Curvature sensors: noise and its propagation

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.