Precision influence of a phase retrieval algorithm in fractional Fourier domains from position measurement error

An iterative structure of amplitude-phase retrieval (APR) was proved to obtain more accurate reconstructed data of both amplitude and phase. However, there is not enough analysis of the precise influence from position measurement error and corresponding error correction. We apply the APR in fractional Fourier domains to reconstruct a sample image and describe the corresponding optical implementation. The error model is built to discuss the distribution of the position measurement error. A corrective method is applied to amend the error and obtain a better quality of retrieved image. The numerical results have demonstrated that our methods are feasible and useful to correct the error for various circumstances.