In this paper we investigate the behavior of various centroiding methods (weighted center of gravity, matched filtering, and correlation) classically used in Shack–Hartmann wavefront sensing when dealing with an elongated asymmetric spot. We study the impact of model errors on these centroiding methods at high signal-to-noise ratios, and, using a one-dimensional formalism, we show that the associated estimates all suffer from a bias uncorrelated with the actual spot displacement if its shape is not known precisely. Additionally, we show that the correlation method provides an estimate with a unitary gain whatever the parameters used, while the other two methods introduce a non-unitary gain in the estimation process. Finally, we show that the sampling of the spot structures after filtering by some convolution kernels is crucial to get an unbiased estimate of the spot displacement.
© 2010 Optical Society of America
Original Manuscript: March 29, 2010
Revised Manuscript: July 20, 2010
Manuscript Accepted: July 21, 2010
Published: September 22, 2010
Damien Gratadour, Eric Gendron, and Gérard Rousset, "Intrinsic limitations of Shack–Hartmann wavefront sensing on an extended laser guide source," J. Opt. Soc. Am. A 27, A171-A181 (2010)