ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
The boresight and atmospheric jitter errors in a satellite tracking experiment are currently estimated by matching the probability density function (PDF) of the received signal counts with a set of PDFs of the signal for several combinations of jitter and boresight errors and then the best choice of jitter and boresight error is accepted via the chi-square test. Here a technique that can estimate atmospheric beam jitter and boresight error directly in a satellite active tracking experiment using the moments of the returns off the satellites is proposed. That is, we use the theoretical PDF for the signal return from a small target and compute the corresponding theoretical PDF moments. We can then form a few equations from these moments with only two unknowns, namely, the jitter and boresight. Solving for the unknowns is then unambiguous and very rapid. The method is valid for small physical cross-section targets and has been verified by using simulation and experimental data. Extending the case to asymmetric jitter and asymmetric boresight is possible.
