Error propagation: a comparison of Shack-Hartmann and curvature sensors

TL;DR

This paper compares the error propagation in Shack-Hartmann and curvature wavefront sensors, analyzing how the error propagation factors vary with the number of sensors and aperture size in adaptive optics.

Contribution

It provides a quantitative analysis of the ratio of error propagation factors between curvature and Shack-Hartmann sensors based on sensor count and aperture size.

Findings

Error propagation ratio increases with number of sensors.

Larger apertures with constant spacing increase the ratio as n^0.4.

More sensors on the same aperture increase the ratio as n^0.8.

Abstract

Phase estimates in adaptive-optics systems are computed by use of wavefront sensors such as Shack-Hartmann or curvature sensors. In either case the standard error of the phase estimates is proportional to the standard error of the measurements; but the error-propagation factors are different. We calculate the ratio of these factors for curvature and Shack-Hartmann sensors in dependence on the number of sensors, n, on a circular aperture. If the sensor spacing is kept constant and the pupil is enlarged, the ratio increases as n^0.4. When more sensing elements are accommodated on the same aperture, it increases even faster, viz. proportional to n^0.8. With large numbers of sensing elements this increase can limit the applicability of curvature sensors.