The effect of phase modulation of scattered radiation on the asymptotic behavior of the contrast ratio of partially coherent speckle fields

We analyze the influence of a weak phase modulation of multiply scattered partially coherent light fields on the variance of fluctuations of the scattered field intensity. It is suggested to perform diagnostics of scattering media by analyzing the probing radiation scattered from a “modulating” medium and determining the speckle intensity index (or contrast ratio) upon introduction of an object studied into the scheme of measurements. The proposed method is experimentally verified on model scattering media.     

Speckle contrast of the sum of N partially correlated speckle patterns

In this paper a general method is presented for calculating the theoretical speckle contrast of a sum of correlated speckle patterns, motivated by the need to suppress the presence of speckle in laser projection displays. The method is applied to a specific example, where correlated speckle patterns are created by sequentially passing light through partially overlapping areas on a diffuser, before being projected onto a screen. This design makes it possible to find a simple expression for the correlation between speckle patterns. When the set of correlations involves symmetry, it is shown that the expression for the speckle contrast becomes simpler. The difference in performance between discretely and continuously varying speckle patterns is also investigated. In an example with speckle reduction by a rotating sinusoidal grating, it is found that continuous variation gives a speckle contrast that is 0.61 times the contrast obtained by discretely summing the maximum number of independent patterns.     

Complex amplitude correlation for compensation of large in-plane motion in digital speckle pattern interferometry

The use of complex amplitude correlation to compensate for large in-plane motion in digital speckle pattern interferometry is investigated. The result is compared with experiments where digital speckle photography (DSP) is used for compensation. An advantage of using complex amplitude correlation instead of intensity correlation (as in DSP) is that the phase change describing the deformation is retrieved directly from the correlation peak, and there is no need to compensate for the large movement and then use the interferometric algorithms. A discovered drawback of this method is that the correlation values drop quickly if a phase gradient larger than pi is present in the subimages used for cross correlation. This means that, for the complex amplitude correlation to be used, the size of the subimages must be well chosen or a third par?meter in the cross-correlation algorithm that compensates for the phase variation is needed. Correlation values and wrapped phase maps from the two techniques (intensity and complex amplitude correlation) are presented.     

Multidirectional speckle photography of density fields in gasdynamic flows

Double-exposure speckle photography is employed experimentally to determine the fields of local density (temperature) values in a freely burning flame, as well as in the region of natural convection near a heated cylinder.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 4, pp. 540–547, April, 1989.     

Electronic speckle photography: measurement of in-plane strain fields through the use of defocused laser speckle

High-accuracy, noncontact measurements of in-plane strain fields have been performed through the use of an electronic-speckle-photography system. The strain fields are extracted from the displacement of defocused laser speckle in a telecentric imaging system. Two different illumination configurations have been suggested, both of which use four illumination directions. Both configurations produce results of an accuracy according to Me/ΔL, where M is the demagnification of the telecentric imaging system, e is the random error in the speckle-displacement fields, and ΔL is the magnitude of the defocusing distance. The maximum defocusing distance possible was found to be restricted by the spatial resolution, especially at high magnifications. In experiments on a semicircularly and a rectangularly notched aluminum sheet, the principal strain field around the notch was measured with a random error in the strain field of less than 10 μstrain (μm/m).     

Complex amplitude correlations of dynamic laser speckle in complex ABCD optical systems

Within the framework of complex ABCD-matrix theory, exact theoretical expressions are derived for the space-time-lagged cross-covariance functions of the fields valid for arbitrary (complex) ABCD-optical systems, i.e., systems that include Gaussian-shaped apertures and partially developed speckle. Specifically, we show and discuss the results for the three generic systems, i.e., free-space propagation, Fourier transform configuration, and imaging. To cope with various surface structures of varying rms surface heights, we apply two models in addition to employing the usual model for surfaces giving rise to fully developed speckle. The theoretical results found for free-space propagation are supported by interferometrically obtained data.     

