Optimal bases for wave-front simulation and reconstruction on annular apertures

For many applications in adaptive optics the eigenfunctions of the power spectrum of turbulence-induced distortions on the actual telescope aperture constitute the ideal basis for modeling wave fronts. The mathematical derivation of these functions is reviewed, and a procedure for their calculation, allowing for a circular central obscuration and leaving considerable freedom in the form of the structure function, is described. Examples of wave-front simulations are presented for a range of power-law structure functions and for Kolmogorov structure functions with an outer scale smaller than the diameter of the region being modeled. (C) 1996 Optical Society of America