A single-shot, spatially resolved wavefront gradient measurement and polarimetry technique is proposed by combining a Shack-Hartmann Wavefront Sensor (SHWFS) and a Star Test Imaging Polarimeter (STIP). By placing the focal plane of the SHWFS at the object plane of the STIP, the gradient and polarization can be retrieved with a position and Stokes retrieval algorithm. The algorithm generates a set of irradiance patterns, using a measurement matrix, from a set of Stokes vectors as system inputs. A normalized cross-correlation is performed with the measured irradiance pattern and each generated irradiance pattern. By searching through this set for the maximum degree of correlation, the Stokes vector and the displacement is retrieved. Using simulated irradiance patterns with noise levels of 5% or less, the algorithm correctly retrieves the Stokes vector and displacement of the measured irradiance pattern and has sub-pixel spread for both. At noise levels of 7.5%, the algorithm demonstrates bias in the Stokes vector retrieval with sub-pixel spread and it correctly retrieves the displacement with sub-pixel spread. At noise levels of 10%, the algorithm demonstrates bias in the Stokes vector retrieval with single-pixel spread and it correctly retrieves the displacement with single-pixel spread in the horizontal direction.
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