Measuring statistical error of Shack-Hartmann wavefront sensor with discrete detector arrays

摘要

A formula is derived that can be used to evaluate the angular position error caused by random noise; when a Shack-Hartmann wavefront sensor is used to measure the wavefront information of the signal, its standard deviation is given by sigma = omega SNR-1 lambda/D + eta V-s(-1/2)lambda/D, where omega is the position-error constant, and it is fully defined in the main text, SNR is the ratio of the signal intensity to the noise intensity, eta is a positive constant, lambda is the measuring wavelength, D is the diameter of the aperture, and V-s is the count of signal photoelectrons. The angular position error is inversely proportional to the signal-to-noise of the signal, and it is concerned with the scale of the discrete detector arrays. The experimental results are in agreement with the formula and prove that the formula can describe the angular position error precisely under the different scales of the discrete detector arrays and different kinds of noise.