The power loss due to propagation through a turbulent medium is considered for an optical-heterodyne detection system whose axis tracks perfectly the instantaneous direction for maximum signal power. Pertinent to both fixed- and tracking-axis cases, the general expression for power reduction is found to be given correctly by neglecting the angular diffraction spread of the local-oscillator field and using the signal field evaluated on the optical axis. A plane and broad incident wave is assumed. The result for the tracking aperture is indicated to be given correctly by ray optics if L«a2/λ, where L is the path length in the turbulent medium, a the aperture radius, and λ the signal wavelength, whereas for a fixed aperture the lateral homogeneity of the field is indicated to suffice without this condition. Refractive-index fluctuations are assumed to be described statistically by the usual Kolmogorov spectrum. For moderate aperture (a≲ae), the power reduction factor Γ is found to be given by Γ≃1-s(a/ae)⅗ with s = 0.125 for a tracking axis and s = 0.955 for a fixed axis, where ae is a certain effective radius for the fixed case. If the improvement due to tracking is extrapolated to arbitrary a/ae by conjecture of a fixed factor of increase in the effective radius, the factor of increase in maximum signal-to-noise ratio achievable by tracking is 11.5. To approach the maximum, the frequency response of the tracking system should extend beyond roughly 50 cps.
DAVID M. CHASE, "Power Loss in Propagation Through a Turbulent Medium for an Optical-Heterodyne System with Angle Tracking," J. Opt. Soc. Am. 56, 33-42 (1966)