Linyan Cui

Generalized modified atmospheric spectral model for optical wave propagating through non-Kolmogorov turbulence

A new generalized modified atmospheric spectral model is derived theoretically for wave propagating through non-Kolmogorov turbulence, which has been reported recently by increasing experimental evidence and theoretical investigation. The generalized, modified atmospheric spectrum considers finite turbulence inner and outer scales and has a spectral power law value in the range of 3 to 5 instead of the standard power law value of 11/3. When the inner scale and outer scale are set to zero and infinity, respectively, this spectral model is reduced to the classical non-Kolmogorov spectrum.

Irradiance scintillation for Gaussian-beam wave propagating through weak non-Kolmogorov turbulence

Kolmogorov turbulence theory based models cannot be directly applied in non-Kolmogorov turbulence case, which has been reported recently by increasing experimental evidence and theoretical investigation. In this study, based on the generalized von Karman spectral model, the theoretical expression of the irradiance scintillation index is derived for Gaussian-beam wave propagating through weak non-Kolmogorov turbulence with horizontal path. In the derivation, the expression is divided into two parts for physical analysis purpose and mathematical analysis convenience. This expression considers the influences of finite turbulence inner and outer scales and has a general spectral power law value in the range 3 to 4 instead of standard power law value of 11/3 (for Kolmogorov turbulence). Numerical simulations are conducted to investigate the influences.

Generalized anisotropic turbulence spectra and applications in the optical waves' propagation through anisotropic turbulence.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this work, two theoretical atmosphere refractive-index fluctuations spectral models are derived for optical waves propagating through anisotropic non-Kolmogorov atmospheric turbulence. They consider simultaneously the finite turbulence inner and outer scales and the asymmetric property of turbulence eddies in the orthogonal xy-plane throughout the path. Two anisotropy factors which parameterize the asymmetry of turbulence eddies in both horizontal and vertical directions are introduced in the orthogonal xy-plane, so that the circular symmetry assumption of turbulence eddies in the xy-plane is no longer required. Deviations from the classic 11/3 power law behavior in the spectrum model are also allowed by assuming power law value variations between 3 and 4. Based on the derived anisotropic spectral model and the Rytov approximation theory, expressions for the variance of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov turbulence. Calculations are performed to analyze the derived spectral models and the variance of AOA fluctuations.

Theoretical expressions of the angle-of-arrival variance for optical waves propagating through non-Kolmogorov turbulence

Based on the generalized exponential spectrum for non-Kolmogorov atmospheric turbulence, theoretical expressions of the angle-of-arrival (AOA) variance are derived for plane and spherical optical waves propagating through weak turbulence. Without particular assumption, the new expressions relate the AOA variance to the receiver aperture, finite turbulence inner and outer scales, and the optical wavelength.

Analytical expressions for the angle of arrival fluctuations for optical waves’ propagation through moderate-to-strong non-Kolmogorov refractive turbulence

The effects of moderate-to-strong non-Kolmogorov turbulence on the angle of arrival (AOA) fluctuations for plane and spherical waves are investigated in detail both analytically and numerically. New analytical expressions for the variance of AOA fluctuations are derived for moderate-to-strong non-Kolmogorov turbulence. The new expressions cover a wider range of non-Kolmogorov turbulence strength and reduce correctly to previously published analytic expressions for the cases of plane and spherical wave propagation through both weak non-Kolmogorov turbulence and moderate-to-strong Kolmogorov turbulence cases. The final results indicate that, as turbulence strength becomes greater, the expressions developed with the Rytov theory deviate from those given in this work. This deviation becomes greater with stronger turbulence, up to moderate-to-strong turbulence strengths. Furthermore, general spectral power law has significant influence on the variance of AOA fluctuations in non-Kolmogorov turbulence. These results are useful for understanding the potential impact of deviations from the standard Kolmogorv spectrum.

Analysis of temporal power spectra for optical waves propagating through weak anisotropic non-Kolmogorov turbulence

Analytic expressions for the temporal power spectra of irradiance fluctuations and angle of arrival (AOA) fluctuations are derived for optical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. In the derivation, the anisotropic non-Kolmogorov spectrum is adopted, which adopts the assumption of circular symmetry in the orthogonal plane throughout the path and the same degree of anisotropy along the propagation direction for all the turbulence cells. The final expressions consider simultaneously the anisotropic factor and general spectral power law values. When the anisotropic factor equals one (corresponding to the isotropic turbulence), the derived temporal power spectral models have good consistency with the known results for the isotropic turbulence. Numerical calculations show that the increased anisotropic factor alleviates the atmospheric turbulences influence on the final expressions.

