, this paper classifies and optimizes the filter array by the K-meansalgorithm and particle swarm algorithm, and obtains the optimal filtercombination under different matrix dimensions. Then, the truncated singularvalue decomposition-convex optimization algorithm is used for high-precisionspectral reconstruction, and the detailed spectral reconstruction process oftwo typical target spectra is described. In terms of spectral evaluation, dueto the strong randomness of the target detected during the working process ofthe spectrometer, the standard value of the target spectrum cannot be obtained.Therefore, for the first time, we adopt the method of joint cross-validation ofmultiple sets of data for spectral evaluation. The results show that when therandom error of positive or negative 2 code values is applied multiple timesfor reconstruction, the spectral angle cosine value between the reconstructedcurves becomes more than 0.995, which proves that the spectral reconstructionunder this algorithm has high stability. At the same time, the spectral anglecosine value of the spectral reconstruction curve and the standard curve canreach above 0.99, meaning that it realizes a high-precision spectralreconstruction effect. A high-precision spectral reconstruction algorithm basedon truncated singular value-convex optimization, which is suitable forengineering applications, is established in this paper, providing importantscientific research value for the engineering application ofmicro-spectrometers.

Research on the spectral reconstruction of a low-dimensional filter  array micro-spectrometer based on a truncated singular value  decomposition-convex optimization algorithm