Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication

A partially coherent quasi-monochromatic Gaussian laser beam propagating in atmospheric turbulence is examined by using a derived analytic expression for the cross-spectral density function. Expressions for average intensity, beam size, phase front radius of curvature, and wave-front coherence length are obtained from the cross-spectral density function. These results provide a model for a free-space laser transmitter with a phase diffuser used to reduce pointing errors.     

Probability Density Functions of Speckle Intensity Produced by Weak Diffusers

By using the discrete cell model for the rough surface of objects, a general expression is derived which gives the probability density function of speckle intensity produced by weak diffusers having an arbitrary phase distribution and an arbitrary cell number, N, of contributions for the formation of speckles. In some special cases, it gives the probability density functions which have been previously derived and are well known in the statistics of speckles. In the case of the small number N = 2, an analytical solution of the probability density function is obtained from that general expression. Some features on the probability density functions of speckles are discussed for the case of small roughness and small number N.     

Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle

Single- and multiple-pulse detection statistics are presented for aperture-averaged direct detection optical receivers operating against partially developed speckle fields. A partially developed speckle field arises when the probability density function of the received intensity does not follow negative exponential statistics. The case of interest here is the target surface that exhibits diffuse as well as specular components in the scattered radiation. An approximate expression is derived for the integrated intensity at the aperture, which leads to single- and multiple-pulse discrete probability density functions for the case of a Poisson signal in Poisson noise with an additive coherent component. In the absence of noise, the single-pulse discrete density function is shown to reduce to a generalized negative binomial distribution. The radar concept of integration loss is discussed in the context of direct detection optical systems where it is shown that, given an appropriate set of system parameters, multiple-pulse processing can be more efficient than single-pulse processing over a finite range of the integration parameter n.     

Some statistical properties of surface slopes via remote sensing considering a non-Gaussian probability density function

Abstract

Theoretical relationships of statistical properties of surface slope from statistical properties of the image intensity in remotely sensed images, considering a non-Gaussian probability density function of the surface slope, are shown. Considering a variable detector line of sight angle and considering ocean waves moving along a single direction and that the observer and the sun are both in the vertical plane containing this direction, new expressions, using two different glitter functions, between the variance of the intensity of the image and the variance of the surface slopes are derived. In this case, skewness and kurtosis moments are taken into account. However, new expressions between correlation functions of the intensities in the image and surface slopes are numerically analyzed; for this case, the skewness moments were considered only. It is possible to observe more changes in these statistical relationships when the Rect function is used. The skewness and kurtosis values are in direct relation with the wind velocity on the sea surface.     

Scattering of inhomogeneous wave by viscoelastic interface crack

Summary The reflection, refraction and scattering of inhomogeneous plane waves of SH type by an interface crack between two dissimilar viscoelastic bodies are investigated. The singular integral equation method is used to reduce the scattering problem into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Then, the singular integral equation is solved numerically by Kurtz's piecewise continous function method. The crack opening displacement and dynamic stress intensity factor characterizing the scattered near-field are estimated for various incident angles, frequencies and relaxation times. The differences on crack opening displacement and stress intensity factor between elastic and viscoelastic interface crack are contrasted. And the effects of incident angle, incident frequency and relaxation time of the viscoelastic material are analyzed and explained by the features of phase lag and energy dissipation of the viscoelastic wave.     

Coherence of two interfering beams modulated by a uniformly moving diffuser

Abstract

Coherence properties are discussed of light which emerges from two pinholes after it has passed through a moving diffuser. The results are used to show how the correlation function of the heights of the diffuser surface and the speed with which the diffuser is moving may be determined from simple interference experiments.     

Role of light intensification by cracks in optical breakdown on surfaces

The intensity distribution of an initially plane light wave incident on planar and conical surface cracks is calculated numerically by using a wave propagation computer code. The results show that light intensity enhancements caused by interference of internal reflections at the crack and the surface are very sensitive to the light polarization, the beam angle of incidence, and the crack geometry (e.g., crack width and orientation with the surface). The light intensity enhancement factor (LIEF) can locally reach 2 orders of magnitude for conical cracks of ideal shape. The electric field direction relative to the crack surfaces determines the light intensity profile around the crack. For normal-incidence illumination on the output surface, total internal reflection at the crack and the surface can occur and leads to higher LIEFs. For identical geometry and illumination conditions, a crack located on the entrance surface of an optic generates electric field enhancements that are weaker than those on the exit surface. As cracks on polished surfaces are randomly oriented, the probability for large intensity enhancements to occur is high. The model is able to predict quantitatively the magnitude of surface laser-induced damage threshold drop and damage propagation enhancement in dielectric materials that are due to cracks.     

