Myopic aberrations: impact of centroiding noise in Hartmann Shack wavefront sensing

The presence of photon noise and readout noise can lead to centroiding errors in a Hartmann Shack wavefront sensor (HS) and hence limit the accuracy of wavefront reconstruction. The aim of this paper is to compare, via Monte Carlo simulations, the accuracy of various centroiding methods in detecting noisy focal spot patterns of the HS while sensing ocular aberrations of myopic eyes.

Myopic ocular aberrations were randomly simulated by using the modal statistics obtained from the measurements of 41 myopic subjects. HS spot patterns were simulated using a fast Fourier method where photon noise and readout noise were added using appropriate statistics. Adopting five different centroiding techniques: (1) centre of gravity, (2) weighted centre of gravity, (3) intensity weighted centroiding, (4) iteratively weighted centre of gravity and (5) matched filter based centroiding along with a zonal based wavefront sensing approach; the wavefronts were estimated and compared, by calculating the root mean square (RMS) wavefront error, with the initially simulated wavefront. The magnitude of readout noise was varied in terms of the maximum number of photons and electrons per subaperture per frame. The RMS error was calculated for each of the centroiding algorithms.

For higher magnitude of readout noise and lesser number of photons per subaperture per frame (n), matched filter, iteratively weighted centre of gravity and intensity weighted centroiding outperform centre of gravity and weighted centre of gravity methods, for an appropriately chosen focal length and subaperture pitch. The plots of RMS error as a function of 'n' show that for lower amplitude of readout noise, computationally efficient centre of gravity and intensity weighted centroiding methods can be safely adopted to obtain high enough reconstruction accuracy. Also, even at greater readout noise levels, for a large enough 'n', intensity weighted centroiding is enough to sense the aberrations with high accuracy. It is shown that the wavefront sensing accuracy depends on the size of the spots and bit resolution of the camera.

Five different centroid detection methods used in a HS in the presence of photon noise and readout noise were analysed in the context of sensing ocular aberrations of myopic subjects and identify cases under which each of these methods is appropriate.