Angle of arrival fluctuations considering turbulence outer scale for optical waves’ propagation through moderate-to-strong non-Kolmogorov turbulence

Based on the generalized von Kármán spectrum and the extended Rytov theory, new analytic expressions for the variance of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through moderate-to-strong non-Kolmogorov turbulence with horizontal path. They consider finite turbulence outer scale and general spectral power law value, and cover a wide range of non-Kolmogorov turbulence strength. When the turbulence outer scale is set to infinite, the new expressions can reduce correctly to previously published analytic expressions [J. Opt. Soc. Am. A, 302188 (2013]. The final results show that the increased turbulence outer scale value enlarges the variance of AOA fluctuations greatly under moderate-to-strong (or strong) non-Kolmogorov turbulence.

Modified anisotropic turbulence refractive-index fluctuations spectral model and its application in moderate-to-strong anisotropic turbulence.

In this study, the modified anisotropic turbulence refractive-index fluctuations spectral model is derived based on the extended Rytov approximation theory for the theoretical investigations of optical plane and spherical waves propagating through moderate-to-strong anisotropic non-Kolmogorov turbulence. The anisotropic factor which parameterizes the asymmetry of turbulence cells or eddies in the horizontal and vertical directions is introduced. The general spectral power law in the range of 3-4 is also considered compared with the conventional classic value of 11/3 for Kolmogorov turbulence. Based on the modified anisotropic turbulence refractive-index fluctuations spectrum, the analytic expressions of the irradiance scintillation index are also derived for optical plane and spherical waves propagating through moderate-to-strong anisotropic non-Kolmogorov turbulence. They are applicable in a wide range of turbulence strengths and can reduce correctly to the previously published results in the special cases of weak anisotropic turbulence and moderate-to-strong isotropic turbulence. Calculations are performed to analyze the derived models.

Influence of asymmetry turbulence cells on the angle of arrival fluctuations of optical waves in anisotropic non-Kolmogorov turbulence.

Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. Very recent analyses of angle of arrival (AOA) fluctuations of an optical wave in anisotropic non-Kolmogorov turbulence have adopted the assumption that the propagation path was in the z-direction with circular symmetry of turbulence cells maintained in the orthogonal xy-plane throughout the path, and one single anisotropy factor was adopted in the orthogonal xy-plane to parameterize the asymmetry of turbulence cells or eddies in both horizontal and vertical directions. In this work, the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane is no longer required, and two anisotropy parameters are introduced in the orthogonal xy-plane to investigate the AOA fluctuations. In addition, deviations from the classic 11/3 spectral power law behavior for Kolmogorov turbulence are allowed by assuming spectral power law value variations between 3 and 4. With the Rytov approximation theory, new theoretical models for the variance of AOA fluctuations are developed for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. When the two anisotropic parameters are equal to each other, they reduce correctly to the recently published results (the circular symmetry assumption of turbulence cells or eddies in the orthogonal xy-plane was adopted). Furthermore, when these two anisotropic parameters equal one, they reduce correctly to the previously published analytic expressions for the cases of optical wave propagation through weak isotropic non-Kolmogorov turbulence.

Video stabilization in atmosphere turbulent conditions based on the Laplacian-Riesz pyramid

Video stabilization in atmosphere turbulent conditions is aimed at removing spatiotemporally varying distortions from video recordings. Conventional shaky video stabilization approaches do not perform effectively under turbulent circumstances due to the erratic motion common to those conditions. Using complex-valued image pyramids, we propose a method to mitigate this erratic motion in videos. First, each frame of a video is decomposed into different spatial frequencies using the Laplacian pyramid. Second, a Riesz transform is adopted to extract the local amplitude and the local phase of each sub-band. Next, low-pass filters are designed to attenuate the local amplitude and phase variations to remove turbulence-induced distortions. Experimental results show that the proposed approach is efficient and provides stabilizing video in atmosphere turbulent conditions.