Isoplanatic angle in finite distance: theory analysis on measurement feasibility

Abstract

Previous studies have shown that the isoplanatic angle (θ₀) can be measured by using plane-wave scintillation. The problem of measuring the isoplanatic angle in a finite distance using spherical-wave scintillation is considered in this Letter. Based on theoretical analysis and numerical evaluation, we found that by selecting suitable aperture size and aperture separations, the isoplanatic angle can be estimated through spherical-wave scintillation and covariance of irradiance in three received apertures using a point source. The error of θ₀ measured by this method is less than 6% in typical turbulence models.

Method of Estimation of Turbulence Integral Parameters

“…The linear combination method shows promise of estimating the real-time P d with high accuracy if the suitable W i (u) can be found. As an application example of this method, one can measure the isoplanatic angle in a finite distance through the combination of one spherical wave scintillation and two covariances of intensity in three receive apertures [10], and the validity of this method was proven by real data from the validation experiment [19].…”

“…However, the covariance functions for the angle of arrival or intensity provide more turbulence information due to their potentially large number of PWFs. The covariance of the tilt phase can be measured from the covariance of the angle of arrival [3,4], and the covariance of the piston amplitude can be measured from the covariance of intensity [6,10].…”

Path dependency and angular anisoplanatism in non-Kolmogorov turbulence

“…However, the isoplanatic angle is sensitive to the distribution of turbulence along the imaging path whereas the Fried parameter depends only on the average value. Specifically, turbulence near to the object being observed has a greater effect than the turbulence near to the telescope with a 5/3 path weighting in Kolmogorov turbulence [6]. The 5/3 weighting clearly originates with from the 2/3 power-law description of Kolmogorov turbulence.…”

“…That is to say, turbulence near to the telescope more strongly affects the spatial coherence of a spherical wave source observed by an imaging system. This duality has been successfully used [6], [16] to infer information about the distribution of turbulence along the imaging path.…”