Advanced techniques for Fourier transform wavefront reconstruction

The performance of Fourier transform (FT) reconstructors in large adaptive optics systems with Shack-Hartmann sensors and a deformable mirror is analyzed. FT methods, which are derived for point-based geometries, are adapted for use on continuous systems. Analysis and simulation show how to compensate for effects such as misalignment of the deformable mirror and wavefront sensor gain. Further filtering methods to reduce noise and improve performance are presented. These modifications can be implemented at the filtering stage, preserving, the speed of FT reconstruction and providing flexibility by allowing on-the-fly filter adaptation. Simulation of a large system shows how compensated FT methods can have equivalent or better performance to slower vector-matrix-multiply methods. The best-performing FT method is the fastest to compute, has lower noise propagation and does not suffer from waffle errors.