Abstract

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 <i>L</i>«<i>a</i><sup>2</sup>/λ, where <i>L</i> is the path length in the turbulent medium, <i>a</i> 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 (<i>a≲a<sub>e</sub></i>), the power reduction factor Γ is found to be given by Γ≃1-<i>s(a/a<sub>e</sub>)</i><sup>⅗</sup> with <i>s</i> = 0.125 for a tracking axis and <i>s</i> = 0.955 for a fixed axis, where a<sub>e</sub> is a certain effective radius for the fixed case. If the improvement due to tracking is extrapolated to arbitrary <i>a/a<sub>e</sub></i> 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.

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