A simple spectrogram model for high-accuracy spectral calibration of VIPA spectrometers

The virtually imaged phased array (VIPA) spectrometer uses the orthogonal dispersion method and has the advantages of compact structure, high spectral resolution, and wide wavelength coverage. It has been widely used in different fields. However, due to the non-linear dispersion of the VIPA etalon and the cross-dispersion structure of the VIPA spectrometer, simple and high-accuracy wavelength calibration remains a challenge. In this paper, a new and simple five-parameter spectrogram model is developed by simplifying the phase-matching equation of the VIPA etalon and considering the angle between the camera and dispersion direction, which can achieve a frequency accuracy better than one pixel. The performance of the model is demonstrated by measuring the CO₂ absorption spectrum in the range of 1.42 to 1.45 μm using a self-designed near-infrared VIPA spectrometer . The reported method is simple and easy to solve with high accuracy, which is conducive to promoting the application of VIPA spectrometers in precision measurement.