Abstract

We discuss the problem of specifying and reconstructing 3-D objects using electromagnetic fields. This problem is of interest in volume holographic optical information processing and in 3-D imaging systems such as synthetic aperture radars. In systems, such as optical neural computers, which make efficient use of large scale holographic transformations, volume holographic optical elements offer the potential for information storage at very high spatial densities. To realize this potential it is necessary to overcome the bottleneck on the recording and reconstruction of volume holograms created by the limited space–bandwidth product of the entrance aperture of a volume medium. Only N² of the N³ degrees of freedom of the volume may be recorded or read out by a single monochromatic exposure. In general, at least N monochromatic exposures are necessary to specify or reconstruct fully a volume hologram. Under polychromatic illumination, a volume hologram may be recorded in a single exposure if the recording beam contains at least N independently controllable frequency components. By decomposing the 3-D field into the eigenfunctions of an imaging system we demonstrate specific limitations on the recording and reconstruction of 3-D information using optical fields. We present a method for writing volume holograms based on eigenmode decomposition of the desired field. Finally, we discuss the amount of information needed to reconstruct targets with fractal dimension between 2 and 3.

© 1988 Optical Society of America