Beam scintillations for ground-to-space propagation. Part I: Path integrals and analytic techniques.

We extend our theory of on-axis beam scintillations [Waves Random Media 4, 243 (1994)] for the case of propagation on slant turbulent paths, where turbulence is concentrated in a relatively thin layer near the transmitter. Our technique is based on the parabolic equation for optical wave propagation and the Markov approximation for the calculation of statistical moments of beam intensity. This first of two companion papers presents the details of the path integral formulation of the solution for the fourth-order coherence function. We also discuss in detail two analytic techniques that can be used for the treatment of the path integrals.