Curvature sensors: noise and its propagation

TL;DR

This paper analyzes the noise characteristics and propagation in curvature sensors, deriving minimum sensing elements, statistical properties of signals, and expressions for error propagation and Strehl loss due to photon noise.

Contribution

It provides a detailed statistical analysis of curvature sensor signals, including noise propagation and optimal sensing element distribution, with new closed-form expressions for error and Strehl loss.

Findings

Gaussian approximation is valid at moderate photon counts.

Higher photon numbers are needed for accurate measurements of small wavefront distortions.

Closed-form expressions for error propagation and Strehl loss are derived.

Abstract

The signal measured with a curvature sensor is here analyzed. In the outset, we derive the required minimum number of sensing elements at the pupil edges, in dependence on the total number of sensing elements. The distribution of the sensor signal is further characterized in terms of its mean, variance, kurtosis and skewness. It is established that while the approximation in terms of a gaussian distribution is correct down to fairly low photon numbers, much higher numbers are required to obtain meaningful sensor measurements for small wavefront distortions. Finally, we indicate a closed expression for the error propagation factor and for the photon-noise induced Strehl loss.