Bessel functions-based reconstruction of non-uniformly sampled diffraction fields

A discrete computational model for the diffraction process is essential in forward problems related to holographic TV. The model must be as general as possible, since the shape of the displayed objects does not bear any restrictions. We derive a discrete diffraction model which suits the problem of reconstruction of diffraction fields from a set of non-uniformly distributed samples. The only restriction of the model is the wave nature of the field. The derivation takes advantage of changing the spatial and frequency coordinates to polar form and ends up with a model stated in terms of Bessel functions. The model proves to be a separable orthogonal basis. It shows rapid convergence when evaluated in the framework of the non-uniform sampling problem.