Dynamic Properties of Laser Speckles on Images Transmitted Through an Image Fibre-bundle

Abstract

The statistical properties of time-varying laser speckles appearing on an image transmitted through an image fibre-bundle are studied experimentally and theoretically. The effect of defocusing on a stage of observation is investigated in relation to the stationarity of the detected speckle intensity. It is shown that a large amount of defocusing produces a stationary speckle field for which the correlation function of the speckle intensity variation is obtained in a stable form. This allows a system for monitoring the velocity of moving objects using an image fibre-bundle to be developed.     

Spectral and Dispersion Analysis of Laser Sources and Multimode Fibres Via the Statistics of the Intensity Pattern

Abstract

The statistics of an intensity pattern at the exit face of a multimode fibre excited by a quasimonochromatic source is analysed by means of an expression for speckle pattern contrast. Theoretical considerations that take advantages of both classical coherence formalism and guided-mode field representation of light propagating in multimode fibres lead to two equivalent expressions for speckle pattern contrast; the first is expressed in the time domain by using a source temporal coherence function and the second is expressed in the frequency domain by using a frequency correlation function of the source spectral density. Moreover, the modal guiding conditions in multimode fibre are in both expressions governed by a maximum group delay time difference. The feasibility of both expressions, especially the second, is demonstrated by analytic expressions for the speckle pattern contrast for seven different spectra, that is the influence of the source temporal coherence as well as the modal dispersion is thus clearly shown.     

Statistical Properties of the Interference Pattern Generated by a Partially Developed Speckle

Abstract

The fluctuations of fringe-pattern intensity are studied theoretically by means of Young's interference experiment applied to speckle. We have studied the fluctuations generated by partially developed Gaussian speckle produced in the far field. The formula for the average contrast of the fringe-pattern intensity is derived and the characteristic values of the contrast fringes are discussed. The theoretical results are compared with experimental data.     

Chromatic Modulation for Optical Fibre Sensing Electromagnetic and Speckle Noise Analysis

Abstract

Changes in the chromaticity of the transmitted electromagnetic field in an optical fibre are considered. An electromagnetic analysis that predicts the radial dependence of the chromaticity at the exit is presented and coupled to a speckle noise analysis which provides an estimate of the error. Theoretical predictions are compared with experimental results and good agreement between the two is demonstrated. The results can be useful in the design of optical fibre sensors which use the chromatic modulation method.     

Speckle noise arising from coherently illuminated polydisperse and continuous size distributions of discs

Abstract

An existing model of the speckle noise affecting images in far-field in-line holographic imaging is extended to distributions of disc-shaped particles which are no longer of uniform diameter. In this model the signal-to-noise ratio in replayed images from ideal in-line holograms in the Fraunhofer regime is limited by the speckle field arising from the overlapping Airy patterns. The original study was motivated by holographic particle image velocimetry and assumed that all the particles were of uniform diameter. We extend this model to cover polydisperse, power-law, exponential and Gaussian distribution functions and include an explicit limit on our maximum particle diameter to ensure that the hologram is recorded in the far-field of all the particles.     

Statistical Properties of Phase Variation in Shearing Speckle Interferometry and Its Effect on Fringe Visibility

Abstract

The statistical properties of two interfering speckle fields indicate a reduction in phase variation as the coherent correlation between them increases. In this paper, the impact of this phenomenon on fringe visibility in shearing speckle interferometry, where two laterally shifted speckle fields are super-imposed, is studied. Work is also done to correlate fringe visibility with the amount of lateral shear based on the limitations imposed by phase variance statistics.     

Phase shift calibration in speckle photography—a first step to practical real-time analysis of speckle correlation fringes

Abstract

The paper is focused on the implemention of phase shift calibration in speckle photography with a view to introducing the possibility of realtime analysis of displacement data obtained by the method. Phase reversal is accomplished by varying pressure within an air-filled quartz cell inserted in the pump beam in a conventional two-beam coupling arrangement. It is shown that phase reversal is achieved when a π-shifted speckle pattern overlaps on an unshifted speckle pattern at the observation plane. This phenomenon is exploited for calibration of the phase shift. Experimental results show good agreement with the theory.     