Theory of partially coherent electromagnetic fields in the space-frequency domain

We construct the coherent-mode representation for fluctuating, statistically stationary electromagnetic fields. The modes are shown to be spatially fully coherent in the sense of a recently introduced spectral degree of electromagnetic coherence. We also prove that the electric cross-spectral density tensor can be rigorously expressed as a correlation tensor averaged over an appropriate ensemble of strictly monochromatic vectorial wave functions. The formalism is demonstrated for partially polarized, partially coherent Gaussian Schell-model beams, but the theory applies to arbitrary random electromagnetic fields and can find applications in radiation and propagation and in inverse problems.     

Statistical analysis of speckle fields in digital laser monitoring of the microstructure of paper

It has been shown that digital dynamic speckle photography is an effective method for quantitative diagnostics of changes in the structure of paper processed by pulsed discharge. A theory of the dynamic statistics of speckle fields and mathematical relations are given. In using optical magnification = 1, the software developed permits fast statistical processing of up to 250,000 microzones in a two-dimensional CCD image of size 20 × 30 mm. The results obtained point to a high spatial and temporal resolution of the method and the possibility of its real-time realization. It has been shown that noise filtering is an important part of speckle image processing. The software permits filtering both in direct calculation of the correlation function and in the Fourier plane with the use of the fast Fourier transform. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 4, pp. 127–137, July–August, 2007.     

A multichannel correlation filter based on a photorefractive crystal for the processing of varying speckle fields

A method for the simultaneous processing of speckle fields generated by several single-fiber multimode interferometers is developed. The method uses a multichannel correlation filter based on a single photorefractive crystal. Mutual influence of the neighboring channels is analyzed, and it is shown that the simultaneous processing of several channels can be performed with the help of a single photorefractive crystal, provided that the interchannel spacing is not smaller than half of the size of the optical field pattern formed in the crystal plane.     

Measuring the complex amplitude of wave fields by means of shear interferometry

This paper presents a treatise on the determination of the complex amplitude of a monochromatic wave field from measurements obtained by a lateral shear interferometer. Both amplitude and phase distributions are recovered from the same set of measurements. Special consideration is given to the case of measurements with large shear. Here, the state of the art in the reconstruction of discontinuous wavefronts is extended by introducing a two-step process. In the first step, the phasors of the underlying wavefront are reconstructed across specific subsets of the measurement grid. In the second step, the individual reconstructions are combined by a novel (to the best of the author's knowledge) convolution approach in the Fourier domain, called residual phasor separation.     

Determination of the 3D fields of displacements by the method of phase-shifting speckle interferometry

For 3D speckle interferometers, we propose a simplified procedure aimed at recording and processing speckle interferograms with single phase shift, which requires the minimum number of images. The results of experiments are presented to confirm the efficiency of the proposed procedure.     

Analyzing the power coupled between partially coherent waveguide fields in different states of coherence

A procedure is described for calculating the power coupled between partially coherent waveguide fields that are in different states of coherence. The method becomes important when it is necessary to calculate the power transferred from a distributed source S to a distributed load L through a length of multimode metallic, or dielectric, waveguide. It is shown that if the correlations between the transverse components of the electric and magnetic fields of S and L are described by coherence matrices M and M', respectively, then the normalized average power coupled between them is (eta) = Tr[MM']/Tr[M]Tr[M'], where Tr denotes the trace. When the modal impedances are equal, this expression for the coupled power reduces to an equation derived in a previous paper [J. Opt. Soc. Am. A 18, 3061 (2001)], by use of thermodynamic arguments, for the power coupled between partially coherent free-space beams.     

