Moment-based space-variant Shack-Hartmann wavefront reconstruction

This article presents an approach for space-variant Shack-Hartmann wavefront reconstruction based on image moment theory. We derive the relation between the moment of a pair of subimages and the local transformation coefficients. A special solution is obtained from this relation using the square guide 'star'. Our moment-based wavefront reconstruction has reduced computational complexity compared to the iteration-based algorithm. We execute image restorations using both the tiling strategy with 5 x 5 PSFs and the conventional strategy with a global average PSF. Our approach is supported by visual and quantitative evaluations.

Automated summary

This article presents an approach for space-variant Shack-Hartmann wavefront reconstruction based on image moment theory. The relation between the moment of a pair of subimages and the local transformation coefficients is derived, and a special solution is obtained using the square guide 'star'. Our moment-based wavefront reconstruction has reduced computational complexity compared to the iteration-based algorithm. Image restorations using both the tiling strategy with 5 x 5 PSFs and the conventional strategy with a global average PSF are executed. Our approach is supported by visual and quantitative evaluations.