Comparison of centroid computation algorithms in a Shack-Hartmann sensor

TLDR

High‑flux Shack‑Hartmann measurements are limited by non‑linearity, spot truncation, distortion, and pixel sampling errors. The study demonstrates the practical impact of centroiding choices by providing application examples. Analytical theory and extensive simulations compare thresholding, weighted centroid, correlation, and quad‑cell algorithms, optimizing parameters for photon flux, readout noise, and turbulence. At low flux, weighted centroid and quad‑cell yield the lowest noise, with weighted centroid remaining linear when weights track spot shifts, and both remain effective down to 10 photons/subaperture with 3‑e readout noise; at high flux, center‑of‑gravity and correlation methods are equivalent and outperform quad‑cell when parameters are tuned.

Abstract

Analytical theory is combined with extensive numerical simulations to compare different flavours of centroiding algorithms: thresholding, weighted centroid, correlation, quad cell (QC). For each method, optimal parameters are defined in function of photon flux, readout noise and turbulence level. We find that at very low flux the noise of QC and weighted centroid leads the best result, but the latter method can provide linear and optimal response if the weight follows spot displacements. Both methods can work with average flux as low as 10 photons per subaperture under a readout noise of three electrons. At high-flux levels, the dominant errors come from non-linearity of response, from spot truncations and distortions and from detector pixel sampling. It is shown that at high flux, centre of gravity approaches and correlation methods are equivalent (and provide better results than QC estimator) as soon as their parameters are optimized. Finally, examples of applications are given to illustrate the results obtained in the paper.