The main purpose of this article is to develop a program package which generates artificial holograms by numerical methods and these computer generated holograms are numerically reconstructed. For the calculation of light propagation needed in the generation of holograms or in the reconstruction of the object from the hologram, we use two strategies. The first is the Fourier-based algorithm where the diffraction integral is approximated as a convolution integral, allowing computation using the fast Fourier transform algorithm. The second uses finite difference discretization to solve the parabolic wave equation. Numerical tests that assess the accuracy of these algorithms are presented. © 2012 American Institute of Physics.