Correlation between the phase and the log-amplitude of a wave through the vertical atmospheric propagation

TL;DR

This paper derives analytical expressions for the correlation between wave phase and log-amplitude during atmospheric propagation, aiding the detection of faint astronomical objects.

Contribution

It provides new analytical formulas for phase-log amplitude correlation in atmospheric turbulence using the Rytov approximation and Mellin transforms.

Findings

Derived angular correlation functions for turbulence profiles

Analytic formulation in the Rytov approximation

Evaluation of correlation properties using synthetic turbulence data

Abstract

Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the confidence level of the detection of faint transient astronomical objects. The properties of the derived angular correlation functions are discussed using usual synthetic turbulence profiles. The close formulation between the phase and the log-amplitude allows an analytic formulation in the Rytov approximation. Equations contain the product of an arbitrary number of hypergeometric functions that are evaluated using the Mellin transforms integration method.