Abstract

The reciprocity theorem of Helmholtz is extended to the clear turbulent atmosphere. Two impulse responses (Green’s functions) are defined to characterize optical propagation in opposite directions between two parallel planar apertures separated by the turbulent atmosphere. It is shown that these impulse responses satisfy the same reciprocity condition as the free-space impulse responses do. This result underlies recent studies of adaptive communication systems for the turbulent channel.

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  1. E. V. Hoversten, IEEE Intl. Conv. Record 15 (11), 137 (1967).
  2. A. A. M. Saleh, IEEE J. QE-3, 540 (1967).
  3. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pt. I.
  4. Strictly speaking, we cannot apply Green's theorem to the volume integral in Eq. (8), because the integrand has singularities at the source points. Equation (9) can be obtained rigorously in a straightforward but tedious manner by use of the fact that, for [Equation] sufficiently small, [Equation] Rather than include this lengthy derivation, we have formally applied Green's theorem to obtain Eq. (9) immediately.

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pt. I.

Hoversten, E. V.

E. V. Hoversten, IEEE Intl. Conv. Record 15 (11), 137 (1967).

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pt. I.

Saleh, A. A. M.

A. A. M. Saleh, IEEE J. QE-3, 540 (1967).

Other

E. V. Hoversten, IEEE Intl. Conv. Record 15 (11), 137 (1967).

A. A. M. Saleh, IEEE J. QE-3, 540 (1967).

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pt. I.

Strictly speaking, we cannot apply Green's theorem to the volume integral in Eq. (8), because the integrand has singularities at the source points. Equation (9) can be obtained rigorously in a straightforward but tedious manner by use of the fact that, for [Equation] sufficiently small, [Equation] Rather than include this lengthy derivation, we have formally applied Green's theorem to obtain Eq. (9) immediately.

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