Some Effects of Spatial and Temporal Coherence in Holography

The following two problems have been investigated theoretically: systematic treatment of image formation in two-beam Fresnel holography from the viewpoint of spatial coherence, and influence of temporal coherence in two-beam Fraunhofer holography.     

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.     

Order Statistics from the Gamma Distribution

This paper deals with order statistics from a gamma or χ² (Pearson Type III) distribution. Expressions are derived for the moments of an order statistic and for the covariance between two order statistics. A table of moments (about the origin as well as the mean) is presented. Equations are derived which are used to solve for the percentage points of the order statistics and a table of the percentage points is given. The problem of the best linear unbiased estimate of the scale parameter of the distribution which is based on order statistics is, briefly, discussed for the censored (type II) case. The modal value of an order statistic is derived and a table of these values is given for the cases of the smallest and the largest order statistics. Applications ‘to life-tests, extreme values, reliability and maintenance are described and illustrated in some cases.     

On the Statistics of Stellar Speckle Patterns and Pupil Plane Scintillation

We report measurements of first-order statistics and temporal correlations of intensity fluctuations in stellar images and in the pupil plane. Measurements in the pupil plane are strongly dependent on zenith angle, whereas simultaneous measurements in the image plane show no such dependence.     

A Note on Moments of Gamma Order Statistics

Previously quadrature approximations were developed to determine the moments of a distribution of the response of a multivariable function when each of the variables is a random variable from a normal distribution. The error was shown to be of the order of the sixth power of the standard deviations of the random variables, but a more useful bound is desired in applied work. Only limited success has been achieved in this direction. It is shown that the best approximating distribution is a Beta distribution of the first kind with β₂ equal to 3 and mean, variance, and β₁ obtained by quadrature, where β₁ and β₂ are standard measures of skewness and kurtosis, respectively. A parametric study of the function X = C_o (a _o, ± y ₁ ± y ₂ ± … ±y_n ) ^m + b _o where the y_i all have the same standard deviation, σ, is conducted both analytically and by quadrature. The mean and variance obtained by quadrature are essentially exact in the range of interest. It is shown that for a large range of σ the above distribution is both a good approximation and a much better approximation than either a normal approximation with the same mean and variance or a linear approximation. The example also shows that the β₂ obtained by quadrature is a poor indicator of the precision of the quadrature approximation.     

Statistics of Speckle Patterns Produced by a Rough Metal Surface

The irradiance in the speckle pattern produced by a rough metal surface illuminated by polarized laser light can be regarded as the sum of the irradiances of two component speckle patterns produced by scattered light polarized in two orthogonal directions. A theoretical analysis is presented which leads to useful approximations for the cross-correlation functions of the component speckle fields both in the far field and in an image of the surface. These results are used to derive the statistics of such speckle patterns.     

The Moments of Log-Weibull Order Statistics

Let X _1n ≤ X _2n ≤,…, ≤ X_nn be the order statistics of a random sample of size n. For any integrable function g(x) define E(i, n) = E(g(X _in )) and M(n) = E(1, n) = E(g(X _1n )). A number of formulae expressing E(i, n) in terms of M(j), j ≤ n, are developed. For example,

These results are applied to obtain the means and variances of the order statistics of a log-Weibull distribution (F(z) = 1 – exp (? exp x)). Tables of these means and variances are given for 1 ≤ i ≤ n, n = 1 (1) 50 (5) 100. The computations were made using a set of 100 decimal place logarithms of integers. Examples of the use of these tables in obtaining weighted least squares estimates from censored samples from a Weibull distribution are also given.     

Spatial and Temporal Coherence of Light in a Fibre Waveguide

Abstract

A general expression for the mutual coherence function of an electromagnetic field propagating in a fibre waveguide is presented by means of classical coherence formalism and the guided modes field representation. Moreover, this expression is applied to a limiting case of the fibre waveguide excitation by cross-spectrally pure, spatially coherent and quasi-monochromatic source with a symmetrical spectrum. In particular, the complex degree of both spatial and temporal coherence at the exit face of a two-mode, weakly-guiding, step-index fibre waveguide is discussed as a function of an exciting condition of guided modes, an intermodal dispersion and a temporal coherence of the source, respectively.     

Study of Induced Temporal Coherence in Optical Parametric Down Conversion

Abstract

Temporal coherence of the idler photon beam induced by a coherent input signal was studied for non-degenerate optical parametric down conversion. When the optical path difference of the interferometer is much longer than the coherence length of the spontaneous idler radiation, the experimental results show that the first-order temporal coherence of the idler photon can be induced by a coherence input signal and the interference fringe visibility is determined by the intensity of the coherent input signal.     

Some General Remarks on Consulting in Statistics

This paper deals with obtaining a prediction interval on a future observation X, in an ordered sample of size n from a two-parameter exponential distribution for the situation where some or all the first r observations X ₁ < X ₂ < … < X _r , 1 ≤ r < s ≤ n, have been observed. The intervals are based on the statistic Z = (X _s , – X _r )/S _v , where S _v , is a function of the observations X ₀ ≡ A < X ₁ < X ₂ < … < X _r , such that X _s – X _r , and S _v , are independent variables and 2vS_v /σ has the distribution χ²(2v). The expressions for the quantiles z_p are given and some problems of numerical determination of z_p 's are discussed. The results can be also applied to related distributions.     

电子束辐照对BBO晶体一阶超极化率的影响

与传统热力学方法不同,本文从辐照电场角度出发研究电子束辐照对BBO（β-BaB2O4）材料的非线性性能影响。利用量子化学方法和有限场方法计算其一阶超极化率β的全部分量,以此分析不同辐照强度下β的改变规律。研究表明：在电子束流强度为50μA的情况下,当射线能量小于400Mev时辐照电场对β的影响不大,平均值βav波动幅度最大仅为3%;此后随射线能量增大βav开始急剧下降,能量越高下降速度越快,420Mev时已经下降10%,材料面临失效的危险。研究结果还表明辐照电场对β三个分量的影响并不一致,随辐照能量增加βx、βy分量呈减小趋势,但βz分量却增加较快,预示着晶体中的共扼π轨道可能受到破坏。     

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.     

Effects of Noise-Induced Coherence on the Performance of Quantum Absorption Refrigerators

We study two models of quantum absorption refrigerators with the main focus on discerning the role of noise-induced coherence on their thermodynamic performance. Analogously to the previous studies on quantum heat engines, we find the increase in the cooling power due to the mechanism of noise-induced coherence. We formulate conditions imposed on the microscopic parameters of the models under which they can be equivalently described by classical stochastic processes and compare the performance of the two classes of fridges (effectively classical vs. truly quantum). We find that the enhanced performance is observed already for the effectively classical systems, with no significant qualitative change in the quantum cases, which suggests that the noise-induced-coherence-enhancement mechanism is caused by static interference phenomena.