Speckle Displacement by a Surface Rotation and Conical Diffraction Phenomena

Abstract

The null displacement ring observed in the speckle pattern when a translucent rough surface is rotated is closely related to the conical diffraction phenomena of the gratings. When the mth diffraction order coincides with the null displacement ring, the displacement of this order and the speckle displacement are null.     

Computation of green’s tensor and wave propagation in the random granular elastic medium

Abstract

A linear differential operator equation involving randomly variable field parameters, characterising the heterogeneous granular elastic medium is considered. The appropriate Green’s tensor is evaluated for the non-deterministic operator equations in the form of Fourier integrals in the frequency space; the exact evaluation is carried out to obtain the 36 components of Green’s tensor. The problem of wave propagation in the random granular elastic medium is then carried out with the help of the associated Green’s tensor. The effect of random variation of parameters on wave propagation in the granular elastic medium is examined. Dispersion equations have been analysed in details.     

On the thermodynamics of the inhomogeneous mixed phase of an ideal type II superconductor

The macroscopic tensor S _ik is defined so as to characterize changes in the structure of the vortex system. This tensor contains only three independent components instead of the six of the strain tensor u _ik which is used commonly to describe deformations of the vortex system. All components of S _ik are independent of the magnetic induction B and can be considered as thermodynamic variables of the system together with B. The stress tensor for an inhomogeneous mixed phase is obtained in these variables. It is shown on the basis of the Ginzburg-Landau current equation that the mixed phase tends to be uniform; inhomogeneities (e.g., macroscopic currents) can penetrate to the uniform phase only up to some distance that diverges at H H _c2. The free energy of a weak inhomogeneous mixed state is discussed; nonlocal features of the vortex system and its special magnetic symmetry are taken into account. This symmetry allows for the existence of contributions to the free energy that are linear in the magnetic field and strains. The equilibrium conditions differ in general from the simple relation j × B = 0, so that the force-free configurations do not correspond to the thermodynamic equilibrium of an ideal material. The connection between the fields B and H is obtained in the form of a differential equation that also includes the structural parameters S _ik. These fields need not be parallel in general. The current distribution in a slab of an ideal type II material in a transverse field is calculated.     

Optical Mode Characterization of the Configuration of a Thin Ferroelectric Liquid Crystal Cell Under an Applied Electric Field

Abstract

It is possible to probe directly the optic dielectric tensor configuration within a thin (about 3·5 μm) smectic layer of a ferroelectric liquid crystal (FLC) by the propagation of prism-coupled leaky Fabry-Perot optic modes. Incident monochromatic polarized light couples into the resonant modes of the system which are then observed as sharp dips in the reflected signal at specific incident angles. This work has shown that the FLC has an optic tensor profile which is consistent with the chevron formation of the smectic layers observed in X-ray scattering measurements. Also it is shown that under the application of a low d.c. applied field the optic dielectric tensor configuration distorts in a manner consistent with the retention of the chevron structure up to fields of about 10⁶ Vm^?1.     

Subpixel Speckle Displacement Measurement Using a Digital Processing Technique

Abstract

This paper deals with the optical measurement of deformations and displacements of diffusing rough surfaces using changes in the speckle pattern obtained by laser illumination. A digitized speckle signal is obtained using a linear charge-coupled device photodetector that produces samples of one-dimensional signals of N pixels. A sequential numerical processing procedure is applied to detect the relative displacement of two speckle signals, corresponding to two different states of the surface; the accuracy is better than one micrometre. The principles of the method and the corresponding algorithms are described. Experimental results are given and these include an analysis of the deformation of video structure under directional traction.     

