Optimal reconstruction algorithm for holographic imaging of finite-size objects

Abstract

This paper introduces the formulation of the optimal image reconstruction algorithm for finite-size objects. For practical data acquisition and computation considerations, the partial discrete (continuous–discrete) model is used for the formulation. The basic constraints utilized in this optimization process are the finite size of the object and the limited spatial-frequency bandwidth of the resultant wave field. The result indicates that the algorithm consists of a linear matrix transformation followed by backward propagation. It is also shown that the bandlimited wave field extrapolation method and backward propagation technique are degenerate cases of this optimal algorithm. In addition to image reconstruction, the formulation of this optimal algorithm can be used to determine the optimal wave field sampling for efficient data acquisition.