Centroiding Undersampled PSFs with a Lookup Table

Reliable centroiding of point spread functions (PSFs) in a star scene is often crucially important for astronomical observations. Accurate determination of angular distances between stars and pointing directions relies on accurate and consistent centroiding, but this is in general not possible with a simple fit for undersampled PSFs. When prominent features of a PSF lie on non-integer pixel values, the undersampling of the pixels does not faithfully represent the PSF, and consistent centroiding is not achievable with a simple fit. We present a method of centroiding that may be useful, especially when dithering is not an option. If the profile of the expected PSF is known fairly well through characterization of the telescope used for observing, one can simulate the PSF at many positions on an oversampled simulated pixel grid and bin the pixels to the level of undersampling appropriate to the detector used for imaging. The true centroid positions are known since the PSFs were simulated, and so one can match up undersampled PSF images to true centroid location, thus forming a lookup table. One then assigns the centroid position of an observed PSF to the position associated with the PSF in the lookup table that has the smallest squared residual with respect to the observed PSF. We examine a few PSF profiles and demonstrate that the lookup table provides better centroid positions compared to a fitting algorithm.