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

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, namely, proportional to n(0.8). With large numbers of sensing elements, this increase can limit the applicability of curvature sensors.