V. S. Rao Gudimetla

Analytical expressions for the log-amplitude correlation function for plane wave propagation in anisotropic non-Kolmogorov refractive turbulence

An analytical expression for the log-amplitude correlation function for plane wave propagation through anisotropic non-Kolmogorov turbulent atmosphere is derived. The closed-form analytic results are based on the Rytov approximation. These results agree well with wave optics simulation based on the more general Fresnel approximation as well as with numerical evaluations, for low-to-moderate strengths of turbulence. The new expression reduces correctly to the previously published analytic expressions for the cases of plane wave propagation through both nonisotropic Kolmogorov turbulence and isotropic non-Kolmogorov turbulence cases. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.

Deep turbulence effects compensation experiments with a cascaded adaptive optics system using a 3.63 m telescope

Compensation of extended (deep) turbulence effects is one of the most challenging problems in adaptive optics (AO). In the AO approach described, the deep turbulence wave propagation regime was achieved by imaging stars at low elevation angles when image quality improvement with conventional AO was poor. These experiments were conducted at the U.S. Air Force Maui Optical and Supercomputing Site (AMOS) by using the 3.63 m telescope located on Haleakala, Maui. To enhance compensation performance we used a cascaded AO system composed of a conventional AO system based on a Shack-Hartmann wavefront sensor and a deformable mirror with 941 actuators, and an AO system based on stochastic parallel gradient descent optimization with four deformable mirrors (75 control channels). This first-time field demonstration of a cascaded AO system achieved considerably improved performance of wavefront phase aberration compensation. Image quality was improved in a repeatable way in the presence of stressing atmospheric conditions obtained by using stars at elevation angles as low as 15 degrees.

Analytical expressions for the log-amplitude correlation function of a plane wave through anisotropic atmospheric refractive turbulence

The effect of anisotropic Kolmogorov turbulence on the log-amplitude correlation function for plane-wave fields is investigated using analysis, numerical integration, and simulation. A new analytical expression for the log-amplitude correlation function is derived for anisotropic Kolmogorov turbulence. The analytic results, based on the Rytov approximation, agree well with a more general wave-optics simulation based on the Fresnel approximation as well as with numerical evaluations, for low and moderate strengths of turbulence. The new expression reduces correctly to previously published analytic expressions for isotropic turbulence. The final results indicate that, as asymmetry becomes greater, the Rytov variance deviates from that given by the standard formula. This deviation becomes greater with stronger turbulence, up to moderate turbulence strengths. The anisotropic effects on the log-amplitude correlation function are dominant when the separation of the points is within the Fresnel length. In the direction of stronger turbulence, there is an enhanced dip in the correlation function at a separation close to the Fresnel length. The dip is diminished in the weak-turbulence axis, suggesting that energy redistribution via focusing and defocusing is dominated by the strong-turbulence axis. The new analytical expression is useful when anisotropy is observed in relevant experiments.

Analytical expressions for the log-amplitude correlation function for spherical wave propagation through anisotropic non-Kolmogorov atmosphere

An analytical expression for the log-amplitude correlation function based on the Rytov approximation is derived for spherical wave propagation through an anisotropic non-Kolmogorov refractive turbulent atmosphere. The expression reduces correctly to the previously published analytic expressions for the case of spherical wave propagation through isotropic Kolmogorov turbulence. These results agree well with a wave-optics simulation based on the more general Fresnel approximation, as well as with numerical evaluations, for low-to-moderate strengths of turbulence. These results are useful for understanding the potential impact of deviations from the standard isotropic Kolmogorov spectrum.

Anisotropic non-Kolmogorov turbulence phase screens with variable orientation

We describe a modification to fast Fourier transform (FFT)-based, subharmonic, phase screen generation techniques that accounts for non-Kolmogorov and anisotropic turbulence. Our model also allows for the angle of anisotropy to vary in the plane orthogonal to the direction of propagation. In addition, turbulence strength in our model is specified via a characteristic length equivalent to the Fried parameter in isotropic, Kolmogorov turbulence. Incorporating this feature enables comparison between propagating scenarios with differing anisotropies and power-law exponents to the standard Kolmogorov, isotropic model. We show that the accuracy of this technique is comparable to other FFT-based subharmonic methods up to three-dimensional spectral power-law exponents around 3.9.

Phase screen simulations of laser propagation through non-Kolmogorov atmospheric turbulence

Phase Screen simulations for laser propagation through non-Kolmogorov turbulence are presented and the results for scintillation index and correlation functions for the intensity are compared with the theory at low turbulence levels at selected non-Kolmogorov exponents. Additional simulation results are presented the strong turbulence region. In particular, effects of transitioning from Kolmogorov to non-Kolmogorov turbulence using their spectral equivalence at the Fresnel scale (as suggested in the literature) on the scintillation index and correlation functions at the receiver are examined for two example paths.

