Wave-front phase estimation from Fourier intensity measurements

Abstract

A novel wave-front sensor that estimates phase from Fourier intensity measurements is described, and an explicit expression is found and numerically evaluated for the Cramtr-Rao lower bound on integrated rms wave-front phase estimation error. For comparison, turbulence-aberrated wave-front phases and corresponding noisy Fourier intensity measurements were computer simulated. An iterative phase-retrieval algorithm was then used to estimate the phase from the Fourier intensity measurements and knowledge of the shape of an aperture through which the wave front passed. The simulation error approaches the lower bound asymptotically as the noise is reduced.

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization

“…It should be noted, however, that occurrences of inconsistent set-theoretic formulations in phase retrieval or other signal recovery problems are far from being academic, as a result of noisy data, measurement errors, or inaccurate a priori information. 21,[46][47][48][49] Several investigations have been devoted to analyzing and coping with this situation in convex problems. [50][51][52][53][54][55] While the infinite-dimensional space L appears to be the most appropriate signal space to model the physics of the problem and to describe the subtle properties of the algorithms in their full generality, we shall also call attention to finite-dimensional versions of the results whenever these happen to differ from their infinitedimensional counterparts.…”

Iterative Noise Reduction in Digital Holographic Microscopy

“…However, if DHM is used to study microscopic samples of large BW, the isolation of the object field component, in the hologram, cannot be realized by this simple spatial filtering procedure. In this case, one of the useful procedures is to perform the elimination of non desired hologram components by iterative procedures (Fienup, 1987;Cederquist et al, 1989;Wu, 2004;Denis et al, 2005;Hwang-Han, 2007;Nakamura, 2007). In this chapter we describe an iterative method that effectively recovers the object field component from the recorded hologram, in both the LOADH and RLOADH setups.…”

Measurement range of phase retrieval in optical surface and wavefront metrology

“…A phaseretrieval algorithm iteratively searches for a phase estimate that defines an optical field that, when digitally propagated to the measurement planes, has intensity distributions in agreement with the measured intensities. The method has been successfully employed in the past for image recovery [1][2][3], wavefront sensing for adaptive optics [4], and for diagnosing the aberrations of the Hubble Space Telescope [5,6]. It will be used to align the segments of the James Webb Space Telescope [7].…”