Statistical properties of laser speckles produced under illumination from a multimode optical fiber
01 Aug 1985-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 2, Iss: 8, pp 1282-1290
TL;DR: In this article, the authors studied the statistical properties of both speckle patterns incident upon and emerging from a diffuse object under illumination of the laser light generated from a multimode optical fiber.
Abstract: In this paper we study the statistical properties of both speckle patterns incident upon and emerging from a diffuse object under illumination of the laser light generated from a multimode optical fiber. The speckle field resulting from the modal noise at the exit face of the optical fiber is treated as a quasi-homogeneous monochromatic source that describes the quasi-stationary state within a finite region and, simultaneously, has the correlation coefficient that remains to be strictly stationary. The speckle pattern at the object plane in the Fresnel-diffraction field is first investigated by analyzing the propagation of the correlation function of the optical fields emerging from the source and found also to be quasi-homogeneous. Next, the correlation function of the optical field produced at the observation plane by scattering from a moving diffuse object under illumination of the above speckle pattern is analyzed in connection with the source parameters.
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TL;DR: In this paper, the statistical properties of dynamic speckles produced by a moving diffuse object were reviewed by providing the space-time correlation function and the power spectrum of speckle-intensity fluctuation for five combined cases of both the optical configuration and the illumination light.
Abstract: The statistical properties of dynamic speckles produced by a moving diffuse object were reviewed by providing the space–time correlation function and the power spectrum of speckle-intensity fluctuation for five combined cases of both the optical configuration and the illumination light. In the optical configuration, three kinds of geometry (free-space, single-lens, and double-lens) were taken, and three kinds of illumination light (a Gaussian beam, a plane-wave beam, and a Gaussian Schell-model beam) were used. Consequently, it was shown that the cross-correlation function and the power spectrum are both Gaussian under some assumptions. From the dynamic properties, two types of speckle motion, boiling and translation, were also evaluated for various conditions of object motion, optical configuration, and illumination light.
209 citations
TL;DR: A numerical simulation and experiment to test speckle reduction using a partially spatially coherent source are reported and low-coherence interferograms of a scattering surface using single-mode and multimode source fibers are recorded.
Abstract: Speckle in optical coherence tomography (OCT) images originates in the high spatial coherence of incident light that enables interference of light backscattered from spatially heterogenous tissue specimens. We report results of a numerical simulation and an experiment to test speckle reduction using a partially spatially coherent source. A Gaussian-Schell model for a partially spatially coherent source is used in the OCT simulation. For the experiment, such a source was generated by a spatially coherent boardband light source and a multimode fiber. The advantage of using a multimode fiber in combination with a broadband source is the large number of photons per coherence volume. To illustrate speckle reduction with a partially spatially coherent source, we record low-coherence interferograms of a scattering surface using single-mode and multimode source fibers. Interferograms recorded using a single-mode source fiber are indicative of those observed using conventional OCT. Speckle in OCT images recorded using a multimode source fiber is substantially reduced.
109 citations
TL;DR: It is shown that the sensitivity of displacement can be in the submicrometer range and the dynamic range of the displacement sensing are quantitatively analyzed.
Abstract: A multimode fiber sensor using the intensity inner product of speckle fields is presented. The sensitivity and the dynamic range of the displacement sensing are quantitatively analyzed. We show that the sensitivity of displacement can be in the submicrometer range. Experimental performances show that the results are consistent with the calculated results.
97 citations
TL;DR: The surface roughness dependence of the intensity correlation function of the speckle pattern, produced in the Fresnel region with fully developed specckle-pattern illumination, has been theoretically investigated and has been discussed in this paper.
Abstract: The surface-roughness dependence of the intensity correlation function of the speckle pattern, produced in the Fresnel region with fully developed speckle-pattern illumination, has been theoretically investigated and has been discussed as follows. This correlation function is represented by two correlation functions of scattered and unscattered components. As the diffuse object becomes rough, the speckle size varies from the speckle size of the illumination light to that obtained with the condition, so that the object is a deep phase screen. The speckle contrast, however, is always one.
48 citations
TL;DR: The fiber ASE source provides a unique combination of high power per mode with both low spatial and low temporal coherence, making it an ideal source for full-field imaging and ranging applications.
Abstract: We design and demonstrate a fiber-based amplified spontaneous emission (ASE) source with low spatial coherence, low temporal coherence, and high power per mode. ASE is produced by optically pumping a large gain core multimode fiber while minimizing optical feedback to avoid lasing. The fiber ASE source provides 270 mW of continuous wave emission, centered at λ=1055 nm, with a full width at half-maximum bandwidth of 74 nm. The emission is distributed among as many as ∼70 spatial modes, enabling efficient speckle suppression when combined with spectral compounding. Finally, we demonstrate speckle-free full-field imaging using the fiber ASE source. The fiber ASE source provides a unique combination of high power per mode with both low spatial and low temporal coherence, making it an ideal source for full-field imaging and ranging applications.
47 citations
References
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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
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
TL;DR: A general theorem is provided for the moments of a complex Gaussian video process that states that an n th order central product moment is zero if n is odd and is equal to a sum of products of covariances when n is even.
Abstract: A general theorem is provided for the moments of a complex Gaussian video process. This theorem is analogous to the well-known property of the multivariate normal distribution for real variables, which states that an n th order central product moment is zero if n is odd and is equal to a sum of products of covariances when n is even.
411 citations
TL;DR: In this paper, the concept of quasihomogeneous sources is introduced and an important reciprocity relation is shown to exist between light in the far zone and in the source plane, which implies that the degree of coherence in far zone is given by the classic form of the van Cittert-Zernike theorem, even though the source may have a high degree of spatial coherence over arbitrarily large areas.
Abstract: The concept of a quasihomogeneous source is introduced. Unlike a source that is strictly homogeneous in its statistical properties, a quasihomogeneous source may be finite. Many physical sources, both primary and secondary ones, are adequately approximated by this model. Coherence and radiometric properties of light generated by such sources (assumed, for simplicity, to be planar) are discussed and an important reciprocity relation is shown to exist between light in the far zone and in the source plane. This relation implies that the degree of coherence in the far zone is given by the classic form of the van Cittert-Zernike theorem, even though the source may have a high degree of spatial coherence over arbitrarily large areas. The reciprocity relation also provides a generalization of a recently derived result that expresses the angular dependence of the radiant intensity in terms of the degree of spatial coherence of light in the source plane. The dependence of all the basic radiometric quantities on the distribution of the optical intensity across the source and on the degree of spatial coherence of the light emerging from the source is discussed and is illustrated, for some typical sources, by computed curves.
287 citations
TL;DR: In this paper, the propagation of partially coherent light beams generated by gaussian Schell-model sources is characterized by two parameters that are analogous to the beam radius and the radius of wavefront curvature of fully coherent gaussian laser beams.
211 citations