Theory and analysis of shells undergoing finite elastic-plastic strains and rotations

Summary In this paper theory and analysis of shells undergoing finite elastic and finite plastic strains and rotations are presented. The shell kinematics are based on a relaxed normality hypothesis allowing transverse normal material fibers to be stretched and bended, whereas shear deformations are neglected. Lagrangean logarithmic membrane and logarithmic bending strain measures are introduced, and it is shown that they can be additively decomposed into purely elastic and purely plastic parts for superposed moderately large strains and unrestricted rotations. The logarithmic strain measures are used to formulate thermodynamic-based constitutive equations for isotropic elastic and plastic material behavior with isotropic and kinematic hardening induced by continuous plastic flow. To analyse path-dependent elastic-plastic shell deformations by iterative procedures the application of logarithmic strain measures allows to realize load steps with corresponding moderate strains and unrestricted rotations. The moderate strain restriction for superposed deformations can be assured by an appropriate update procedure. Formulae are given to determine exactly the rotational change of the reference configuration during the update. Finally, the principle of virtual work with corresponding elastic-plastic material tensor is formulated and it is shown that the weak form of the virtual work leads to the Lagrangean equilibrium equations and boundary conditions well-known from the nonlinear theory of elastic shells.

Notation

3-D and 2-D continuum F deformation gradient - U right Cauchy-Green stretch tensor - R rotation tensor - E Green strain tensor - e Almansi strain tensor - H Lagrangean logarithmic strain tensor - Kirchhoff stress tensor in the 3-D continuum - Cauchy stress tensor - () ^e reference to an elastic deformation - () ^p reference to a plastic deformation - (^–), (⁺) reference to a first and a second superposed deformation, respectively - (^*) reference to an alternative decomposition of the superposed deformation - AB composition of the two tensorsA andB - A ^T transposed ofA - A ² square ofA - A ^–1 inverse ofA Shell theory u displacement field of the shell space - v displacement field of the middle surface - h, shell thickness in the initial and the current state - thickness coordinate, - g _i ,g ⁱ base vectors in the undeformed shell space,i{1, 2, 3} - base vectors in the deformed shell space - a ,a surface base vectors on the undeformed middle surface =0, {1, 2} - , surface base vectors on the deformed reference surface =0 - n, unit normal vector on the surface =0 in the initial and the deformed configuration, respectively - b, curvature tensor of the surface =0 in the initial and current state - Green membrane strain tensor - Green bending strain tensor - Green second order strain tensor - g logarithmic membrane strain tensor - k logarithmic bending strain tensor - p logarithmic second order strain tensor - T plane Kirchhoff stress tensor - N stress resultant tensor - stress couple tensor - second order stress resultant tensor     

Superposition of Two Dynamic Speckle Patterns

Abstract

A model is proposed to explain the influence of blood flow and moving surrounding tissue on laser light scattering. Blood and tissue are represented by two sets of scatterers which are moving in arbitrary directions with different velocities. The real dynamic speckle pattern is thought to be composed of the coherent superposition of the two speckle patterns due to the scattering on these two sets of scatterers. The model describes the spectrum of the speckle intensity in an arbitrary observation point. No special assumptions must be made concerning the geometry of illumination and the position of the observation point. A measuring value B for the determination of the blood flow is derived from the speckle intensity. The model also provides the dependence of B on density and mean velocity of each set of scatterers. It has been shown that the main contribution of the tissue movement on B can be compensated by a control measurement and that the sensitivity of B due to blood velocity variations depends on the density of both sets of scatterers and on the tissue velocity.     

Simulation of Time-evolving Speckle Patterns Using Kolmogorov Statistics

Abstract

We present a new approach for simulating time-evolving speckle patterns, by combining the shift of a rigid phase screen with its evolution. Thus, the two time-scales associated with speckle boiling and speckle motion can be adjusted independently. The statistical properties of the phase perturbation and the speckle pattern are investigated by using the temporal phase structure function and the temporal intensity correlation. We found a very good agreement with experimental results.     

