Speckle pattern

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Laser speckle on a digital camera image from a green laser pointer.

A speckle pattern is a random intensity pattern produced by the mutual interference of coherent wavefronts that are subject to phase differences and/or intensity fluctuations. Prominent examples include the seemingly random pattern created when a coherent laser beam is reflected off a rough surface, and the highly magnified image of a star through imperfect optics or through the atmosphere (see speckle imaging). Each point in the intensity pattern is a superposition of each point of the rough surface contributing with a random phase due to path length differences. If the surface is rough enough to create pathlength differences exceeding a wavelength, the statistics of the speckle field will correspond to a random walk in the complex plane. If the contributions are large, corresponding to a large illuminated surface, the field will follow a circular complex distribution, where both the real and imaginary parts are normally distributed with a zero expected value and the same standard deviations. Furthermore, the real and imaginary parts are uncorrelated. This gives a negative exponential distribution for the intensity. This is the root of the classic speckle appearance—mainly dark areas with bright islands.

The spatial distribution of the speckle is dependent upon the viewing angle. Large angle gives a small autocorrelation function and small angle gives a large coarse with larger viewing distance.

In the output of a multimode optical fiber, a speckle pattern results from a superposition of mode field patterns. If the relative modal group velocities change with time, the speckle pattern will also change with time. If differential mode attenuation occurs, modal noise results.

[edit] Speckle technique

An object with a rough surface, when illuminated with light from laser, exhibits a speckled appearance. This salt-and-peppery appearance is not observed when the object is illuminated with ordinary light. The formation of such a speckle pattern is due to the high coherence of the laser light. Since variations in the surface are greater than the wavelength, coherent light scattered by the individual elements of the surface interferes to form a stationary pattern. The speckle pattern appears to scintillate or sparkle when there is any relative movement of the surface and the observer.

Though the observations of this phenomenon extend over nearly a century, speckles came into prominence only after the invention of the laser. The speckle phenomena also have analogues in other fields; examples are the reflection of radio waves from rough surfaces such as the ground, and ultrasonic imaging etc. The speckle pattern was initially considered the bane of holographers as holographic reconstructions were accompanied by grainy noise. It was later realized that these speckle patterns could carry information about the object's surface deformations, and that speckled wave fronts could interfere. The speckle pattern formed in the space due to self-interference among the propagating scattered waves is called “objective speckles”. The speckle pattern formed by imaging a diffuse object illuminated by a coherent beam is called a “subjective speckle pattern”.