Determination of Spectrometer-Detector Parameters from Calibration Spectra and the Use of the Parameters in Spectrometer Calibrations

The grating equation is used to generate quadratic calibration equations for multichannel detectors with perpendicular and tilted focal planes. The quadratic coefficients are not independent and contain terms that are used to solve for spectrometer-detector parameters. The parameters can be calculated from a quadratic fit at one spectrometer position, but more accurate values can be obtained from quadratic fits at two spectrometer positions. The calculations show that the detector focal plane is tilted by about two degrees. Once values for the spectrometer-detector parameters are obtained from calibrations using at least three lines at one or two spectrometer positions, only one calibration line at any spectrometer position is required to obtain accuracies on the order of 0.1 cm⁻¹ over a several thousand wavenumber range. The main cause of spectrometer drift is a change in the diffraction angle and/or the spectrometer included angle. This drift is almost totally compensated by the one-line calibration, which adjusts the diffraction angle. A neon pen lamp is used to generate the calibration spectra. Using standard air wavelengths compared to true wavelengths can produce calibration errors of 0.1 to 0.6 cm⁻¹; the magnitude depends on local conditions and how the laser wavelength is treated.