Comprehensive influence of in-plane displacement,double-aperture orientation and wedge-shearing direction on slope fringe formation in speckle shearing interferometry

Abstract

The comprehensive influence of the in-plane displacement, double-aperture orientation and wedge-shearing direction on the slope fringe formation in speckle shearing interferometry is discussed in this paper. The results show that the two in-plane displacement components have an influence on the slope fringe formation and that the double-aperture orientation and wedge-shearing direction also have an important influence on the slope fringe formation. A theoretical analysis and experimental results are given. The experimental results are in good agreement with the theoretical analysis.     

Complex Degree of Coherence Due to Tilted Planar Sources

Abstract

The complex degree of coherence (CDC) due to a quasi-monochromatic spatially incoherent source can be displayed by performing a two-step procedure. The CDC information is encoded in the spectral content of the speckle pattern produced via a diffuser placed at the plane where the CDC is to be studied. In a second step, the recorded speckle is Fourier analysed. We apply this method to the study of tilted incoherent sources, for which the CDC is no longer an homogeneous function. A relationship is found that links the size of the speckle halo in the Fourier plane (where CDC information exists), and the tilt angle of the source plane. Some experimental results are shown in order to illustrate the method. Finally, some possible extensions and applications of our study are mentioned.     

Digital speckle radiography—a new ballistic measurement technique

Abstract

Digital speckle radiography is a measurement technique which is capable of visualizing internal flow fields within an opaque material undergoing a ballistic impact. This recent development has been successfully applied to the study of polyester, cement, sand and glass targets. The technique is based on digital speckle photography but, instead of producing the required speckle pattern by traditional means, the specimen is seeded with a layer of X-ray opaque filings. By utilizing two X-ray heads and varying the delays and position of the seeded layer, a full three-dimensional displacement map can be built up. The theories behind the technique are introduced, and results presented from two-dimensional displacement measurements on sand subjected to rod impact and three-dimensional measurements of cement being impacted by a shaped charge jet.     

On stresses conjugate to Eulerian strains

Summary. A stress is considered conjugate to a strain if the product of the stress and an objective rate of the strain has a trace which is equal to the rate of work per unit volume. Using Kronecker product relations, apparently new expressions for stresses conjugate to the Finger strain B, the Euler strain , the Eulerian (right) stretch tensor V, and log(V) are determined. In addition, a nonclassical strain p is introduced which permits a constitutive equation expressing its Truesdell rate in terms of B and the Truesdell rate of the Cauchy stress. We regard a tensor as a strain if (a) it is not affected by rigid body motion and (b) its current value, given suitable compatibility conditions, determines the current displacement field to within a rigid body translation and rotation. By these criteria e is not strictly a strain and instead we later refer to it as a pseudostrain.     

Completely passive method of speckle reduction utilizing static multimode optical fibre and two-dimensional diffractive optical element

ABSTRACT

In this paper, we present experimental results on speckle noise suppression using a completely passive method. The passivity of the method is achieved owing to the absence of any mechanical, electronic, or other dynamic influences on the optical scheme elements. In the experiment, a multimode semiconductor 520?±?5-nm laser with a spectral bandwidth of 2?nm, static two-dimensional (2D) and 2?×?1D diffractive optical elements (DOEs), as well as multimode single-core optical fibre and multimode optical fibre bundle were used. The dependence of the speckle reduction efficiency as a function of the optical fibre type and optical fibre length was measured for different DOEs. A speckle contrast of 0.148 and speckle reduction coefficient of 2.38 were obtained for a 2.5-m-long multimode optical fibre bundle. The experimental results confirmed that it is possible to construct completely passive optical circuits with reduced speckle noises using static multimode optical fibres and diffraction optical elements.