Speckle pattern
From Wikipedia, the free encyclopedia
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.
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Occurrence in outer space
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 sunlight is 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.[1]
Explanation
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 path-length 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.[2]
Subjective 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
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 [3] 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.
Near-field speckles
Objective speckles are usually obtained in the far field (also called Fraunhofer region, thatis the zone where Fraunhofer diffraction happens). This means that they are generated "far" from the object that emits or scatters light. Speckles can be observed also close to thescattering object, in the near field (also called Fresnel region, that is, the region where Fresnel diffraction happens). This kind of speckles are called Near Field Speckles. See near and far field for a more rigorous definition of "near" and "far".
The statistical properties of a far-field speckle pattern (i.e., the speckle form and dimension)depend on the form and dimension of the region hit by laser light.By contrast, a very interesting feature of near field speckles is thattheir statistical properties are closely related to the form and structure of the scattering object:objects that scatter at high angles generate small near field speckles, and vice versa.Under Rayleigh-Gans condition, in particular, speckle dimension mirrors the average dimensionof the scattering objects, while, in general, the statistical properties of near fieldspeckles generated by a sampledepend on the light scattering distribution. [4] [5]
Actually, the condition under which the near field speckles appear has beendescribed as more strict than the usual Fresnel condition: see[6]
Applications
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 in optical heterodyne detection.
In the case of near field speckles, the statistical properties depend on the light scatteringdistribution of a given sample. This allows to use the near field speckles analysisas a way to detect the scattering distribution; this is the so-called near-field scatteringtechnique [7].
Reduction
Speckle is considered to be a problem in laser based display systems like the Laser TV. Speckle is usually quantified by the speckle contrast. Speckle contrast reduction is essentially the creation of many independent speckle patterns, so that they average out on the retina/detector. This can be achieved by, [8]
- Angle diversity: Illumination from different angles.
- Polarization diversity: Use of different polarization states.
- Wavelength diversity: Use of laser sources which differs in wavelength by a small amount.
Rotating diffusers which destroys the spatial coherence of the laser light can also be used to reduce the speckle. Moving/vibrating screens may also be solutions. The Mitsubishi Laser TV appears to use such a screen which requires special care according to their product manual.
Synthetic array heterodyne detection was developed to reduce speckle noise in coherent optical imaging and coherent DIAL LIDAR.
References
- ^ This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188).
- ^ McKechnie, T.S. 1976. Image-plane speckle in partially coherent illumination. Optical and Quantum Electronics 8:61-67.
- ^ Dainty C (Ed), Laser Speckle and Related Phenomena, 1984, Sprinter Verlag, ISBN 0387131698
- ^ M. Giglio, M. Carpineti and A. Vailati, 2000, Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function
",Phys. Rev. Lett. 85: 1416--1419 - ^ M. Giglio, M. Carpineti, A. Vailati and D. Brogioli, 2001,Near-field intensity correlations of scattered light, Appl. Opt. 40: 4036
- ^ R. Cerbino, Correlations of light in the deep Fresnel region: an extended van Cittert and Zernike theorem, Phys. Rev. A 75 5: 53815-1-4
- ^ D. Brogioli, A. Vailati and M. Giglio, 2002,Heterodyne near-field scattering,Appl. Phys. Lett. 81 22: 4109
- ^ Jahja I. Trisnadi, 2002. Speckle contrast reduction in laser projection displays. Proc. SPIE Vol. 4657, p. 131-137, Projection Displays VIII.
See also
External links
- Seeing speckle in your fingernail
- Research group on light scattering and photonic materials
- Ph. D. thesis: D. Brogioli, "Near Field Speckles"
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