Abstract

In an echelle spectrometer equipped with a prism cross-dispersion element, wavelength calibration is very difficult because of the complex, nonlinear interaction between the prism and the echelle grating. From the spectrometer geometry and the dispersion equations for the prism and the grating, a detailed mathematical model for wavelength calibration is derived that fits the refractive index of the prism in real time. An expression relating the refractive index, wavelength, and image coordinates is constructed, and standard wavelength sources and image positions are adopted to timely calculate the refractive index, which is affected by ambient factors such as temperature and air pressure. Experimental results indicate that the fitting accuracy of the refractive index in real time approaches 104, while the wavelength accuracy approaches 103  nm for the entire spectral range.

© 2016 Optical Society of America

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