We propose a method for diffraction simulation with both shifted destination window and a large oblique illumination. Based on the angular spectrum theory, we first derive a generalized transfer function (GTF) and a generalized point-spread function (GSPF) suitable for free-space diffraction simulation when both a shifted destination window and a large oblique illumination are taken into account. Then we analyze the sampling error caused by sampling of the GTF and the GSPF for numerical simulation based on fast Fourier transform (FFT), and find out an analytical formula for determining a criteria distance of Zc. Theoretical analysis and simulation results prove that the FFT-based GTF sampling algorithm is valid for diffraction simulation with a diffraction distance less than or equal to Zc, while the FFT-based GSPF sampling is only suitable for the simulation with a distance larger than or equal to Zc. Based on theoretical analysis, we propose the hybrid GTF-GSPF algorithm suitable for simulation of both near- and far-field diffractions with shifted destination window and large oblique source illumination at the same time. Finally, some simulation results are given to verify the feasibility of the algorithm.

A method for fast reconstruction of off-axis digital holograms based on digital multiplexing algorithm is proposed. Instead of the existed angular multiplexing (AM), the new method utilizes a spatial multiplexing (SM) algorithm, in which four off-axis holograms recorded in sequence are synthesized into one SM function through multiplying each hologram with a tilted plane wave and then adding them up. In comparison with the conventional methods, the SM algorithm simplifies two-dimensional (2-D) Fourier transforms (FTs) of four N*N arrays into a 1.25-D FTs of one N*N arrays. Experimental results demonstrate that, using the SM algorithm, the computational efficiency can be improved and the reconstructed wavefronts keep the same quality as those retrieved based on the existed AM method. This algorithm may be useful in design of a fast preview system of dynamic wavefront imaging in digital holography.

A simple noniterative algorithm for retrieval of the unknown phase shifts in phase-shifting holography is proposed. In this algorithm, the phase shift value between two phase-shifting holograms can be calculated through a simple analytical formula that is derived according to the fact that there exist some points whose intensity difference between two phase-shifting holograms is equal to zero. Both the simulated and experimental results demonstrated the feasibility of this so-called zero difference algorithm over a wide range of phase shifts.

A phase derivative (PD) method is proposed for reconstruction of off-axis holograms. In this method, a phase distribution of the tested object wave constrained within 0 to pi radian is firstly worked out by a simple analytical formula; then it is corrected to its right range from -pi to pi according to the sign characteristics of its first-order derivative. A theoretical analysis indicates that this PD method is particularly suitable for reconstruction of slightly off-axis holograms because it only requires the spatial frequency of the reference beam larger than spatial frequency of the tested object wave in principle. In addition, because the PD method belongs to a pure local method with no need of any integral operation or phase shifting algorithm in process of the phase retrieval, it could have some advantages in reducing computer load and memory requirements to the image processing system. Some experimental results are given to demonstrate the feasibility of the method.

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