Wavefront estimation for adaptive optics systems on ground‐based telescopes

Here M(x, y) is the telescope’s pupil indicator function, i.e. is 1 inside the pupil and 0 otherwise, and the function φ(x, y) denotes the phase error, or simply the phase, and is determined by the deviation from planarity of the incoming wavefronts of light at the point (x, y). In Figure 1, we plot (2) in the diffraction limited case, i.e. when φ = 0, and with a nonzero φ generated by a physically realistic model. Note the negative effect of nonzero phase error on the right-hand side PSF. The job of the AO system is to remove the phase error from incoming wavefronts by introducing a counter wavefront φDM via, e.g., a deformable mirror (see Beckers [2]). Assuming the PSF has the form (2), the phase corrected PSF will have the form