holography and optical processing with

redundancy

emmett n.leith

the university of michigan, u.s.a.

the laser offers significant advantages for holography and optical processing. however, the extreme coherence of the laser presents problems. Imagery format with coherent light is quite noisy. the noise effects may, in practice, be divided into two categories, although in principle they are not fundamentally different. the first is the artifact problem, in which isol ted scattering centers, such as scratches in lens surfaces, or dust particles, produce diffraction patterns which persist and contaminate the Image. the second problem is the well-known laser speckle.

both problems may be avoided, while yet retaining the coherence needed for optical processing or holography, by introducing redundancy into the system. there are numerous ways achieving this result; come methods are sophisticated, others less so. the objective is to obtain the maximum benefits with the minimum redundancy, since this comes with considerable sacrifice.

the most basic technique is to employ a diffuser, but with an imaging system of much lower f-number than is required for the resolution which is to be attained. the diffuser eliminates the artifact noise, and the speckles will be beyond the resolution of the final detector. this and other related methods may be described in a unifying way by stating that we have broadaned the spatial-frequency bandwidth of the signal and thus increased its immunity to noise.

this method is inefficient, since the increase in spatial frequency bandwidth to achieve a specified level of noise sup-

pression is very great. we must seek other, more efficient, ways to produce the desired results.

we may, for example, design diffusers in some special way, so that they attain the desired result without the tremendous increases in spatial-frequency bandwidth. one method is to use diffraction gratings, which broaden the spatial-frequency spectrum in a non-random manner. such devices are much more efficient than random diffusers. in particular, by using the self-imaging properties of phase-gratings, the artifact noise may be suppressed without producing the speckle problem. another method, due to gabor, involves designing diffusers in accordance with pulse codes, in such a manner that the spatial variations of intensity in the fremel diffraction pattern are regular and of high-frequency periodicity. subsequent low-pass spatial-filtering of the Image gives a smooth, nearly noise-free Image. another technique involves designing pseudo-random diffusers whose diffraction patterns display a regularity in the sense that the field assumes specific values at specific sample points; the Image thus formed by the system may be sampled in these locations, and a noise-free Image produced from these samples.

other techniques involve reduction of the temporal or spatial coherence of the source. to utilize these methods, techniques must be developed so as to minimize the degrading effects of a loss of either type of coherence.

were coherent-illumination Imagery to be vastly improved so as to be comparable in quality to conventional, incoherent Imagery, the impact would be substantial. various applications of holography, particularly microscopy, would become highly useful. spatial filtering methods, particularly in the area of Image restoration, would become immensely more practical.