Statistical error of a compact high-resolution Shack-Hartmann wavefront sensor with a discrete detector array

The noise characteristics of a compact high-resolution Shack-Hartmann wavefront sensor with an extended pupil to sensor distance have been measured. The standard deviation, sigma, of the angular position error caused by random noise conforms to theoretical predictions of discrete detector arrays described by sigma(tot) = lambda/D(omega/SNR + eta/root V-s), where omega is the position error constant, SNR is the signal-to-noise ratio, eta is the geometric aperture constant, and V-s is the sum of the signal's total counts. The agreement both confirms the theoretical derivation of this useful formula and shows that measurement of ocular aberrations under laboratory conditions at working distances greater than 30 cm introduces negligible additional error. (C) 2010 Optical Society of America