Practical high-resolution spectroscopy with a spatial heterodyne spectrometer: Determination of instrumental function for lineshape recovery

The spatial heterodyne spectrometer (SHS) is a well-recognized platform for its high resolving power in various use cases of spectroscopy. Same as other spectrometer topologies, the SHS, unfortunately, also suffers from classical challenges such as distorted lineshape due to the instrumental function. The goal of this work is to tackle this persisting issue through a simple numerical approach. With the inherent characteristics of an SHS interferogram, we report the direct extraction and determination of the instrumental function in its numerical representation from an SHS interferogram; this instrumental function was further used for spectral data processing that enables significant improvements in spectral resolution through deconvolution algorithms. Here, we systematically discuss the recognition of the embedded instrumental function among various ingredients within an interferogram. To verify the numerical approach, lithium was chosen as the model sample, resembling the use of SHS in an isotopic analysis application. Specifically, the resonance transition of lithium D-lines (P-2(1/2,3/2) <- S-2(1/2)) was selected to assess the performance of the spectral processing. With the spectral deconvolution, the spectral features that represent the Li-6 and Li-7 were nearly baseline-separated, allowing for the accurate measure of the isotopic abundance without external references or algorithm adjustments (e.g., curve fitting).