Low-rank reconstruction for mid-infrared spectroscopy using broadband ultra-wide-angle photonic filters and IReg algorithm

Abstract

In this study, a broadband mid-infrared photonic filter is designed. It has the advantages of polarization insensitivity, ultrawide angle, high manufacturability, and easy integration. For infrared spectrum reconstruction, the use of filters as spectral sampling channels can eliminate the influence of slits or complex optical splitting elements in spectral imaging technology. Further, we propose a low-rank matrix logarithm regularization algorithm based on a three-segment filter function (IReg algorithm) combined with the designed filter for a variety of mid-infrared detector front ends, which can significantly suppress noise interference. Here, we demonstrate that the stability of the spectral reconstruction accuracy under the large disturbance environment obtained by the IReg algorithm is much higher than those of the L2 and L1 algorithms. In the low-dimensional matrix state, the accuracy and stability of the ill-conditioned linear equations are guaranteed, the anti-noise ability is enhanced, the effect of data dimensionality reduction is realized, and the accuracy of mid-infrared spectral reconstruction is improved.

Keywords

• Filter
• Low-rank
• Ultra-wide-angle
• Infrared spectral reconstruction