A singular value decomposition for the Shack-Hartmann based wavefront reconstruction

作者：Kindermann Stefan^*; Neubauer Andreas; Ramlau Ronny

来源：Journal of Computational and Applied Mathematics, 2012, 236(8): 2186-2199.

DOI：10.1016/j.cam.2011.09.041

• Adaptive optics
• Inverse problems
• Singular value decomposition

We study the problem of reconstructing a wavefront from measurements of Shack-Hartmann-type sensors. Mathematically, this leads to the problem of reconstructing a function from a discrete set of averages of the gradient. %26lt;br%26gt;After choosing appropriate function spaces this is an underdetermined problem for which least squares solutions and generalized inverses can be used. We explore this problem in more detail for the case of periodic functions on a quadratic aperture, where we calculate the singular value decomposition of the associated forward operator. The nonzero singular values can be estimated which shows that asymptotically, with increasing number of measurements, the reconstruction problem becomes an ill-posed problem.

• 出版日期2012-2