Discrete calculation of the off-axis angular spectrum based light propagation

Light propagation in a free space is a common computational task in many computer generated holography algorithms. A solution based on the angular spectrum decomposition is used frequently. However, its correct off-axis numerical implementation is not straightforward. It is shown that for long distance propagation it is necessary to use digital low-pass filtering for transfer function calculation in order to restrict source area illumination to a finite area. It is also shown that for short distance propagation it is necessary to introduce frequency bands folding in transfer function calculation in order to simulate finite source area propagation. In both cases it is necessary to define properly interpolation filters that reconstruct continuous nature of the source area out of its sampled representation. It is also necessary to zero-pad properly source area sampling in order to avoid artifacts that stem from the periodic nature of the fast Fourier transform.