Least-squares based inverse reconstruction of in-line digital holograms

We present a least-squares solution for the inverse problem in in-line digital holography which is based on a point source model. We demonstrate that by reformulating the reconstruction problem as an inverse problem and by integrating a contour gradient based auto-focus search algorithm into the reconstruction routine, a more fundamental solution for the inversion of a hologram can be attained. With this approach the inversion can be calculated without any prior knowledge of the object's shape/size and without imposing any constraints on the imaging system. In a proof-of-concept study we show that our method facilitates a more accurate reconstruction, as compared to conventional methods, and that it facilitates object localization with an accuracy on the order of the optical wavelength.