Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies

When a digital holographic reconstruction is performed, digital diffraction effects occur at the borders when the hologram amplitudes at the two opposite border points are different on each vertical or horizontal line. We propose a method of digital hologram extension to reduce such diffraction effects. The method consists of extending the size of the digital hologram and of filling the extended part by complex values that minimize, according to a numerical criterion, the highest spatial frequencies. The theoretical aspects of the method are given and the results from a demonstration are provided.