A broadband spectral inversion method for spatial heterodyne spectroscopy

Spatial heterodyne spectroscopy (SHS) is a Fourier-transform spectroscopic technique with many advantages, such as high throughput, good robustness (no moving parts), and high resolving power. However, in the basic theory of SHS, the relationship between the wavenumber and the frequency of the interferogram is approximated to be linear. This approximation limits the spectral range of a spatial heterodyne spectrometer to a narrow band near the Littrow wavenumber. Several methods have been developed to extend the spectral range of the SHS. They use echelle gratings or tunable pilot mirrors to make a SHS instrument work at multiple narrow spectral bands near different Littrow wavenumbers. These solutions still utilize the linear relationship between the wavenumber and the frequency of the interferogram. But they need to separate different spectral bands, and this will increase the difficulty of post processing and the complexity of the SHS system. Here, we solve this problem from another perspective: making a SHS system work at one broad spectral band instead of multiple narrow spectral bands. As in a broad spectral range, the frequency of the interferogram will not be linear with respect to the wavenumber anymore. According to this non- linear relationship, we propose a broadband spectral inversion method based on the stationary phase theory. At first, we describe the principles and the basic characters of SHS. Then, the narrow band limitation is analyzed and the broadband spectral inversion method is elaborated. In the end, we present a parameter design example of the SHS system according to a given spectral range, and the effectiveness of this method is validated with a spectral simulation example. This broadband spectral inversion method can be applied to the existing SHS system without changing or inserting any moving components. This method retains the advantages of SHS and there is almost no increase in complexity for post processing.