Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. II. Correlation function estimation by numerical processing

1978 ◽  
Vol 9 (1) ◽  
pp. 15-24 ◽  
Author(s):  
F Martin ◽  
J Borgnino
Keyword(s):  
Correlation Function ◽  
Statistical Analysis ◽  
Atmospheric Turbulence ◽  
Function Estimation ◽  
Numerical Processing

scholarly journals A method of generating a random optical field using the Karhunen-Loeve expansion to simulate atmospheric turbulence

2020 ◽  
Vol 44 (1) ◽  
pp. 53-59
Author(s):  
S.N. Khonina ◽  
S.G. Volotovskiy ◽  
M.S. Kirilenko
Keyword(s):  
Numerical Simulation ◽  
Correlation Function ◽  
Atmospheric Turbulence ◽  
Random Environment ◽  
Random Medium ◽  
Optical Field ◽  
Phase Singularity ◽  
Vortex Beams ◽  
Simulation Results ◽  
Random Field Generation

It is proposed to use the random field generation in the numerical simulation of the propagation of radiation through a random medium using method based on the Karhunen–Loeve expansion with various types of correlation operators to describe turbulence simulators. The properties of the calculated simulators of a random medium with a Gaussian correlation function were investigated in modeling the propagation of Laguerre-Gaussian vortex beams. The simulation results showed that an increase in the order of the optical vortex leads, as in the experiment, to lower stability of the phase singularity of the beams to random optical fluctuations. The similarity of the simulation results and the optical experiments indicates the promise of the proposed approach for the synthesis of random environment simulators.

scholarly journals On the Correlation Function of an Arbitrary Distributed Continuous Markov Process

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Correlation Function ◽  
Diffusion Coefficients ◽  
Function Estimation ◽  
Stationary Probability Distribution ◽  
Nonlinear Stochastic Differential Equations ◽  
Continuous Markov Process ◽  
Current Value ◽  
Non Gaussian ◽  
The Given ◽  
And Diffusion

Continuous Markov processes widely used as a tool for modeling random phenomena in numerous applications, can be defined as solutions of generally nonlinear stochastic differential equations (SDEs) with certain drift and diffusion coefficients which together governs the process’ probability density and correlation functions. Usually it is assumed that the diffusion coefficient does not depend on the process' current value. Sometimes, in particular for presentation of non- Gaussian real processes this assumption becomes undesirable, leads generally to complexity of the correlation function estimation. We consider its analysis for the process with arbitrary pair of the drift and diffusion coefficients providing the given stationary probability distribution of the considered process.

Sign in / Sign up

Export Citation Format

Share Document