Wave-front phase estimation from Fourier intensity measurements

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. 1