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A speckle pattern is an 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. The term speckle pattern is also commonly used in the experimental mechanics community to describe the pattern of physical speckles on a surface which is useful for measuring displacement fields via digital image correlation. A speckle pattern is an 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. The term speckle pattern is also commonly used in the experimental mechanics community to describe the pattern of physical speckles on a surface which is useful for measuring displacement fields via digital image correlation. Speckle patterns typically occur in diffuse reflections of monochromatic light such as laser light. Such reflections may occur on materials such as paper, white paint, rough surfaces, or in media with a large number of scattering particles in space, such as airborne dust or in cloudy liquids. The speckle effect is a result of the interference of many waves of the same frequency, having different phases and amplitudes, 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. In the limit of many interfering waves the distribution of intensities (which go as the square of the vector's length) becomes exponential P ( I ) d I = 1 μ exp ( − I / μ ) d I {displaystyle P(I)dI={frac {1}{mu }}exp(-I/mu )dI} , where μ {displaystyle mu } is the mean intensity. 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.

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