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.     

Spatial speckle correlometry in applications to tissue structure monitoring

Asymptotic behavior of temporal autocorrelation functions of speckle intensity fluctuations induced by tissue scanning with a focused probe beam is experimentally studied for the transition from a single-scattering to a multiple-scattering mode. Such parameters as the exponential factor (or the Hurst coefficient) and the Hausdo dimension are proposed for the characterization and the visualization of the variations of the studied tissues' optical properties in generalized form. We studied reversible transition between various scattering modes stimulated by the application of certain chemical agents to the human sclera samples using speckle intensity correlation analysis; corresponding results are presented. The possibilities of the scattering structures imaging with local estimations of the exponential factor of speckle intensity fluctuations are shown in in vitro experiments with samples of human skin epidermis.     

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.     

Contrast Enhancement of Gaussian Speckles Produced by Centrosymmetrical Objects

Abstract

It is well known that the contrast of Gaussian speckles produced under ordinary optical configurations is at most 1. It is also known, however, that under some special situations even Gaussian speckles can have contrast values higher than 1. As an example of such a situation, this paper discusses the first-order statistics of speckle patterns produced in the Fraunhofer region of objects having centrosymmetrical structures. The first-order statistics of Gaussian speckles is first reviewed with special emphasis on the optical conditions which produce the contrast enhancement. Enhanced contrast and the intensity distributions which deviate from the negative exponential density are elucidated theoretically in the case of speckles produced by random objects containing centrosymmetrical structures. Some experimental verifications are also given for the speckle patterns produced by randomly distributed circular apertures containing some symmetrical pairs.     

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.     

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.     

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.     

Can laser speckle flowmetry be made a quantitative tool?

The ultimate objective of laser speckle flowmetry (and a host of specific implementations such as laser speckle contrast analysis, LASCA or LSCA; laser speckle spatial contrast analysis, LSSCA; laser speckle temporal contrast analysis, LSTCA; etc.) is to infer flow velocity from the observed speckle contrast. Despite numerous demonstrations over the past 25 years of such a qualitative relationship, no convincing quantitative relationship has been proven. One reason is a persistent mathematical error that has been propagated by a host of workers; another is a misconception about the proper autocorrelation function for ordered flow. Still another hindrance has been uncertainty in the specific relationship between decorrelation time and local flow velocity. Herein we attempt to dispel some of these errors and misconceptions with the intent of turning laser speckle flowmetry into a quantitative tool. Specifically we review the underlying theory, explore the impact of various analytic models for relating measured intensity fluctuations to scatterer motion, and address some of the practical issues associated with the measurement and subsequent data processing.     

Correlation distance of dynamic speckles

The translational and boiling motions of dynamic speckles produced in the Fresnel diffraction field under illumination of a Gaussian beam are investigated in detail. The speckle motion is analyzed from the space-time cross-correlation function of speckle intensity fluctuations detected at the two points in the receiving plane. The correlation distance of time-varying speckles is compared with the translation distance of the spatial speckle pattern. The optical conditions for the translational and boiling motions of dynamic speckles are examined and expressed in a diagram. The characteristics for the correlation distance of time-varying speckle intensity fluctuations are finally verified by several experiments.     

Fringe visibility analysis with different scale apertures in speckle photography

Abstract

The use of different scale aperture pupils for image recording in speckle photography is analysed. In particular a double-exposure specklegram is considered. The ensemble-average intensity in the Fourier plane is analytically derived and fringe visibility is investigated. The theoretical results are verified by in-plane displacement translation experiments.     

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.     

Speckle Intensity Due to Strong and Weak Scatterers in the Presence of Amplitude-correlated Multipaths

The speckle intensities of both strong scatterers and weak scatterers are modelled as the superposition of N sinusoidal waves whose amplitudes are taken to be correlated random variables in order to account for multipath correlations. Explicit expressions are obtained for the first three moments of the speckle intensity when the correlated amplitudes are gaussian-distributed about a non-zero mean. These moments approach their large-N asymptotic values independently of the amplitude correlation function. The contrast and skewness parameter are also evaluated, and simplified formulae obtained when N is large. As the number of multipaths become very large, the speckle intensity PDFs tend to limiting functional forms by reason of the central limit theorem; an investigation was made to determine the influence of amplitude correlations on the parameters entering into these limiting functional forms. The implication of these very large- N asymptotic results is that amplitude correlations are probably not significant in so far as altering the basic structure of the speckle intensity PDF. However, when N is not large, the amplitude correlations play a significant role.     

Precision of moment-based estimation of the degree of polarization in coherent imagery without polarization device

We propose and analyze a statistical method to estimate the degree of polarization of light from a single speckle intensity image by analyzing the statistical distribution of the light intensity. The optimal precision of such an estimation method is evaluated by computing the Cramer-Rao bounds for several speckle degrees. Two moment-based estimators of the square degree of polarization are introduced and characterized. For the first time to our knowledge, it is shown theoretically and through simulations that the estimators are almost efficient for high orders of speckle. The robustness of the method is discussed for the case when the intensity fluctuations do not follow the standard speckle model.     

Measurement of Small Lateral Vibrations of Speckle Patterns Using a Non-steady-state Photo-EMF in GaAs: Cr

Abstract

We report the observation of a non-steady-state photo-EMF generated in a semi-insulating GaAs: Cr crystal by vibrating speckle patterns. The experimentally observed basic dependences of the output signal on the vibration frequency and amplitude as well as on the light intensity are in reasonable agreement with those observed earlier for vibrating sinusoidal light patterns. Using this novel technique, lateral vibrations of diffusely scattering objects can be easily detected over a wide range of frequencies and amplitudes.     

激光大气传输光斑统计概率接收孔径效应

本文综合考虑湍流大气对激光斑纹强度、光束传输方向的调制作用和有限接收孔径的光强起伏、相位起伏平滑作用等因素,从理论上研究了激光斑纹强度、相位起伏概率密度函数和孔径平滑作用,求得了高阶强度矩的孔径平滑因子。     

Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics

Abstract

The paper describes the possibility of using the speckle pattern decorrelation for determination of small deformation tensor components of an elementary object surface area in an optical image field. The relationship between the small-deformation tensor and the speckle field displacement is analysed in detail. The studied problem is presented from the approximation viewpoint of both wave and geometrical optics.     

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.     

Quantum Statistical Properties of Mixed Degenerate and Non-degenerate Parametric Processes

Abstract

Quadrature and integrated intensity fluctuations are found for mixed degenerate and non-degenerate optical parametric processes in single and compound modes. Additionally to quantum statistical effects for single processes new phenomena can occur arising from the coupling of both the processes, which can support squeezing of vacuum fluctuations and sub-Poisson photon statistics in single and compound modes.     

Back-action-induced Squeezed Light in a Detuned Quantum Non-demolition Scheme

Abstract

We describe the experimental observation and theoretical interpretation of a squeezing effect which occurs through the coupling of two light beams in a three-level atomic system. The origin of this effect can be attributed to the transfer of the intensity fluctuations of one beam to the phase fluctuations of the other one, followed by an optical feedback onto the intensity of the initial beam. The first step of the information transfer is similar to the one which occurs in a quantum non-demolition (QND) measurement of the intensity. The feedback effect is obtained through mixing of the phase and intensity quadratures, due to the detuning of the optical cavity which contains the nonlinear medium. Therefore the information obtained by the QND measurement is used to correct the intensity fluctuations of the signal beam by a build-in mechanism, which does not require any use of external electronics.