First-Order Statistical Properties of Optical Speckle

2020 ◽  
Author(s):  
Joseph W. Goodman
Keyword(s):  
Statistical Properties ◽  
First Order

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (03) ◽  
pp. 648-668
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind. Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals First-order statistical properties of ultrasonic speckles back-scattered from a kind of weak scattering interface

2003 ◽  
Vol 52 (6) ◽  
pp. 1438
Author(s):  
Zhu Hong-Mao ◽  
Wu Yan-Yang ◽  
Huang Zhong-Wen ◽  
Wang Yin-Guan ◽  
Zhu Cheng
Keyword(s):  
Statistical Properties ◽  
First Order ◽  
Weak Scattering

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (3) ◽  
pp. 648-668 ◽  
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind.Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals Some first-order and higher-order statistical properties of polarization speckle (Erratum)

2021 ◽  
Author(s):  
Shengzhu Xiao ◽  
Jianlin Nie ◽  
Steen G. Hanson ◽  
Mitsuo Takeda ◽  
Wei Wang
Keyword(s):  
Higher Order ◽  
Statistical Properties ◽  
First Order

scholarly journals Some first-order and higher-order statistical properties of polarization speckle

2021 ◽  
Author(s):  
Shengzhu Xiao ◽  
Jianlin Nie ◽  
Steen G. Hanson ◽  
Mitsuo Takeda ◽  
Wei Wang
Keyword(s):  
Higher Order ◽  
Statistical Properties ◽  
First Order

Properties of Acoustical Speckle in the Presence of Phase Aberration Part I: First Order Statistics

1988 ◽  
Vol 10 (1) ◽  
pp. 12-28 ◽  
Author(s):  
Gregg E. Trahey ◽  
Stephen W. Smith
Keyword(s):  
Tissue Characterization ◽  
Imaging System ◽  
Focal Point ◽  
Phase Error ◽  
Random Phase ◽  
Statistical Properties ◽  
First Order ◽  
Phase Errors ◽  
Speckle Patterns ◽  
Phase Aberrations

The first order statistical properties of acoustical speckle patterns are studied as a function of several types of random and structured phase error. Such errors may arise from tissue velocity inhomogeneities or limitations in the acoustical imaging system. In this paper, we review the theory describing the statistical properties of speckle, describe a computer model which predicts the mean speckle brightness in the presence of phase aberrations, and report experiments in which we measure the effect of these aberrations on speckle brightness and variance. We find that the average speckle brightness is significantly reduced by even mild phase aberrations. The phase aberrations studied include focal point errors, random phase errors, and structured errors. Good agreement is found between experiment and computer simulation. We then discuss the implications of these results for imaging through aberrating media, tissue characterization and phase compensation methods.

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