Spectrum reconstruction based on the constrained optimal linear inverse methods

The dispersion effect of birefringent material results in spectrally varying Nyquist frequency for the Fourier transform spectrometer based on birefringent prism. Correct spectral information cannot be retrieved from the observed interferogram if the dispersion effect is not appropriately compensated. Some methods, such as nonuniform fast Fourier transforms and compensation method, were proposed to reconstruct the spectrum. In this Letter, an alternative constrained spectrum reconstruction method is suggested for the stationary polarization interference imaging spectrometer (SPIIS) based on the Savart polariscope. In the theoretical model of the interferogram, the noise and the total measurement error are included, and the spectrum reconstruction is performed by using the constrained optimal linear inverse methods. From numerical simulation, it is found that the proposed method is much more effective and robust than the nonconstrained spectrum reconstruction method proposed by Jian, and provides a useful spectrum reconstruction approach for the SPIIS.