Iterative wave-front reconstruction for open-loop metrology applications: Shack-Hartmann and shearing interferometer wave-front sensing using Fourier or Multigrid reconstructors

Numerous techniques exist to reconstruct the wave-front in Shack-Hartmann and shearing interferometer wave-front sensors. Two of these techniques involve solving the least-squares wave-front reconstruction via Fourier transform or Multigrid methods. These two techniques operate on a square grid and are sensitive to both nonlinearities and to the methods used to extend the gradients beyond the aperture to the edges of the square grid. Both of these sensitivities can lead to large residual wave-front errors when reconstructing large aberrations. In this article we introduce an iterative computational loop in the reconstruction process which is designed to improve the reconstruction variances introduced by these parameters. This technique allows for accurate reconstruction of large phases which can arise in applications such as open-loop compensation of atmospheric turbulence, aberrometers and metrology. In this article, it is demonstrated that large aberrations can be accurately reconstructed utilizing this iterative method with Fourier or Multigrid reconstructors.