Minimum - pixel holograms

Canonical minimal-pixel hologram geometries are presented in the context of a generalized image relay system. We illustrate that the number of pixels ultimately depends only on the physical parameters of the displayed image (the Smith-Lagrange optical invariant). Various choices of synthetic optical geometries lead to pixel aspect ratios that are found to be good matches to available display technologies. We explore geometries in which the spatial light modulator is imaged at either the imageplane or the viewer-plane, or astigmatically imaged to both at the same time. This increases the variety of candidate aspect ratios considerably, and brings us closer to a workable match with foreseeable optical technologies that will make holographic video a practical reality. 1.INTRODUCTION The problem of synthesizing free-standing spatial images has occupied the thoughts of researchers for over one and a half centuries. When optical holography was invented by Denis Gabor in 1949, it was thought that a satisfactory solution to the problem of creating autostereoscopic images was finally found. However, holography has several limitations that keep it from being a viable medium for the routine presentation of 3-D images. It seemed that the price that one had to pay for being able to see realistic three-dimensional images was to produce and view them under severely restricting conditions. Most of the restrictions arose from the use of coherent light to record and reconstruct the image. In 1965, inspired by the work of Kozma and Kelly1, Brown and Lohmann2 realized that holograms could be synthesized using computers by modeling the process by which optical holograms were recorded. A computer-generated hologram (CGH) may be defined as a numerical representation of an interference pattern. Once the physics of holography was known, it was a simple matter to produce CGHs. Some of the earliest CGHs were complex amplitude masks with applications in spatial filtering. The extension to computed display holograms is conceptually straightforward. However, simple calculations by Leith and his colleagues in 1965 showed that it would be impossible to compute display holograms because of the enormous number of samples involved. The possibility of producing CGHs that could be transmitted and reconstructed optically at a remote location in real-time was ruled out. Recently, the Spatial Imaging Group at MIT reported the successful implementation of a system that could display a computer-generated holographic image in real-time. The engineering and computational