Theoretical design and analysis of a double-diffraction cross-dispersion spatial heterodyne spectrometer

With the continuous advancement of spectral analysis, higher demands are placed on spectrometer resolution in scientific research. The Spatial Heterodyne Spectrometer (SHS), offering high sensitivity, compactness, and high spectral resolution, is a promising candidate for high-resolution detection. However, the resolution of conventional SHS is still limited by grating width and groove density, restricting further improvement of SHS spectral resolution. Here, we propose a double-diffraction cross-dispersed SHS, in which double diffraction paths are introduced into the interferometer arms to enhance spectral resolution. Theoretical analysis and numerical simulations indicate that, in the two-diffraction mode, the spectral resolution nearly doubles compared with the single-diffraction mode, achieving a spectral resolution better than 0.03 nm. This approach increases resolution without increasing the instrument size or increasing groove density, offering a new approach to designing high-resolution, high-sensitivity spectrometers with potential applications in Raman spectroscopy and atmospheric remote sensing.