High-accuracy spectral reduction algorithm for the échelle spectrometer

A spectral reduction algorithm for an échelle spectrometer with spherical mirrors that builds a one-to-one correspondence between the wavelength and pixel position is proposed. The algorithm accuracy is improved by calculating the offset distance of the principal ray from the center of the image plane in the two-dimensional vertical direction and compensating the spectral line bending from the reflecting prism. The simulation and experimental results verify that the maximum deviation of the entire image plane is less than one pixel. This algorithm ensures that the wavelengths calculated from spectrograms have a high spectral resolution, meaning the precision from the spectral analysis reaches engineering standards of practice.