Wavefront reconstruction with defocus and transverse shift estimation using Kalman filtering

Many wavefront reconstruction techniques estimate the amplitude and phase from multiple intensity measurements. One can generate phase diversity among these intensity measurements by varying certain parameters in the optical system. These parameters are subject to noise and disturbances, which might strongly degrade the accuracy of the reconstruction. In this paper we present the use of stochastic filtering techniques to estimate the system variables in a multiple-image phase retrieval framework. An iterated extended Kalman filter is shown to effectively reduce the normalized mean-square-error of the reconstructed wavefront by estimating the defocus and transverse shifts of a moving camera in simulation. Experiments are conducted using two different test objects, and the results clearly demonstrate the enhancement of detail and contrast of the wavefront when using the filter. A quadratic phase introduced by a convex lens is used with a binary mask as one of the test objects. The focal length estimated from the unwrapped phase agrees with the ( ± 1% tolerance) value provided by the manufacturer.