Using Non-Negative Matrix Factorization to Improve Calibration of the Keck OSIRIS Integral Field Spectrograph

Abstract: Integral Field Spectrographs (IFS) often require non-trivial calibration techniques to process raw data. The OH Suppressing InfraRed Imaging Spectrograph (OSIRIS) at the W. M. Keck Observatory is a lenslet-based IFS that requires precise methods to associate the flux on the detector with both a wavelength and a position on the detector. During calibration scans, a single column lenslet mask is utilized to keep light from adjacent lenslet columns separate from the primary lenslet column, in order to uniquely determine spectral response of individual lenslets on the detector. Despite employing a single column lenslet mask, an issue associated with such calibration schemes may occur when light from adjacent masked lenslet columns leaks into the primary lenslet column. Incorrectly characterizing the flux due to additional light in the primary lenslet column results in one form of crosstalk between lenslet columns, which most clearly manifest as non-physical artifacts in the spectral dimension of the reduced data. We treat the problem of potentially blended calibration scans as a source separation problem and implement Non-negative Matrix Factorization (NMF) as a way to separate blended calibration scan spectra. After applying NMF to calibration scan data, extracted spectra from calibration scans show reduced crosstalk of up to 26.7$\pm$0.5$\%$ while not adversely impacting the signal-to-noise ratio. Additionally, we determined the optimal number of calibration scans per lenslet column needed to create NMF factors, finding that greatest reduction crosstalk occurs when NMF factors are created using one calibration scan per lenslet column.