Design and theoretical analysis of a conical-diffraction-based cross-dispersed spatial heterodyne spectrometer

A conical-diffraction-based cross-dispersed spatial heterodyne spectrometer (CDCDSHS) is presented. Conical diffraction is introduced, and one grating in the SHS is rolled around the central normal of its surface to expand the spectral range. The two-dimensional fringes are generated by the longitudinal-dispersion grating and the lateral-dispersion gratings through conical diffraction. Mathematical expressions are given for the parameter of an interferogram with varying spectral features and for the intensity distribution. Two examples are numerically simulated to demonstrate the performance of the spectrometer. The simulations show that the designed spectrometer can limit the interferogram of each spectral feature to be recorded by certain given rows of pixels on the charge-coupled device to avoid multiplexing disadvantages, and it can obtain clear features in each detailed spectrum with a higher signal-to-noise ratio than the conventional SHS while eliminating the need for filters or moving parts. Replacing the lateral-dispersion grating in the designed spectrometer with a mosaic grating can increase the spectral resolution and broaden the detectable spectral range. The designed spectrometer is also compact, very stable, and high-throughput. All mentioned advantages make the CDCDSHS a good prospect in broadband, high-resolution, high-sensitivity spectral measurement.