Gemini Planet Imager Observational Calibrations IX: Least-Squares Inversion Flux Extraction

The Gemini Planet Imager (GPI) is an instrument designed to directly image planets and circumstellar disks from 0.9 to 2.5 microns (the $YJHK$ infrared bands) using high contrast adaptive optics with a lenslet-based integral field spectrograph. We develop an extraction algorithm based on a least-squares method to disentangle the spectra and systematic noise contributions simultaneously. We utilize two approaches to adjust for the effect of flexure of the GPI optics which move the position of light incident on the detector. The first method is to iterate the extraction to achieve minimum residual and the second is to cross-correlate the detector image with a model image in iterative extraction steps to determine an offset. Thus far, this process has made clear qualitative improvements to the cube extraction by reducing the Moir\'{e} pattern. There are also improvements to the automated routines for finding flexure offsets which are reliable to with $\sim0.5$ pixel accuracy compared to pixel accuracy prior. Further testing and optimization will follow before implementation into the GPI pipeline.