Establishment and calibration of a spectral reduction model for argon-filled broadband echelle grating spectrometer

A spectral reduction model (SRM) introducing the refractive index parameter of the light transmission medium is proposed for the argon-filled high-resolution broadband echelle grating spectrometer (EGS). This model is essentially established based on a mathematical modeling method, combining the optical design parameters and the structure of the broadband EGS, and considering a new factor accounting for the variation of the refractive index of the medium inside the instrument due to the argon filling. By employing geometric optics principles to evaluate the light transmission path and imaging position, a mapping relationship between the wavelength and the coordinate position of the detector pixel is constructed to achieve accurate spectral conversion. To enhance the accuracy of the model, the SRM is further calibrated, and the key parameters of the medium refractive index, the grating incidence angle, the prism vertex angle, the grating offset angle, and the system focal length are optimized in the SRM. The obtained results reveal that in the argon-filled broadband EGS, the SRM is capable of achieving accurate conversion of spectral information, and the position deviation of the calibrated SRM is within 2 pixels, which proves the accuracy and reliability of the model. This study presents a high-precision implementation approach for the EGS in broadband spectral detection and provides ideas and directions for the design and optimization of spectrometers in similar gas environments.