Moment-matching method for extraction of asymmetric beam jitters and bore sight errors in simulations and experiments with actively illuminated satellites of small physical cross section

Optical returns from remote resident space-based objects such as satellites suffer from pointing and tracking errors. In a previously reported paper [Appl. Opt.46, 5608 (2007)APOPAI0003-693510.1364/AO.46.005608], we developed a moment-matching technique that used the statistics of time series of these optical returns to extract information about bore sight and symmetric beam jitter errors (symmetric here implies that the standard deviations of the jitter measured along two orthogonal axes, perpendicular to the line of sight, are equal). In this paper, we extend that method to cover the case of asymmetric beam jitter and bore sight. The asymmetric beam jitter may be due to the combination of symmetric atmospheric turbulence beam jitter and optical beam train jitter. In addition, if a tracking control system is operating, even the residual atmospheric tracking jitter could be asymmetric because the power spectrum is different for the slewing direction compared to the cross-track direction. Analysis of the problem has produced a set of nonlinear equations that can be reduced to a single but much higher-order nonlinear equation in terms of one of the jitter variances. After solving for that jitter, all the equations can be solved to extract all jitter and bore sight errors. The method has been verified by using simulations and then tested on experimental data. In order to develop this method, we derived analytical expressions for the probability density function and the moments of the received total intensity. The results reported here are valid for satellites of small physical cross section, or else those with retroreflectors that dominate the signal return. The results are, in general, applicable to the theory of noncircular Gaussian speckle with a coherent background.

Approach to atmospheric laser-propagation theory based on the extended Huygens–Fresnel principle and a self-consistency concept

We propose a self-consistency condition based on the extended Huygens-Fresnel principle, which we apply to the propagation kernel of the mutual coherence function of a partially coherent laser beam propagating through a turbulent atmosphere. The assumption of statistical independence of turbulence in neighboring propagation segments leads to an integral equation in the propagation kernel. This integral equation is satisfied by a Gaussian function, with dependence on the transverse coordinates that is identical to the previous Gaussian formulation by Yura [Appl. Opt.11, 1399 (1972)APOPAI0003-693510.1364/AO.11.001399], but differs in the transverse coherence lengths dependence on propagation distance, so that this established version violates our self-consistency principle. Our formulation has one free parameter, which in the context of Kolmogorovs theory is independent of turbulence strength and propagation distance. We determined its value by numerical fitting to the rigorous beam propagation theory of Yura and Hanson [J. Opt. Soc. Am. A6, 564 (1989)JOAOD60740-323210.1364/JOSAA.6.000564], demonstrating in addition a significant improvement over other Gaussian models.

Differential piston phase variance in non-Kolmogorov atmospheres

We derive a generalized expression for the differential piston phase variance in non-Kolmogorov turbulence. Specifically, our result applies in the case where index of refraction is described by a power-law medium with an exponent between 0 and 1. Kolmogorov assumptions of homogeneity and isotropy are maintained. After some development, our expression is derived using the Mellin-transform techniques and may be generalized to other forms for the three-dimensional index of refraction turbulence power spectrum. This analytical result has two regions of convergence. The separation between these regions is defined by a characteristic time given as the ratio of the mean wind speed and aperture size. By evaluating this expression, we find the differential piston phase variance exhibits a power-law behavior roughly proportional to that of the medium. In addition, we find that piston phase variance decreases with increase in aperture size. We also find that the differential piston phase variance is independent of aperture size as the power law approaches unity.

Image reconstruction for coherent imaging for space surveillance and directed energy applications

Imaging of distant objects in a terrestrial environment involves propagation of light through significant turbulence. Conventional methods for imaging for these applications are radar or focal plane imaging. Both of these methods have limitations, such as object rotation rate and post-processing. A different class of imaging approaches involving coherent illumination has several advantages (a) reduced sensitivity to illumination conditions, (b) reduced sensitivity to object rotation, (c) the use of arrayed receivers that are lighter and lower in cost, and (d) snapshot reconstruction of aberrated images with just one or a few frames. These advantages must be balanced by the challenges of speckle noise in the image reconstructions, and more difficult algorithms. Coherent pupil-plane and focal-plane techniques are investigated for image formation. The associated algorithms include root-reconstruction techniques, phase smoothing methods, polynomial fit approaches, blind iterative deconvolution, and multi-frame blind deconvolution (MFBD). These techniques and algorithms are surveyed for speed and quality of image formation.