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
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.
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
When light radiating from a distant object passes through extended turbulence, the light is scintillated. Such scintillated light may be received by an optical system and passed to a camera in the focal plane, and used to track an object. Such trackers often use centroid trackers. Then a laser or other light may be projected back toward the object, steered by the centroid measured on the tracker. The presence of scintillation on the tracker return will cause a jitter error in the pointing of projected light, if the projected light's intensity differs from that of the incoming scintillation pattern. This error is caused by a lack of full-field conjugation of the tilt component of the received return. This error is considered, for horizontal path conditions, as a difference between centroid tilt and gradient tilt. The estimated error is typically not large, and is estimated by both simulation and analytic means, and these are found to agree for conditions of interest. The possibility of means for correction of this error is discussed briefly.
ABSTRACT
A pupil plane imaging system, consisting of a camera and optics that image the entrance pupil of a telescope, measures scintillation induced by atmospheric turbulence. Algorithms are developed to estimate the distribution of turbulence from scintillation assuming the well known relationship between scintillation scale size and the range of turbulence layer. The algorithms were exercised using a 75 cm pupil within a 1 meter telescope located at North Oscura Peak in New Mexico, based on light from a source 52.6 km away. Estimates of the C(n)(2) profile over the path are derived using coarse range bins. From the C(n)(2) profile, an estimate of Fried's transverse coherence length was computed and compared with that from other sensors. The algorithm is tested in several ways. Error sources are discussed, including the intrinsic insensitivity of the technique to turbulence near the pupil.
ABSTRACT
Closed-form integral expressions are developed for the mean and variance of power and energy received from a diffusely reflective object upon illumination by laser radiation with partial temporal coherence. Expressions are presented in dimensionless form and analytic approximations to the integrals are given for signal variations at a receiver caused by fully developed laser speckle. Results are presented in terms of three parameters: the mutual Fresnel number of the receiver and object, the number of longitudinal modes of the illuminating source, and the dimensionless mode spacing of the illuminating source. The calculations assume high light levels and free-space geometry.
