Variance Of Intensity Fluctuations Research Articles

Application of third-order correlation between intensity fluctuations to determination of scattering potential of quasi-homogeneous medium.

Within the first-order Born approximation, we introduce the third-order correlation between intensity fluctuation (CIF) of light scattered from a quasi-homogeneous (QH) medium. By utilizing the Gaussian moment theorem for describing the scattering potential statistics, analytic forms are derived for the third-order, normalized CIF and variance of intensity fluctuations (VIF) of the far-zone scattered field. It is found that the normalized CIF of the scattered field is proportional to the product of Fourier transforms of the strengths of the scattering potential, while the variance of intensity fluctuations (VIF) of the scattered field is the cube of the Fourier transform of the normalized correlation coefficient (NCC) of the scattering potential. Based on the derived formulas, we show that the correlation function of the scattering potential of the medium can be determined from the scattering equations where the third-order CIF properties of the scattered field must be known in advance.

Ultraviolet background fluctuations with clustered sources

We develop a count-in-cells approach to the distribution of ultraviolet background fluctuations that includes source clustering. We demonstrate that an exact expression can be obtained if the clustering of ionizing sources follows the hierarchical ansatz. In this case, the intensity distribution depends solely on their 2-point correlation function. We show that the void scaling function of high redshift mock quasars is consistent with the Negative Binomial form, before applying our formalism to the description of HeII-ionizing fluctuations at the end of helium reionization. The model inputs are the observed quasar luminosity function and 2-point correlation at redshift $z\sim 3$. We find that, for an (comoving) attenuation length $\lesssim $ 55 Mpc, quasar clustering contributes less than 30% of the variance of intensity fluctuations so long as the quasar correlation length does not exceed 15 Mpc. We investigate also the dependence of the intensity distribution on the large-scale environment. Differences in the mean HeII-ionizing intensity between low- and high-density regions could be a factor of few if the sources are highly clustered. An accurate description of quasar demographics and their correlation with strong absorption systems is required to make more precise predictions.

Fluctuations of energy density of short-pulse optical radiation in the turbulent atmosphere.

Fluctuations of energy density of short-pulse optical radiation in the turbulent atmosphere have been studied based on numerical solution of the parabolic wave equation for the complex spectral amplitude of the wave field by the split-step method. It has been shown that under conditions of strong optical turbulence, the relative variance of energy density fluctuations of pulsed radiation of femtosecond duration becomes much less than the relative variance of intensity fluctuations of continuous-wave radiation. The spatial structure of fluctuations of the energy density with a decrease of the pulse duration becomes more large-scale and homogeneous. For shorter pulses the maximal value of the probability density distribution of energy density fluctuations tends to the mean value of the energy density.

Pointwise implementation of dynamic laser speckle technique

The paper proposes pointwise implementation of correlation-based algorithms for processing time sequences of 2D dynamic speckle patterns of a diffuse object illuminated with a laser light in order to obtain a spatial map of physical or biological activity across its surface. Both temporal correlation and structure functions were studied with and without the pointwise normalization by the variance of intensity fluctuations in time. The performance of the algorithms was checked by simulation of dynamic speckle patterns at a given spatial distribution of the temporal correlation radius of activity and by dynamic speckle measurement of a test object. The obtained set of high contrast and high spatial resolution activity maps proves the efficiency of the normalized correlation-based algorithms to indicate regions of varying activity even at non-uniform illumination and reflectivity across the object.

Reconstruction of the radial dependence of the structural characteristic of the refractive index in a supersonic gas flow from laser beam intensity fluctuations

A method for reconstructing the radial dependence of the structural characteristic of the refractive index of air in an axisymmetric supersonic gas flow from the variance of intensity fluctuations of a laser beam that is transmitted through the flow at different distances from the jet symmetry axis is proposed. An expression that relates the relative intensity variance on the beam axis as a function of the aiming distance and the radial dependence of the structural characteristic is obtained. To invert this expression, the Abelian transformation is used. The parameters of the jet module of an AT-326 wind tunnel at the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences are modeled.

Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media

We have measured pulsed microwave transmission through quasi-one-dimensional quasi-1D samples with lengths up to three times the localization length as determined from measurements of the variance of intensity fluctuations. Measurements are analyzed using four complementary approaches, each appropriate in a specific time range: i diffusion theory; ii self-consistent localization theory SCLT with a renormalized diffusion coefficient in space and frequency, Dz,; iii a dynamic single parameter scaling DSPS model, which reflects the decay of localized modes which do not overlap in space and frequency; and iv simulations of 1D random media. For times up to twice the diffusion time D, diffusion theory gives an excellent fit to the data. For times up to 4D, the slowing of the decay rate of transmission is in accord with SCLT. For longer times, transmission decays more slowly than the predictions of the SCLT, indicating the inability of this modified diffusion theory to capture the decay of long-lived localized states. Beyond the Heisenberg time, the decay rate approaches the predictions of the DSPS model, reflecting the increasing proportion of wave energy in longlived localized states. The decay rates obtained from 1D simulations are then in good agreement with measurements in quasi-1D samples and coincide with decay rates given by the DSPS model.

