Accounting for focal shift in the Shack-Hartmann wavefront sensor

The Shack-Hartmann wavefront sensor samples a beam of light using an array of lenslets, each of which creates an image onto a pixelated sensor. These images translate from their nominal position by a distance proportional to the average wavefront slope over the corresponding lenslet. This principle fails when the lenslet is focused to maximize peak intensity and it is partially illuminated, leading to image centroid bias. Here, we show that this bias is due to the low Fresnel number of the lenslets that shifts the diffraction focus away from the geometrical focus. We then demonstrate how the geometrical focus can be empirically found by minimizing the bias in partially illuminated lenslets.