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The images acquired by means of coherent radiation have a speckled-like appearance caused by random intensity distribution which is formed when the incident waves are either reflected from a rough surface or propagate through a transmission medium with random refractive index fluctuations. Although we are concerned with the speckle fields generated when laser light is scattered, it should be mentioned that closely related phenomena arise also in other regions of the electromagnetic spectrum: synthetic aperture radar imagery, scattering of x rays by liquids, and also for particles like electron scattering by amorphous carbon films. We should not omit the occurrence of the phenomenon in ultrasound imagery. The speckle in images was regarded first as an adverse side effect of the coherency, but later it was found that the speckle process itself is carrying useful information. Now, contributions to the study of speckle patterns are related to the following main areas: fundamental statistical properties, reducing speckle in radar, optical and holographic systems, measurement of surface roughness, applications in information processing using random carriers, applications in metrology and stellar speckle interferometry. The readers interested in a far deeper mathematical understanding of the properties of electromagnetic fields scattered by rough surfaces are suggested to consult the standard reference in this field, Beckman and Spizzichino. This paper presents a qualitative model-based approach to the study of coherent- light imagery systems, relying on Fourier analysis applied to complex speckle fields. The model includes the effect of the object roughness, the free space propagation, the optical system, and the image acquisition and processing system, and generates synthetic images simulating the behavior of the real system. The model was used to describe a time-averaging electronic speckle pattern interferometer (ESPI) system for mechanical vibrations analysis, developed by the authors at The Polytechnic Institute of Bucharest in collaboration with The Laboratory for Laser Developments, The Atomic Physics Institute of Bucharest.
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