Speckle pattern

A speckle pattern is a random intensity pattern produced by the mutual interference of a set of wavefronts. This phenomenon has been investigated by scientists since the time of Newton, but speckles have come into prominence since the invention of the laser and have now found a variety of applications.

Where speckle occurs

A familiar example is the random pattern created when a laser beam is scattered off a rough surface - see picture. A less familiar example of speckle is the highly magnified image of a star through imperfect optics or through the atmosphere (see speckle imaging). A speckle pattern can also be seen when you look at sunlight scattered by a fingernail.

The speckle effect is observed when radio waves are scattered from rough surfaces such as ground or sea, and can also be found in ultrasonic imaging. 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.

How speckle occurs

The speckle effect is a result of the interference of many waves, having different phases, which add together to give a resultant wave whose amplitude, and therefore intensity, varies randomly. If each wave is modelled by a vector, then it can be seen that if a number of vectors with random angles are added together, the length of the resulting vector can be anything from zero to the sum of the individual vector lengths—a 2-dimensional random walk, sometimes known as a drunkard's walk.

When a surface is illuminated by a light wave, according to diffraction theory, each point on an illuminated surface acts as a source of secondary spherical waves. The light at any point in the scattered light field is made up of waves which have been scattered from each point on the illuminated surface. If the surface is rough enough to create pathlength differences exceeding one wavelength, giving rise to phase changes greater than 2π, the amplitude, and hence the intensity, of the resultant light varies randomly.

If light of low coherence (i.e. made up of many wavelengths) is used, a speckle pattern will not normally be observed, because the speckle patterns produced by individual wavelengths have different dimensions and will normally average one another out. However, speckle patterns can be observed in polychromatic light in some conditions. [McKechnie, T.S. 1976. Image-plane speckle in partially coherent illumination. Optical and Quantum Electronics 8:61-67.]

ubjective speckles

When an image is formed of a rough surface which is illuminated by a coherent light (e.g. a laser beam), a speckle pattern is observed in the image plane; this is called a “subjective speckle pattern” - see image above. It is called "subjective" because the detailed structure of the speckle pattern depends on the viewing system parameters; for instance, if the size of the lens aperture changes, the size of the speckles change. If the position of the imaging system is altered, the pattern will gradually change and will eventually be unrelated to the original speckle pattern.

This can be explained as follows. Each point in the image can be considered to be illuminated by a finite area in the object. The size of this area is determined by the diffraction-limited resolution of the lens which is given by the Airy disk whose diameter is 2.4λu/D where u is distance between the object and the lens, and D is the diameter of the lens aperture. (This is a simplified model of diffraction-limited imaging).

The light at neighbouring points in the image has been scattered from areas which have many points in common and the intensity of two such points will not differ much. However, two points in the image which are illuminated by areas in the object which are separated by the diameter of the Airy disk, have light intensities which are unrelated. This corresponds to a distance in the image of 2.4λv/D where v is the distance between the lens and the image. Thus, the ‘size’ of the speckles in the image is of this order.

The change in speckle size with lens aperture can be observed by looking at a laser spot on a wall directly, and then through a very small hole. The speckles will be seen to increase significantly in size.

Objective speckles

When laser light which has been scattered off a rough surface falls on another surface, it forms an “objective speckle pattern”. If a photographic plate or another 2d optical sensor is located within the scattered light field without a lens, a speckle pattern is obtained whose characteristics depend on the geometry of the system and the wavelength of the laser. The speckle pattern in the figure was obtained by pointing a laser beam at the surface of a mobile phone so that the scattered light fell onto an adjacent wall. A photograph was then taken of the speckle pattern formed on the wall (strictly speaking, this also has a second subjective speckle pattern but its dimensions are much smaller than the objective pattern so is not seen in the image) The light at a given point in the speckle pattern is made up of contributions from the whole of the scattering surface. The relative phases of these waves vary across the surface, so that the sum of the individual waves varies randomly. The pattern is the same regardless of how it is imaged, just as if it were a painted pattern.

The "size" of the speckles is a function of the wavelength of the light, the size of the laser beam which illuminates the first surface, and the distance between this surface and the surface where the speckle pattern is formed. This is the case because when the angle of scattering changes such that the relative path difference between light scattered from the centre of the illuminated area compared with light scattered from the edge of the illuminated changes by λ, the intensity becomes uncorrelated. Dainty [Dainty C (Ed), Laser Speckle and Related Phenomena, 1984, Sprinter Verlag, ISBN 0387131698] derives an expression for the mean speckle size as λz/L where L is the width of the illuminated area and z is the distance between the object and the location of the speckle pattern.

Applications of Speckle

When lasers were first invented, the speckle effect was considered to be a severe drawback in using lasers to illuminate objects, particularly in holographic imaging because of the grainy image produced. It was later realized that speckle patterns could carry information about the object's surface deformations, and this effect is exploited in holographic interferometry and electronic speckle pattern interferometry. The speckle effect is also used in stellar speckle astronomy, speckle imaging and in eye testing using speckle.

Speckle is the chief limitation of coherent imaging and Optical heterodyne detection.


External links

* [http://www.sciencenewsforkids.org/pages/puzzlezone/muse/muse0705.asp/ Seeing speckle in your fingernail]
* [http://luxrerum.icmm.csic.es/?q=node/research/interference/ Research group on light scattering and photonic materials]

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