Analysis of the optical method of caustics for dynamic crack propagation

In the interpretation of experimental data on dynamic crack propagation in solids obtained by means of the optical method of caustics, it has been customary to neglect the effect of material inertia on the stress distribution in the vicinity of the crack tip. In this paper, the elastodynamic crack tip stress field is used to establish the exact equations of the caustic envelope formed by the reflection of light rays from the surface of a planar solid near the tip of a propagating crack. These equations involve the instantaneous crack tip speed, the material parameters and the instantaneous dynamic stress intensity factor, and they can be used to determine the stress intensity factor for given material parameters and crack tip speed. The influence of inertial effects on stress intensity factor measurements for system parameters typical of experiments with PMMA specimens is considered. It is found that the stress intensity factor values inferred through a dynamic analysis may differ by as much as 30–40% from values based on a quasi-static analysis.     

Long-range correlations of elastic fields in semi-flexible fiber networks

The mechanical properties of semi-flexible networks have been the subject of intense theoretical and experimental studies concerned primarily with the understanding of the complex behavior of biological systems such as the cell. Here it is shown that the elasticity of these networks, both elastic constants and elastic fields, while fluctuating significantly with position, is long-range correlated and the correlation functions exhibit power law scaling. The correlations are lost when the fiber stiffness is reduced. The range of scales over which correlations are observed is bounded below by the mean fiber segment length and above by the filament persistence length. Therefore, these networks can be regarded as stochastic fractal elastic media over the respective range of scales. This implies that no scale decoupling exists and no representative volume element can be identified on scales below the upper correlation cut-off scale.     

Evolution of the scintillation index and the optical vortex density in speckle fields after removal of the least-squares phase

Knowledge of the behavior of stochastic optical fields can aid the understanding of the scintillation of light propagating through a turbulent medium. For this purpose, we perform a numerical investigation of the evolution of the scintillation index and the optical vortex density in a speckle field after removing its continuous phase. We find that both the scintillation index and the vortex density initially drop and then increase again to reach an equilibrium level. It is also found that the initial rate of decrease in both cases is 1 order of magnitude faster than the eventual rate of increase. Their detail shapes are however different. Therefore different empirical functions are used to fit the shapes of these curves.     

Parametric estimation of the square degree of polarization from two intensity images degraded by fully developed speckle noise

Active polarimetric imagery systems allow one to reveal polarimetric characteristics of the scene. Among them, the degree of polarization allows one to have information about the polarizing nature of an imaged object. Its estimation is standardly done from four images of the scene. Reducing this number of images can be of great interest for industrial applications, allowing in particular reduction of cost in terms of money and acquisition time. We propose a parametric method to estimate the square degree of polarization from only two measurements when coherent illumination is considered and when the images are corrupted with fully developed speckle, and we characterize the performances of the estimation.     

Singularities and perturbations for far-field caustics in the neighborhood of a crack tip

Summary Adapting the principle of least time by Fermat, the farfield caustics around a crack tip were studied as a variational problem. The singular reflected rays were probed and classified using singularity theory; furthermore the singular directions were also defined.In addition, applying perturbation theory the stress intensity factor at a crack tip is evaluated, considering higher-order terms of the Muskhelishvili complex potential.It was shown that higher approximations can be achieved with this method from caustics engendered from initial curves of a larger than usual radius convenient for problems of plasticity and elastic anisotropy.With 6 Figures     

Laser monitoring of the flow velocity in lymphatic microvessels based on a spatiotemporal correlation of the dynamic speckle fields

A method and the corresponding experimental setup for the in vivo laser monitoring of temporal variations in the velocity and direction of flow in lymphatic microvessels are described. Experimental results on the laser monitoring of flow in the mesenteric microvessels of rat are presented. The method is based on an analysis of the statistical properties of the dynamic speckle fields and provides for a high spatial resolution. The results of determination of the lymph flow velocity by the proposed method agree well with analogous data of functional transmission microscopy.     

Knowledge production and the structure of collaboration networks in two scientific fields

In this paper the relationship between knowledge production and the structure of research networks in two scientific fields is assessed. We investigate whether knowledge production corresponds positively or negatively with different types of social network structure. We show that academic fields generate knowledge in different ways and that within the fields, different types of networks act as a stimulant for knowledge generation.