A hierarchical wavefront reconstruction algorithm for gradient sensors

ELT-scale extreme adaptive optics systems will require new approaches to compute the wavefront when the computational burden of applying a MVM is no longer practical. An approach is demonstrated which is hierarchical in transforming wavefront slopes into 1D estimates, then 2D estimates, and finally to actuator values. Using a combination of algebraic expressions, sparse representation, and a conjugate gradient solver, the number of non-parallelized operations for reconstruction on a 100 × 100 sub-aperture sized problem can be as little as ∼ 6 × 106 or O(N3/2), which is approximately the same as for the application of a MVM solution parallelized over 100 threads. To reduce the effects of noise propagation, a noise reduction algorithm which ensures continuity of the measurements can be utilized but with a speed penalty.