Structural approach to the Adaptive Optics tomography problem: the volume turbulence reconstruction

Adaptive Optics as a relatively new trend in the modern optical systems allows correcting the perturbations related to light propagation in the turbulent atmosphere obtaining the diffraction-limited images. Because it requires computer processing of large information flow in real time, a key problem lays in finding the mathematical algorithms with reduced computational complexity. The paper proposes the approach, which takes into account structural properties of both atmospheric turbulence and the most active optical system. The possibility was demonstrated of one-dimensional accounting of sparse and convolution-like (Toeplitz) structure of adaptive correction in one algorithm. The analysis is made of Multi-Conjucate Adaptive Optics and the comparison was conducted of the nature complexity of the algorithm induced by this strucute with the complexity of sparse algorithm. It was demonstrated how the structural approach can be applied to the quite laborious tomographic turbulence volume reconstruction phase with obtaining due to this a significant computational speed-up.