Computational spectroscopy via singular-value decomposition and regularization.

Computational spectrometer based on a broadband diffractive optic was demonstrated with high spectral resolution over large bandwidth and high photon utilization efficiency. In this paper, we analyze such a spectrometer using singular value decomposition and propose a faster spectrum reconstruction algorithm with excellent accuracy by regularization. A new definition of spectral resolution based upon the Fourier analysis of singular vectors is described as well.