Abstract

A matrix method is developed for calculating the heterodyne efficiency of an optical receiver, taking into account the local oscillator field distribution, the receiving optics, and the atmospheric turbulence. The heterodyne efficiency in a circular symmetric receiver is given by a product of several matrices, each representing one of the optical parameters of the system, such as defocusing, Fresnel number of the optical system, central obscuration, or atmospheric coherence radius.

© 1983 Optical Society of America

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References

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1981

1980

1979

1976

1975

1974

1972

1971

P. A. Belanger, R. Tremblay, Can. J. Phys. 49, 1290 (1971).
[CrossRef]

1969

1967

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

1964

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

Abbas, M. M.

Belanger, P. A.

P. A. Belanger, R. Tremblay, Can. J. Phys. 49, 1290 (1971).
[CrossRef]

Buhl, D.

Clifford, S. F.

Cohen, S. C.

Collins, S. A.

Degnan, J. J.

Fried, D. L.

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

Fukumitsu, O.

Gagliardi, R. M.

R. M. Gagliardi, S. Karps, Optical Communications (Wiley, London, 1976).

Gradszteyn, I. S.

I. S. Gradszteyn, I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1980).

Karps, S.

R. M. Gagliardi, S. Karps, Optical Communications (Wiley, London, 1976).

Klein, B. J.

Kostiuk, T.

McElroy, J. H.

McGuire, D.

Moreland, J. P.

Mumma, M. J.

Rye, B. J.

Ryzhik, I. M.

I. S. Gradszteyn, I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1980).

Saga, N.

Slepian, D.

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

Tanaka, K.

Teich, M. C.

M. C. Teich, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic, New York, 1970), Vol. 5, p. 361.
[CrossRef]

Tremblay, R.

P. A. Belanger, R. Tremblay, Can. J. Phys. 49, 1290 (1971).
[CrossRef]

Wandzura, S.

Yura, H. T.

Appl. Opt.

Bell Syst. Tech. J.

D. Slepian, Bell Syst. Tech. J. 43, 3009 (1964).

Can. J. Phys.

P. A. Belanger, R. Tremblay, Can. J. Phys. 49, 1290 (1971).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Proc. IEEE

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

Other

R. M. Gagliardi, S. Karps, Optical Communications (Wiley, London, 1976).

M. C. Teich, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic, New York, 1970), Vol. 5, p. 361.
[CrossRef]

E. D. Hinkley, Ed., Laser Monitoring of the Atmosphere (Springer, Berlin, 1976).
[CrossRef]

I. S. Gradszteyn, I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1980).

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Equations (29)

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SNR = ( η het P s ) / ( h ν B ) ,
η het = η Q A A d r 1 d r 2 J S ( r 1 , r 2 ) u * L B ( r 1 ) u L B ( r 2 ) D | u LO ( r ) | 2 d r A J S ( r , r ) d r ,
P X ( r ) = { 1 r X , 0 otherwise ,
u B ( r ) = u L B ( r ) P A ( r ) , u L ( r ) = U LO ( r ) P D ( r ) , I ( r ) = J s ( r , r ) P A ( r ) .
η het = η Q 0 J s ( ρ ) M L ( ρ ) ρ d ρ 0 | u L ( r ) | 2 r d r 0 I ( r ) r d r ,
M L ( ρ ) = 0 u * B ( r ) u B ( r + ρ ) r d r .
J s ( ρ ) = J s ( ρ ) · P 2 ξ a 2 ( ρ ) ξ 1 ,
η het = 2 π η Q 0 J ˜ s ( ω ) | u ˜ B ( ω ) | 2 ω d ω 0 | u L ( r ) | 2 r d r 0 I ( r ) r d r ,
f ˜ ( ω ) = 0 f ( r ) J 0 ( ω r ) r d r ,
u ˜ B ( ω ) = A 1 η 1 d x 2 exp [ i F 2 ( c 1 ) x 2 2 ] K 0 ( a 2 ω x 2 ) 0 1 u ( x 1 ) × exp ( i F 1 c x 1 2 ) K 0 ( c α 2 x 1 x 2 ) d x 1 ,
J ˜ s ( ω ) = A 2 0 1 f t ( x ) K 0 ( 2 ξ a 2 ω x ) d x ,
T n ( x ) = 2 ( 2 n + 1 ) x 1 / 2 P n ( 1 2 x 2 ) ,
0 1 T n ( x ) T m ( x ) d x = δ n , m ( Kronecker delta )
0 1 T n ( x 1 ) K 0 ( c x 1 x 2 ) d x 1 = 2 ( 2 n + 1 ) J 2 n + 1 ( c x 2 ) c x 2 .
u ( x ) = i = 0 u i T i ( x ) ,
f t ( x ) = j = 0 f j T j ( x ) ,
K 0 ( c x 1 x 2 ) = m , n = 0 M c ( n , m ) T n ( x 1 ) T m ( x 2 ) .
u ˜ B ( ω ) = A 1 m , k , l , j , i = 0 I ( m , k ) · L F 2 ( c 1 ) ( k , l ) · M c α 2 ( l , j ) · L F 1 c ( j , i ) · u * i 2 ( 2 m + 1 ) J 2 m + 1 ( a 2 ω ) a 2 ω ,
L Δ ( j , i ) = 0 1 T j ( x ) exp ( i Δ x 2 ) T i ( x ) d x ,
I ( m , k ) = η 1 T m ( x ) T K ( x ) d x .
u ˜ B ( ω ) = m = 0 2 ( 2 m + 1 ) b m J 2 m + 1 ( a 2 ω ) a 2 ω .
B = A 1 I × L F 2 ( c 1 ) × M c α 2 × L F 1 c × U ,
M tot = A 1 × I × L F 2 ( c 1 ) × M c α 2 × L F 1 c .
J ˜ s ( ω ) = 2 ξ a 2 n = 0 2 ( 2 n + 1 ) f n J 2 n + 1 ( 2 ξ a 2 ω ) ω .
η het = A 3 × U × M tot × K × M tot × U ,
K ( i , j ) = l = 0 ( 2 i + 1 ) ( 2 j + 1 ) ( 2 l + 1 ) S ( i , j , l ) f l ,
S ( i , j , l ) = 0 J 2 i + 1 ( x ) J 2 j + 1 ( x ) J 2 l + 1 ( 2 ξ x ) x 2 d x .
S ( i , j , l ) = 1 8 ξ 1 ( 2 ξ ) 2 ( i + j ) Γ ( 1 + l i j ) · m , n Γ ( i + j l + m + n ) Γ ( i + j l ) · ( i + j + l + m + n ) ! ( 2 i + 1 + m ) ! ( 2 j + 1 + n ) ! m ! n ! ( 1 2 ξ ) 2 ( m + n ) .
[ ( M tot × K × M tot ) η het ] U = 0

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