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Charnotskii M.,Zel Technologies, LLC
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2013

Monte Carlo (MC) simulation of phase front perturbations by atmospheric turbulence finds numerous applications for design and modeling of the adaptive optics systems, laser beam propagation simulations, and evaluating the performance of the various optical systems operating in the open air environment. Accurate generation of two-dimensional random fields of turbulent phase is complicated by the enormous diversity of scales that can reach five orders of magnitude in each coordinate. In addition there is a need for generation of the long "ribbons" of turbulent phase that are used to represent the time evolution of the wave front. This makes it unfeasible to use the standard discrete Fourier transform-based technique as a basis for the MC simulation algorithm. We propose a new model for turbulent phase: the sparse spectrum (SS) random field. The principal assumption of the SS model is that each realization of the random field has a discrete random spectral support. Statistics of the random amplitudes and wave vectors of the SS model are arranged to provide the required spectral and correlation properties of the random field. The SS-based MC model offers substantial reduction of computer costs for simulation of the wide-band random fields and processes, and is capable of generating long aperiodic phase "ribbons." We report the results of model trials that determine the number of sparse components, and the range of wavenumbers that is necessary to accurately reproduce the random field with a power-law spectrum. © 2013 Optical Society of America.


Charnotskii M.,Zel Technologies, LLC
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2013

A recently published sparse spectrum (SS) model of the phase front perturbations by atmospheric turbulence [J. Opt. Soc. Am. A 30, 479 (2013)] is based on the trigonometric series with discrete random support. The SS model enables fewer computational efforts, while preserving the wide range of scales typically associated with turbulence perturbations. We present an improved version of the SS model that accurately reproduces the powerlaw spectral density of the phase fluctuations in the arbitrary wide spectral band. We examine the higher-order statistics of the SS phase samples for four versions of the SS model. We also present the calculations of the long-exposure Strehl numbers and scintillation index for the different versions of the SS model. A nonoverlapping SS model with a log-uniform partition emerges as the most appropriate for the atmospheric turbulence representation. © 2013 Optical Society of America.


Charnotskii M.,Zel Technologies, LLC
Proceedings of the International Offshore and Polar Engineering Conference | Year: 2012

We propose a novel Sparse Spectrum (SS) model of the sea surface, where each surface realization contains a finite, possibly random, number of sinusoidal components with random frequency, phase and amplitude. Unlike the FFT-based model, the number of spectral components forming the surface is determined by the sea state, but not the desired spatial resolution and domain size. A single constraint on the probability distribution of the wave vectors, and the amplitude variances of the components allows the SS surface to conform to any prescribed spectral density. The SS model is capable of providing a well-defined statistics of the individual waves that are important for the marine engineering and remote sensing applications. Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE).


Charnotskii M.,Zel Technologies, LLC
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2011

We use a rigorous Markov approximation-based propagation model to calculate statistical properties of the instantaneous turbulent Point Spread Function (PSF) for the weak and strong turbulence condition. Long-Term PSF is well known and is currently widely used for the estimates of the optical system performance and simulation of the image distortions caused by turbulence. We discuss some peculiarities of the Long-Term PSF that are related to the specifics of the propagation in turbulence, and are often overlooked in the recent literature. Models for the Short-term PSF have been used since mid-1960's, and were the subject of some recent publications. We review the recently published model and present sample calculations of the Short-term PSF. We calculate the variances of the power in the instantaneous PSF and the Strehl ratio at the average PSF center, and correlation between the total power and the Strehl ratio. This information allows modeling the instantaneous PSF with random width and height. Analysis of the calculation results shows that for the most practical situations random Strehl ratio is a product of two uncorrelated random variables - power and axial directivity. © 2011 SPIE.


Charnotskii M.,Zel Technologies, LLC
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2012

This review paper addresses typical mistakes and omissions that involve theoretical research and modeling of optical propagation through atmospheric turbulence. We discuss the disregard of some general properties of narrow- angle propagation in refractive random media, the careless use of simplified models of turbulence, and omissions in the calculations of the second moment of the propagating wave. We also review some misconceptions regarding short-exposure imaging, propagation of polarized waves, and calculations of the scintillation index of the beam waves. © 2012 Optical Society of America.

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