Digital holography: 30 years later

Digital holography is analysis, synthesis and simulation of wave fields by means of digital computers and processors. Since first publications in digital holography, more then 30 years have passed. From then on, the ideas of digital holography formulated at that time has found quite a number of applications and implementations. But not all of them Some old dreams such as that of holographic television, display and virtual reality still have not come true and some results and methods were left on the roadside. In the paper, a brief review of digital holography is presented and some "roadside" subjects such as discrete representation of optical transforms and Monte Carlo methods for synthesis of computer generated display holograms and studying speckle noise in coherent imaging systems are revisited. In particular, it is shown (i) how, by an appropriate selection of a "virtual" pseudo-random diffuser, one can generate Fourier holograms of 3-D objects that can reconstruct their images from different observation directions and (ii) how such distortions in measuring diffusely scattered wave fields (holograms) for computer reconstruction as limitation of the hologram size, limitation of its dynamic range and quantization affect speckle contrast in reconstructed images.