Abstract

The SNR for an underwater optical heterodyne detection system is defined and an equation for this ratio is derived. The equation allows computation of the SNR when the fields to be mixed have nonuniform irradiance profiles and are partially coherent. Effects of backscattered light on the SNR are considered. Curves showing the effect of backscattered light on the SNR are presented.

© 1972 Optical Society of America

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References

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  1. S. Q. Duntley, J. Opt. Soc. Am. 53, 214 (1963).
    [CrossRef]
  2. H. Hodara, R. Marquedant, A. Merrill, S. Swiadek, Tetra Tech Report No. 104 (Tetra Tech, Inc., Pasadena, California, 1967), p. 37.
  3. S. G. Varnado, A. H. LaGrone, AGARD Conf. Proc. 77, 27 (1970).
  4. J. N. Lahti, Appl. Opt. 8, 1815 (1969).
    [CrossRef] [PubMed]
  5. H. Hodara, R. J. Marquedant, Appl. Opt. 7, 527 (1968).
    [CrossRef] [PubMed]
  6. D. M. Chase, J. Opt. Soc. Am. 56, 33 (1966).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), Chap. 10.
  8. J. N. Lahti, C. M. Nagel, Appl. Opt. 9, 115 (1970).
    [CrossRef] [PubMed]

1970 (2)

S. G. Varnado, A. H. LaGrone, AGARD Conf. Proc. 77, 27 (1970).

J. N. Lahti, C. M. Nagel, Appl. Opt. 9, 115 (1970).
[CrossRef] [PubMed]

1969 (1)

1968 (1)

1966 (1)

1963 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), Chap. 10.

Chase, D. M.

Duntley, S. Q.

Hodara, H.

H. Hodara, R. J. Marquedant, Appl. Opt. 7, 527 (1968).
[CrossRef] [PubMed]

H. Hodara, R. Marquedant, A. Merrill, S. Swiadek, Tetra Tech Report No. 104 (Tetra Tech, Inc., Pasadena, California, 1967), p. 37.

LaGrone, A. H.

S. G. Varnado, A. H. LaGrone, AGARD Conf. Proc. 77, 27 (1970).

Lahti, J. N.

Marquedant, R.

H. Hodara, R. Marquedant, A. Merrill, S. Swiadek, Tetra Tech Report No. 104 (Tetra Tech, Inc., Pasadena, California, 1967), p. 37.

Marquedant, R. J.

Merrill, A.

H. Hodara, R. Marquedant, A. Merrill, S. Swiadek, Tetra Tech Report No. 104 (Tetra Tech, Inc., Pasadena, California, 1967), p. 37.

Nagel, C. M.

Swiadek, S.

H. Hodara, R. Marquedant, A. Merrill, S. Swiadek, Tetra Tech Report No. 104 (Tetra Tech, Inc., Pasadena, California, 1967), p. 37.

Varnado, S. G.

S. G. Varnado, A. H. LaGrone, AGARD Conf. Proc. 77, 27 (1970).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), Chap. 10.

AGARD Conf. Proc. (1)

S. G. Varnado, A. H. LaGrone, AGARD Conf. Proc. 77, 27 (1970).

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), Chap. 10.

H. Hodara, R. Marquedant, A. Merrill, S. Swiadek, Tetra Tech Report No. 104 (Tetra Tech, Inc., Pasadena, California, 1967), p. 37.

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Figures (2)

Fig. 1
Fig. 1

Illustration of the SNR concept in underwater optical detection systems.

Fig. 2
Fig. 2

SNR as a function of receiver radius for an underwater optical heterodyne detection system.

Equations (9)

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SNR = [ ( P i . f . ) ρ 1 - ( P i . f . ) ρ 2 ] / P N .
V ( r ¯ , t ) = A ( r ¯ , t ) exp { j [ ω t + φ ( r ¯ , t ) ] } ,
V T ( r ¯ , t ) = V 0 ( r ¯ , t ) + V s ( r ¯ , t ) + V b ( r ¯ , t ) .
P i . f . = E [ i i . f . 2 ¯ ] .
P i . f . = 2 ( η e h ν ) 2 A A [ Γ o ( r ¯ , r ¯ ; o ) Γ s ( r ¯ , r ¯ ; o ) ] d 2 r ¯ d 2 r ¯ + 2 ( η e h ν ) 2 A A [ Γ o ( r ¯ , r ¯ ; o ) Γ b ( r ¯ , r ¯ ; o ) ] d 2 r ¯ d 2 r ¯ .
SNR = 2 P N ( η e h ν ) 2 A A γ o ( r ¯ , r ¯ ; o ) [ I o ( r ¯ ) ] 1 2 [ I o ( r ¯ ) ] 1 2 × { γ s 1 ( r ¯ , r ¯ ; o ) [ I s 1 ( r ¯ ) ] 1 2 [ I s 1 ( r ¯ ) ] 1 2 - γ s 2 ( r ¯ , r ¯ ; o ) [ I s 2 ( r ¯ ) ] 1 2 [ I s 2 ( r ¯ ) ] 1 2 } d 2 r ¯ d 2 r ¯ .
P N = ( 2 e 2 B η / h ν ) ( P s + P b + P o ) ,
SNR max = η h ν B ( P o + P s + P b ) A A { γ o ( r ¯ , r ¯ ; o ) [ I o ( r ¯ ) ] 1 2 × [ I 0 ( r ¯ ) ] 1 2 γ s ( r ¯ , r ¯ ; o ) [ I s ( r ¯ ) ] 1 2 [ I s ( r ¯ ) ] 1 2 } d 2 r ¯ d 2 r ¯ .
P b = b P L 0 z e - 2 α ξ { 1 - [ ξ / ( ξ 2 + a 2 ) 1 2 ] } d ξ ,

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