Investigation of Performance Degradation of Shack Hartmann Wavefront Sensing Due to Pupil Irradiance Profile

Abstract

Wavefront sensing using a Shack-Hartmann sensor has been widely used for estimating wavefront errors or distortions. The sensor combines the local slopes, which are estimated from the centroids of each lenslet image, to give the overall wavefront reconstruction. It was previously shown that the pupil-plane irradiance profile effects the centroid estimation. Furthermore, a previous study reported that the reconstructed wavefront from a planar wavefront with a Gaussian pupil irradiance profile contains large focus and spherical aberration terms when there is a focus error. However, it has not been reported yet how seriously the pupil irradiance profiles, which can occur in practical applications, effect the sensing errors. This paper considered two cases when the irradiance profiles are not uniform: 1) when the light source is Gaussian and 2) when there is a partial interference due to a double reflection by a beam splitting element. The images formed by a Shack-Hartmann sensor were simulated through fast Fourier transform and were then supposed to be detected by a noiseless CCD camera. The simulations found that sensing errors, due to the Gaussian irradiance profile and the partial interference, were found to be smaller than RMS <TEX>${\lambda}/50$</TEX> when <TEX>${\lambda}$</TEX> is <TEX>$0.6328\;{\mu}m$</TEX>, which can be ignored in most practical cases where the reference and test beams have the same irradiance profiles.