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 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 $\lesssim$a_e), the power reduction factor Γ is found to be given by

with s = 0.125 for a tracking axis and s = 0.955 for a fixed axis, where a. is a_e certain effective radius for the fixed case. If the improvement due to tracking is extrapolated to arbitrary a/a_e 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.

© 1966 Optical Society of America

Effect of a Turbulent Medium on the Power Pattern of a Wavefront-Tracking Circular Aperture*

G. R. Heidbreder and R. L. Mitchell
J. Opt. Soc. Am. 56(12) 1677-1684 (1966)

Consideration of Atmospheric Turbulence in Laser Systems Design

J. I. Davis
Appl. Opt. 5(1) 139-147 (1966)

Multiple Scattering of Light in a Turbulent Atmosphere

P. M. Livingston
J. Opt. Soc. Am. 56(12) 1660-1667 (1966)

Propagation of an Infinite Plane Wave in a Randomly Inhomogeneous Medium

D. L. Fried and J. D. Cloud
J. Opt. Soc. Am. 56(12) 1667-1676 (1966)

Validity of the Rytov Approximation in Optical Propagation Calculations*

W. P. Brown
J. Opt. Soc. Am. 56(8) 1045-1052 (1966)