Accounting for intensity variation within pixels of Shack-Hartmann wavefront sensors

The accuracy of centroiding algorithms in Shack-Hartmann wavefront sensing is limited by the implicit approximation of uniform pixel illumination. Iterative centroiding algorithms are further limited by the consideration of full pixels to define the image domain for centroiding. Here, we demonstrate two practical and complementary approaches to mitigate both these sources of error. First, we consider partial or ‘fractional’ pixels to maintain centroiding area symmetry around the center of mass. Secondly, we propose methods to perform piece-wise polynomial interpolation to calculate intensity distribution within pixels, which is then used to estimate the centroid within each pixel area. This approach that accounts for intensity non-uniformity across pixels notably reduces centroid errors up to a factor of 5 across lenslet image widths ranging from 1.33 to 3.10 pixels full-width-half-maximum (FWHM). Consequently, wavefront sensing errors decrease from 14 % to 4 %, on average, for FWHM = 1.35 pixels, demonstrating a substantial benefit when the number of pixels per lenslet is minimized to enhance the signal-to-noise ratio or increase frame rate.