Analysis of numerical reconstruction of lensless Fourier transform holograms

Based on the theory of recording lensless Fourier transform holograms and the structure of CCD, the numerical reconstruction of the under-sampled lensless Fourier transform holograms are studied with Fourier spectrum. An important conclusion is achieved: when the Shannon sampling condition is not fulfilled in recording the holograms, a objective with limited size can be still reconstructed. At the same time, the changed characteristics of the reconstructed images are analyzed. Experimental results show a good agreement with theoretical analysis.