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Journal ArticleDOI

Dynamic statistical properties of laser speckle due to longitudinal motion of a diffuse object under Gaussian beam illumination

01 Jul 1980-Journal of the Optical Society of America (Optical Society of America)-Vol. 70, Iss: 7, pp 827-834
TL;DR: In this article, the authors investigated the statistical properties of laser speckle produced in the far-field diffraction region from a diffuse object moving longitudinally along the optical axis under illumination of a Gaussian beam.
Abstract: The dynamic statistical properties of laser speckle produced in the far-field diffraction region from a diffuse object moving longitudinally along the optical axis under illumination of a Gaussian beam are investigated theoretically and experimentally. Although the spatial structure of speckle patterns varies in time owing to the longitudinal motion of the object, the time-varying speckle intensity detected at the center of the far-field diffraction plane is found to follow a statistically stationary variation. The autocorrelation function and power spectral density of the speckle intensity variations are studied with relation to the illuminating condition of the Gaussian beam.
Citations
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01 Jan 1981
TL;DR: In this paper, the statistical properties of dynamic speckles produced in the diffraction and image fields by the diffuse object moving in a plane with constant velocity are examined in detail, and two typical speckle motions of translation and boiling are interpreted for various optical configurations in the Diffraction and Image Fields.
Abstract: In connection with the parameters of the optical configuration used to produce speckles and under illumination of a Gaussian beam over a moving diffuse object, this paper discusses the statistical properties of dynamic speckles produced in the diffraction and image fields by the diffuse object moving in a plane with constant velocity. Especially, the space-time correlation function of the dynamic speckle intensity is examined in detail. Two typical speckle motions of translation and boiling are interpreted for various optical configurations in the diffraction and image fields. As one of the interesting applications of dynamic speckles to metrology, various methods for velocity measurements of the diffuse object are introduced.

197 citations

Journal ArticleDOI
TL;DR: In this article, the statistical properties of dynamic speckles produced in the diffraction and image fields by the diffuse object moving in a plane with constant velocity are examined in detail, and two typical speckle motions of translation and boiling are interpreted for various optical configurations in the Diffraction and Image Fields.
Abstract: In connection with the parameters of the optical configuration used to produce speckles and under illumination of a Gaussian beam over a moving diffuse object, this paper discusses the statistical properties of dynamic speckles produced in the diffraction and image fields by the diffuse object moving in a plane with constant velocity. Especially, the space-time correlation function of the dynamic speckle intensity is examined in detail. Two typical speckle motions of translation and boiling are interpreted for various optical configurations in the diffraction and image fields. As one of the interesting applications of dynamic speckles to metrology, various methods for velocity measurements of the diffuse object are introduced.

186 citations

Patent
23 Mar 2009
TL;DR: In this article, a surface sensing apparatus, one embodiment having a source of coherent radiation capable of outputting wavelength emissions to create a first illumination state to illuminate a surface and creating a first speckle pattern, an emission deviation facility capable of influencing the emission to illuminate the surface and create a second illumination state and a second pattern.
Abstract: Disclosed is a surface sensing apparatus, one embodiment having a source of coherent radiation capable of outputting wavelength emissions to create a first illumination state to illuminate a surface and create a first speckle pattern, an emission deviation facility capable of influencing the emission to illuminate the surface and create a second illumination state and a second speckle pattern, and a sensor capable of sensing a representation of the first and a second speckle intensity from the first and second speckle pattern. Also disclosed are methods of sensing properties of the surface, one embodiment comprising the steps of illuminating the surface having a first surface state with the source of coherent radiation emission, sensing a first speckle intensity from the surface, influencing a relationship of the surface to the emission to create a second surface state and sensing a second speckle intensity from the surface at the second surface state.

118 citations

Book ChapterDOI
TL;DR: In this article, the statistical properties of dynamic speckle patterns produced by moving diffuse objects are discussed and the spatial and temporal integration of intensity and the surface roughness dependence are also considered.
Abstract: Publisher Summary This chapter discusses the statistics of dynamic speckles. Dynamic speckle arises as a consequence of interference of the waves that are scattered from diffuse objects in motion or random media undergoing the temporal change of their structures. The chapter discusses the statistical properties of dynamic speckle patterns produced by moving diffuse objects. The fundamental properties of dynamic speckles formed in the free-space and imaging geometries are described. The spatial and temporal integration of intensity and the surface-roughness dependence are also considered. The chapter focuses on the speckles arising from various types of the object motion and also discusses the differences of their temporal behaviors. The effect of the wavelength distribution of the incident light on resultant intensity fluctuations is considered. The speckled-speckle patterns produced by illuminating a moving diffuser with static and dynamic speckle patterns are also discussed. Some salient features of doubly-scattered speckle patterns, as distinct from singly-scattered normal speckles are presented.

41 citations

Journal ArticleDOI
TL;DR: In this paper, an optical method for detection of in-plane movement of a diffusing object is presented, based on spatial filtering of the laser speckle pattern, which is produced by illumination of the object with coherent light.
Abstract: We present an optical method for detection of in-plane movement of a diffusing object. The technique is based on spatial filtering of the laser speckle pattern, which is produced by illumination of the object with coherent light. Two interlaced differential comb photodetector arrays act as a periodic filter to the spatial-frequency spectrum of the speckle pattern intensity. The detector produces a zero-offset, periodic output signal versus displacement that permits measurement of the movement at arbitrarily low speed. The direction of the movement can be detected with the help of the quadrature signal, which is produced by a second pair of interlaced comb photodetector arrays. When speckle size and period of the comb photodetector arrays are matched, the output signal versus displacement is quasi-sinusoidal with statistical amplitude and phase. First- and second-order statistics of the signal are investigated. First the probability density function and the autocorrelation function of the complex Fourier transform of the speckle pattern intensity are determined. Then the statistical properties of the spectrum of the filtered signal and of the signal itself are calculated. It turns out that the amplitude of the signal is Rayleigh distributed. Both the autocorrelation function of the signal and the probability density function of the measured phase difference for a given displacement are calculated. The potential accuracy of displacement measurements is analyzed. In addition, the signal quality is investigated with respect to the geometry of the detector. The theoretical results are experimentally verified.

