Accurately measuring hyperspectral imaging distortion in grating spectrographs using a clustering algorithm

Grating-based spectrographs suffer from smile and keystone distortion, which are problematic for hyperspectral data applications. Due to this, spectral lines will appear curved and roughly parabola-shaped. Smile and keystone need to be measured and corrected for accurate spectral and spatial calibration. In this paper, we present a novel method to accurately identify and correct curved spectral lines in an image of a spectrum, using a clustering algorithm we developed specifically for grating spectrographs, inspired by K-means clustering. Our algorithm will be used for calibrating a multi-object spectrograph (MOS) based on a digital micromirror device (DMD). For each spectral line in a spectrum image, our algorithm automatically finds the equation of the parabola which models it. Firstly, the positions of spectral peaks are identified by fitting Gaussian functions to the spectrum image. The peaks are then grouped into a given number of parabola-shaped clusters: each peak is iteratively assigned to the nearest parabola-shaped cluster, such that the orthogonal distances from the parabola are minimized. Smile can then be measured from the parabolas, and keystone as well if a marked slit is used. Our method has been verified on real-world data from a long-slit grating spectrograph with sub-pixel error, and on simulated data from a DMD-based MOS. Compared to traditional approaches, our method can measure distortions automatically and accurately while making use of more spectral lines. With a precise model and measurement of distortion, a corrected hyperspectral data cube can be created, which can be applied for real-time data processing.