Weighted Fried reconstructor and spatial-frequency response optimization of Shack–Hartmann wavefront sensing

Abstract

Two modified Fried wavefront reconstructors are proposed, both based on an enhanced geometry that combines and balances those of Fried and Hudgin with an additional weight. The optimal weights for both of them are derived with the analytical frequency response functions, which can provide near-unity spatial frequency response over broad bandwidth to the Shack-Hartmann wavefront sensing system. Comparisons between the proposed reconstructors and the classical ones are presented in the frequency domain, and simulations have further confirmed the frequency characteristic and the reconstruction performance of the new reconstructors. It is expected that the optimized reconstructors can help improve the performance of adaptive optics systems for high-power laser wavefront control and other relevant optical systems that require high-accuracy wavefront sensing.

Comparison of Surface Shape Control Algorithms for Deformable Mirror

“…In the Fourier frequency domain, the control vector errors can be formulated in a general form as [8,9],…”

“…1 (for Fried and weighted Fried I, only parts of the curves are drawn). It shows that RBCs produce more uniform and better frequency response, and nearly uniform frequency response can be acquired by optimizing the reconstructor [8,9]. When the spatial sampling rate is not so high that aliasing will occur with high order harmonics.…”

A frequency-response-optimized Shack–Hartmann zonal wavefront reconstructor based on Fan’s model

“…19 However, these analyses did not consider the low-pass effect of the microlens, limiting the frequency response to the reconstruction process rather than the entire wavefront sensing system. Li et al 20 proposed two weighted Fried reconstructors and examined the frequency response of the entire system. Nevertheless, the model's complexity and the need to calculate weight values pose challenges.…”