Wavelength Calibration of Linear Array Spectrometers Using Cubic Hermite Spline Interpolation

Wavelength calibration of linear array spectrometers is conventionally performed by fitting a polynomial function of pixels to calibration data consisting of spectral lines with known wavelengths and their pixel locations. Alternatively, a multiparameter physical model of the optical system can be constructed and the parameters optimized to reproduce the calibration data. Here, a new spectrometer wavelength calibration method is introduced with two distinguishing features: the reference calibration points are treated as fixed points, and are used as nodes for cubic Hermite spline interpolation between those points. Conveniently, in the Hermite form of cubic splines, the calibration data, i.e., the calibration wavelengths together with the slopes at those calibration points, explicitly appear as the parameters of the interpolating functions. The slopes are derived from the grating equation and the physical model of the optical system. As a result, the calibration curve is fully determined without the need for intermediate calculations such as polynomial regression or model parameter fitting. Zero residual error is ensured at those reference points and interpolation errors in the intervals between reference points are very low, approaching the limit of spectral line peak location uncertainty. The calibration procedure is demonstrated for a compact flat-field spectrometer. This method improves and simplifies the spectrometer wavelength calibration procedure and offers a convenient method of calibration for systems with limited computing resources.