The Effect of Uncertainty in Defocus Distance on the Wave-frontReconstruction with the Phase-diversity Algorithm

The phase-diversity algorithm is a wave-front sensing technique for obtaining estimates of both the precise object image and the distribution of wave fronts.It involves the simultaneous collection of a pair of short-exposure images:one is the typical focal-plane image and the other is the aberrated image on a defocused plane(with known aberration functions and aberration scales there).With these images, one can use the optimization theory to minimize the cost function to recover the precise image of object as well as the phase aberration.In this paper, based on the phase-diversity algorithm, we numerically simulate the intensity distributions of the focal-plane image and aberrated image under the circumstances that the uncertainty of the aberration function is due to defocus.We further implement the wave-front reconstruction and image recovery of the simulated extended scenes(object)by applying a limited-memory BFGS method to deal with the optimization problem.Owing to the errors in measurement and mechanical manufacturing, the uncertainty in defocus distance is practically inevitable.So in the simulation of this paper, we study and analyze the effect of such an uncertainty on the wave-front reconstruction with the phase-diversity algorithm.