Random phase plate for wavefront sensing via phase retrieval and a volume speckle field

A random phase plate is prepared by illuminating a photoresist plate with a fully developed speckle field and using the developed phase plate (DPP) as a diffuser. Wavefront sensing is implemented using phase retrieval based on the recording of speckle intensity patterns at various distances from the DPP and the wave propagation equation. The effects of the roughness height of the DPP on the phase retrieval are investigated. From simulations a roughness height of lambda/10 results in a speckle field that yields good phase reconstruction for the spherical test wavefront incident on the DPP. From the experiments different portions of the DPP that received varying exposures are examined. A section of the phase plate with a characteristic roughness height facilitated the generation of a speckle field that is optimum for the phase retrieval algorithm. Thus a random phase plate with varying roughness height allows optimized measurements of wavefronts with different curvatures. Analytical expressions describing the second-order intensity statistics (fourth-order field statistics) for a field traversing a specific diffuser are presented. This DPP will not give rise to a fully developed speckle field, but knowing the statistics of the depth of the DPP will facilitate a rigorous treatment of the problem.     

Competing risks mixture model for traffic incident duration prediction

Traffic incident duration is known to result from a combination of multiple factors, including covariates such as spatial and temporal characteristics, traffic conditions, and existence of secondary accidents but also the clearance method itself. In this paper, a competing risks mixture model is used to investigate the influence of clearance methods and various covariates on the duration of traffic incidents and predict traffic incident duration. The proposed mixture model considers the uncertainty in any of five clearance methods that occurred. The probability of the clearance method is specified in the mixture by using a multinomial logistic model. Three candidate distributions, namely, generalized gamma, Weibull, and log-logistic are tested to determine the most appropriate probability density function of the parametric survival analysis model. The unobserved heterogeneity is also incorporated into the mixture model in a way that allows parameters to vary across observations based on the three candidate distributions. The methods are illustrated with incident data from Singaporean expressways from January 2010 to December 2011. Regression analysis reveals that the probability of different clearance methods and the duration of traffic incidents are both significantly affected by various factors, such as traffic conditions and incident characteristics. Results show that the proposed mixture model is better than the traditional accelerated failure time model, and it predicts traffic incident duration with reasonable accuracy, as shown by the mean average percent error.     

横浪中船舶的随机混沌运动

采用概率密度函数和数值模拟的方法研究随机横浪中船舶的混沌运动特性和发生混沌运动的临界参数条件。综合考虑非线性阻尼、非线性恢复力矩以及白噪声横浪激励,建立了船舶的横摇非线性随机微分方程。用随机Melnikov均方准则确定混沌运动的系统参数域后,应用路径积分法求解随机微分方程得到了响应的概率密度函数。研究发现:当噪声强度大于混沌临界值时,船舶出现随机混沌运动;对于高的白噪声激励强度,系统响应有两种较大可能的状态并在这两个状态间随机跳跃,这时船舶的运动不稳定并可能发生倾覆。     

Calculation of the statistical characteristics of the light reflected by a rough random cylindrical homogeneous Gaussian surface

Statistical characteristics of light reflected by a rough random cylindrical homogeneous Gaussian surface are investigated using a modified method of specular points, as developed by Gardashov. In this proposed method, a special procedure for determining the light intensity near the caustics has been formulated. The probability distribution of the intensity of reflected light is expressed in terms of a special function, which is determined by the characteristic function of distribution of radii of curvature at the specular points and the distribution density of the number of specular points. The distribution of radii of curvature, derived by Gardashov, and expressed in terms of dimensionless radii of curvature, has a simple expression which does not contain any parameter of the surface (as a surface rms deviation, etc.). Consequently, it is universally valid and applicable to any cylindrical homogeneous Gaussian surface. After modification, the infinite dispersion of the reflected light intensity turns into a finite. The relationship between the distributions of reflected light intensity and the number of specular points, in the form of a Fredholm integral equation of the first kind is obtained. The kernel of the integral equation is expressed in terms of a characteristic function of the radii of curvature at specular points. The validity of formulae and relationships, thus derived, is tested by numerical simulations.     

