Drum dispersion equation for Littrow-type prism spectrometers

A simple analytic procedure has been developed for calibrating the wavelength drum of a Littrow-type prism spectrometer. Only three measured drum readings are required to specify the drum calibration over a broad wavelength range (uv to ir) with an accuracy of the order of the instrumental accuracy. This procedure can be applied to different prism materials for which measurements of refractive index have been performed. It is based on an approximate expression, derived from geometrical optics, relating the drum reading D(lambda) to the calculated refractive index n(lambda): D= A - B(a(2) - n(2))((1/2)). The index n(lambda) is calculated from the appropriate parametric equation. The temperature for the n(lambda) values need not be exactly that of the prism temperature during measurements. This expression was investigated for wavelengths in the range 0.3 micro to 2.25 micro using a sodium chloride prism. Computed drum positions D agreed with measured drum positions to within experimental error. Unknown wavelengths were computed from their measured drum positions to within the accuracy of the measurements.