Abstract

Interest in wavelength multiplexing in holography derives naturally from the need for realistic color rendition as well as from resolution requirements. Imaging in coherent illumination is compromised by speckle. Speckle is prejudicial to quality, sharpness, contrast—in a word, to the fidelity of reproduction or holographic reconstruction. In incoherent light these patterns are canceled by spatial phase averaging. Incoherent light can indeed be regarded as a superposition of a very large number of coherent components whose phase factors are distributed at random. It is demonstrated that the averaging effect, ultimately caused by the law of large numbers, is achieved by the superposition of only three components, thus allowing simultaneously a true color rendition and an improvement in spatial resolution. The spatial statistical behavior of the amplitude of the sum of three intrinsically coherent waves, when they are incoherently superposed in an imaging system, is investigated. A random variable representing the amplitude of this sum is introduced. Then the cumulative probability function and the probability density function of the resulting amplitude are calculated. The white-light (infinite-wave illumination) case and the purely coherent (one-wave) case are analyzed. The results are interpreted with a heuristic vector model.

© 1997 Optical Society of America

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