37 citations

References
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ReportDOI
01 Dec 1963
TL;DR: In this article, the first order statistics of the observed electric-field strength, the observed light intensity, and observed light phase are examined, and the autocorrelation functions of the complex field and intensity processes are investigated, and that of the electric field is found to be proportional to the Fourier transform of the light intensity distribution incident on the scattering surface.
Abstract: : When laser light strikes a diffuse object, such as paper, the scattered light has been observed to possess a granular spatial structure. The statistical properties of these so-called 'sparkle patterns,' as seen by an observer in the far field of the scattering spot, are investigated. The first order statistics of the observed electric-field strength, the observed light intensity, and the observed light phase are examined. The electric field is reasoned to be a complex normal random variable; the intensity a real, exponentially distributed random variable; and the phase a uniformly distributed random variable. Higher order statistics of these random processes are also discussed. The autocorrelation functions of the complex field and the intensity processes are investigated, and that of the electric field is found to be proportional to the Fourier transform of the light-intensity distribution incident on the scattering surface. Spatial averages of the light intensity are considered and are found to converge to corresponding ensemble averages when either the area of the scattering spot or the average area grows large.

1,526 citations

Book ChapterDOI
01 Jan 1975
TL;DR: In this article, the first-order statistics of the complex amplitude, intensity and phase of speckle are derived for a free-space propagation geometry and for an imaging geometry.
Abstract: Since speckle plays an important role in many physical phenomena, it is essential to fully understand its statistical properties. Starting from the basic idea of a random walk in the complex plane, we derive the first-order statistics of the complex amplitude, intensity and phase of speckle. Sums of speckle patterns are also considered, the addition being either on an amplitude or on an intensity basis, with partially polarized speckle being a special case. Next we consider the sum of a speckle pattern and a coherent background, deriving the first-order probability density functions of intensity and phase. Attention is then turned to second-order statistics. The autocorrelation function and power spectral density are derived, both for a free-space propagation geometry and for an imaging geometry. In some cases the recorded speckle pattern may be spatially integrated or blurred, and accordingly consideration is given to the statistics of such patterns. Finally, the relationship between detailed surface structure and the resulting speckle pattern is explored, with emphasis on the effects of the surface autocorrelation function and the effects of finite surface roughness.

1,217 citations

Book ChapterDOI
TL;DR: The statistical properties of a speckle pattern depend, in general, on both the coherence of the incident light and the statistics of the scattering surface or medium as discussed by the authors, and it was found that the value of the r.m.s. height variation of a scattering surface strongly influenced the statistical properties, even for surfaces with a Gaussian distribution of surface heights.
Abstract: Publisher Summary This chapter discusses the statistics of speckle patterns. The statistical properties of a speckle pattern depend, in general, on both the coherence of the incident light and the statistics of the scattering surface or medium. In a large number of practical situations normal speckle patterns are produced; the statistics of these speckle patterns are well-established both theoretically and experimentally, and in particular, they do not depend on the detailed scattering properties of the scattering medium. When examining the effects of polychromatic illumination on speckle statistics, it was found that the value of the r.m.s. height variation of a scattering surface strongly influenced the statistical properties of the scattered intensity. In addition, the chapter shows that the general relationship between the scattered intensity and the scattering surface may be very complicated, even for surfaces with a Gaussian distribution of surface heights.

136 citations

Journal ArticleDOI
TL;DR: In this paper, the Bose-Einstein properties of a light beam scattered by a rotating ground glass with average-size inhomogeneities of approximately 1 μm were investigated.
Abstract: We report some experimental results concerning the statistical properties of a light beam scattered by a rotating ground glass with average-size inhomogeneities of approximately 1 μm. Photocount statistics measured at different scattering angles and for different angular velocities of the ground glass have confirmed the known result that the scattered-light amplitude is a stochastic gaussian variable. The Bose–Einstein nature of the photocount statistics has been verified with an accuracy of a few parts per thousand. Self-beating measurements on the scattered light of a He–Ne laser in a TEM00 configuration have shown that the power spectrum is a gaussian function of the frequency. The dependence of its half-width on the angular velocity of the ground glass and on the focal length of the lens that focuses the beam on the scattering surface has been measured. The experimental results agree very closely with our theoretical predictions.

111 citations

Journal ArticleDOI
TL;DR: In this paper, a new method for measuring the in-plane velocity of a moving diffuse object by using the technique of zero-crossings for the intensity fluctuation of spatially integrated laser speckles is proposed.
Abstract: This paper proposes a new method for measuring the in-plane velocity of a moving diffuse object by using the technique of zero-crossings for the intensity fluctuation of spatially integrated laser speckles The scattered speckle pattern is detected in the diffraction field by a finite-aperture photodetector whose output current is analyzed, after removal of its dc component, by counting zero-crossings The number of zero-crossings per second for the signal is investigated theoretically and found to depend linearly on the object’s velocity The theoretical results are confirmed experimentally for translational speckles detected by the photodetector having circular apertures of various sizes The excellent agreement between theoretical and experimental results shows that the new method allows measurement of the velocity of a moving object in real time with good accuracy

67 citations