Donut: measuring optical aberrations from a single extra-focal image

We propose a practical method to calculate Zernike aberrations from analysis of a single long-exposure defocused stellar image. It consists in fitting the aberration coefficients and seeing blur directly to a realistic image binned into detector pixels. This "donut" method is different from curvature sensing in that it does not make the usual approximation of linearity. We calculate the sensitivity of this technique to detector and photon noise and determine optimal parameters for some representative cases. Aliasing of high-order un-modeled aberrations is evaluated and shown to be similar to a low-order Shack-Hartmann sensor. The method has been tested with real data from the SOAR and Blanco 4m telescopes.