In all methods of photographic optical processing presented here, the carrier frequency is derived from an intensity speckle pattern, the advantage of which is to spread out information in the Fourier plane. Furthermore, they are based on the fact that the Fourier spectrum of two laterally translated speckle patterns displays Young’s fringes, the visibility of which represents the correlation of the speckle patterns. The problems of comparing intensities of two transparencies, multiplexing optical signals, and detecting small translations of a diffuse object will be successively considered. The optical process of comparing two transparencies <i>A</i> and <i>B</i> is the following. The two signals are modulated by the same speckle pattern and recorded successively on a photographic plate which is laterally translated between the exposures. After processing, <i>H</i> displays Young’s fringes at infinity. If the intensity distributions of <i>A</i> and <i>B</i> are not identical, the two corresponding speckle images are not completely correlated and therefore the fringe visibility is not maximum. The difference <i>A – B</i> can easily be obtained by filtering the minima of the fringes. For multiplexing operations, each of the signals to be stored is modulated by a speckle pattern and recorded atleast twice on a photographic plate which is laterally translated between successive exposures. The amount of translation given to the plate is different for each of the signals. The spectrum of the photographic record has as many fringe systems as the signals. By filtering the maxima of a particular fringe system, the corresponding signal is reconstructed and the others are removed. Small translations of a diffuse object can be detected by illuminating the object with a speckle pattern and recording its image before and after the motion in the same way as above. The decorrelation of the two recorded speckle patterns is only due to the motion of the object which can thus be revealed by visibility of the corresponding Young’s fringes. With such a method it is not possible to detect the direction of the translation suffered by the object. We suggest therefore an interferometer consisting of a Michelson interferometer in which both mirrors are replaced by two scattering surfaces <i>O</i><sub>1</sub> and <i>O</i><sub>2</sub> shifted longitudinally. The interferometer is illuminated by a parallel beam of laser light, and a photographic plate twice records (before and after the translation of one of the surfaces) irradiances lying in the Fourier plane of <i>O</i><sub>1</sub> and <i>O</i><sub>2</sub>. After processing, <i>H</i> exhibits Moiré fringes. These fringes are rectilinear if the translation suffered by the object is lateral and they are circular if the translation is longitudinal. The sensitivity of the interferometer depends only on the geometrical characteristics of the recording setup.
© 1976 Optical Society of America
Marie May and Maurice Françon, "Correlation and information processing using speckles," J. Opt. Soc. Am. 66, 1275-1282 (1976)