Protein aggregation in live cells: N&B analysis of Huntingtin

The aggregation of the huntingtin (Htt) protein is thought to be responsible for Huntington's disease. One problem is the detection of the different size of aggregates and the stages of aggregation directly in live cells. Recently we develop a method (N&B) to detect the size of aggregates and the number of particles in every pixel of a confocal image. N&B can be performed on the entire cells simultaneously so it is possible to follow the kinetics of aggregation. This method is based on the variance of intensity fluctuations of particles as they diffuse through the excitation volume. We performed experiments in transfected COS7 using different lengths of the polyglutamine sequence (Httex1 97QP-GFP, Httex1 46QP-GFP and Httex1 25QP-GFP). We can determine the presence of units, small aggregates and inclusion bodies in different parts of cell and their time evolution.. We observed the presence of Htt throughout the cell and that oligomer formation starts in the cytoplasm. At higher protein concentration aggregation occurs in the nucleus. When an inclusion body forms in the cytoplasm, all Htt including that in the nucleus, is recruited by the inclusion body. We found aggregates, which have a size of 5-10 protein units, diffusing in membrane tubules. We suggest that these aggregates my represent the precursors for protein nucleation events. We estimated that the inclusion body is formed by hundred of protein units. In different cell types the aggregation follows a similar dynamic. Our studies have shown the protein aggregation size distribution in live and how the nucleation events progress in real time. Support by U54 GM064346 CMC (MD, EG), NIH-P41-RRO3155 (EG), P50-GM076516 (EG,GO).

Gaussian-to-Lévy statistical crossover in a random amplifying medium: Monte Carlo simulation

We report Monte Carlo simulations of photons diffusing through a random amplifying medium and study the statistics of emitted intensity fluctuations. We observe a crossover from the Gaussian to the Lévy statistics corresponding to divergence of the variance of intensity fluctuations, as we go to large gain and strong scattering, consistent with our earlier analytical and experimental works. In the limit of very high gain, our simulations suggest a “Lévy microscope effect”, where the emitted mean intensity is expected to diverge, and the sum of intensities is dominated by the typical largest event.

Coexistence of Localized and Delocalized Surface Plasmon Modes in Percolating Metal Films

Near-field intensity statistics in semicontinuous silver films over a wide range of surface coverage are investigated using near-field scanning optical microscopy. The variance of intensity fluctuations and the high-order moments of intensity enhancement exhibit local minima at the percolation threshold. This reduction in local field fluctuations results from resonant excitation of delocalized surface plasmon modes. By probing the modification of the critical indices for high-order moments of intensity enhancement caused by the delocalized states, we provide the first experimental evidence for the coexistence of localized and delocalized surface plasmon modes in percolating metal films.

Analytical Expression for the Reduction of XPM-Induced Crosstalk by Walk-Off

Wavelength division multiplexing (WDM) is an attractive scheme to increase the capacity of the already installed optical links. However, the effect of cross-phase modulation (XPM) causes nonlinear crosstalk in intensity modulated direct detection WDM systems based on dispersive fibers and thus could limit the total number of channels that such a system can support. On the other hand, the interference among channels decreases due to the so-called walk-off with growing difference in group velocity and channel spacing, respectively. Considering the propagation of Gaussian pulses, a formula which describes analytically this diminution as a function of the differential group delay is derived. Since the data signals transmitted in different channels are statistically independent XPM induces random-like intensity fluctuations. The theoretical results for their variance are verified by means of simulations. For comparison purposes, the variance of intensity fluctuations induced by pulses with edges steeper than those of a Gaussian pulse is calculated numerically.

Beam propagation in focusing media with random-axis misalignments: Second- and higher-order moments

A novel statistical technique which allows the asymptotic evaluation of second- and higher-order averaged observables related to the stochastic complex parabolic equation is applied to the problem of beam propagation in a focusing medium characterized by random-axis misalignments. Analytical and numerical results concerning on- and off-axis statistics (e.g., the variance of intensity fluctuations, modal power transfer, the probability distribution density of the log-irradiance, etc.) are presented, and comparisons are made with previously reported findings.

Focused Laser Irradiance Fluctuations in a Turbulent Medium

A standard diagrammatic technique is used to obtain an integral representation for the fourth moment of the field of irradiance in a random weakly inhomogeneous medium. For the case of an incident focused coherent wave, it is shown that the spectral and correlation properties of the random field of intensity depend in an essential manner upon the magnitude of the phase structure function, computed on the transmitter aperture size. The region of large values of this parameter is of particular concern, where an analytical expression for the correlation function of intensity fluctuations is derived, and saturation of the magnitude of the normalized variance of intensity fluctuations is investigated.