桅杆的非线性随机研究

通过引入微小白噪声摄动 ,将桅杆的非线性动力方程转变成 Ito随机微分方程的形式 ,采用路径积分推导出该噪声模型响应概率密度函数的形式解 ,根据该函数的分布特征和平均 Poincaré图研究桅杆响应特性受激励参数的影响和混沌现象。算例分析表明 :桅杆响应特性依赖于激励的频率及其强度 ,而与激励方向基本无关 ;共振频率附近激励强度的增长将导致桅杆出现混沌运动 ,结构在水平面内各方向上产生大幅振荡 ,这是造成结构疲劳损伤累积的重要起因。     

Uniform scattering patterns from grating-diffuser cascades for display applications

A cascade of a thick grating and a thin diffuser is shown to scatter radiation efficiently and uniformly over a wide angle. Cascading the grating with a diffuser causes the single-beam power spectrum of the diffuser to be replicated at each diffraction angle of the grating. The grating period is chosen so that the first diffraction order falls near the one-half point of the power-spectrum peak of the diffuser. The relative strengths of the diffraction orders are optimized to obtain uniformity of the resulting intensity distribution in the plane of the diffraction orders. The intensity distribution in the perpendicular plane is governed solely by the diffuser. Such a cylindrical system is considered on the basis of the requirements for projection TV's of a large horizontal span (100 degrees ) and a narrower vertical span (~15 degrees ). Broadband illumination is studied by consideration of three simultaneously illuminating wavelengths. Experimental results are given for a cascade of a grating formed in photoresist and an etched-glass diffuser.     

Experimental Investigation of Some Statistical Properties of Monochromatic Speckle Patterns

Statistical properties of monochromatic, polarized speckle patterns were studied experimentally. The intensity correlation function, the probability density of the spatial derivative of the intensity, and the average number of level crossings of the intensity were measured. The results are compared with theory and a high measuring accuracy obtained using lock-in detection.     

Mie scattering in the time domain. Part 1. The role of surface waves

We computed the Debye series p=1 and p=2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p=1,2 surface wave glory in the time domain.     

The effect of electric field intensity on the microwave sintering of zirconia

One variable in the conventional sintering of a dielectric material such as zirconia is the thermal intensity of phonons incident on the zirconia particles. When sintering is accomplished through the impression of a microwave field on zirconia particles, the rate that sintering occurs is a partial function of the electric field intensity. How the electric field intensity “E” varies over the surface of the zirconia particles will be discussed in this communication.     

Speckle with a finite number of steps

The statistical properties of classical, fully developed speckle must be modified when the speckle is generated by a random walk with a finite number of steps. It is shown that for such speckle, the standard negative-exponential probability density function for speckle intensity often overestimates the probability that the intensity exceeds a given threshold. In addition, while any linear transformation of the fields in a classical speckle pattern does not change the intensity statistics, the same is not true for finite-step speckle. The implications of these facts in certain applications are discussed.     

Nucleation and growth of sputtered and evaporated trigonal selenium films

Critical nucleation temperature experiments, scanning electron microscopy and light microscopy were used to study the nucleation and growth of trigonal Se films deposited by evaporation and sputtering on both gold and anodized aluminum substrates. The major nucleation and growth processes were shown to be the condensation of Se₂ molecules followed by their polymerization into Se_n chains, where n can be very large. In sputtering, these chains have a higher surface mobility, due in part to their higher residual kinetic energy, and thus they can form large trigonal Se crystallites. The high incident kinetic energies also allow the Se to break through the surface contamination of the substrate. This is important since the Se chain mobility should also be dependent on the surface free energy and on the nucleation site density of the substrate. Very adherent large-grained trigonal Se films were grown by sputtering on Au substrates. It was shown that nucleation sites for the large trigonal Se crystallites were not created by the incident flux but are inherent on the substrate. The high energy incident flux did, however, increase nucleation probability for the initial Se₂ condensation. For sputtering on anodized aluminum substrates the combination of low surface energy and high nucleation site density decreased chain mobility and thus prevented formation of large crystallites.     

Second-order statistics of integrated intensities and detected photons,the exact analysis I. Theory

Abstract

We express the exact probability density distribution function as the product of a gamma distribution and a series of associated Laguerre polynomials, with the expansion coefficients determined by moments of the integrated intensity. Orthogonal polynomials with respect to the exact probability distribution function are then expanded in similar fashion. These polynomials are then used to construct an expansion of the joint probability distribution function in the second-order photoelectron statistics. Since the polynomials are identical with the corresponding Laguerre polynomials when the exact probability distribution function is the gamma distribution, the new polynomials are generalized versions of the associated Laguerre polynomials. The joint photoelectron statistics may be studied with these new polynomials.     

Determination of correlation properties of moving diffuser by spectral analyses of the scattered light emerging from two pinholes

Abstract

Correlation properties of light scattered by a moving diffuser are determined by studying the spectral characteristics of the light that emerges from two pinholes placed after the diffuser. These properties are used to determine the correlation functions of the heights of diffuser surface and the speed of the diffuser. The phase of the light on the two pinholes after it has passed through the moving diffuser, is also determined.