Spectral reduction model for an echelle spectrometer based on a digital micromirror device and photomultiplier

For an echelle spectrometer based on a digital micromirror device and photomultiplier, a lens group is placed in front of the digital micromirror device and used to converge the two-dimensional spectrum and correct aberration. The matching spectral reduction model is deduced by establishing the mathematical models of the imaging mirror and lens group. According to the known wavelength and corresponding coordinates, the refractive index of the prism is fitted, and the spectrum is divided into three parts to calibrate. Experimental results of a mercury lamp show that the maximum deviations of x and y coordinates are 3.4 pixels and 2.3 pixels in the corrected spectral reduction model. The deviations are in the range of the errors permitted, which means the extraction of order and wavelength satisfy the requirement of the spectrometer.