Abstract

In the heterodyne receiver considered here, a coherent optical signal and incoherent gaussian background radiation impinge on a photosensitive surface together with the beam from a laser functioning as a local oscillator. The moment-generating function for the output current is derived. When the laser beam is much stronger than either signal or background, the output current consists of an IF signal and gaussian noise. The effective signal-to-noise ratio that determines the detectability of the signal is calculated as a function of the signal and local-oscillator fields at the photosurface. An integral equation is given for the local-oscillator field that maximizes the signal-to-noise ratio; it involves the signal field and the coefficient of partial coherence of the background. For a uniform background, the local-oscillator field must be a replica of the signal field.

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  1. A. T. Forrester, J. Opt. Soc. Am. 51, 253 (1961).
  2. M. Ross, Laser Receivers (John Wiley & Sons, Inc., New York, 1966).
  3. C. W. Helstrom, Statistical Theory of Signal Detection (Pergamon Press, Oxford, 1960), Ch. IV, Sec. 2, pp. 91–95.
  4. L. Mandel, Proc. Phys. Soc. (London) 81, 1104 (1963).
  5. Ref. 3, Ch. I, Sec. 3, pp. 11–15
  6. R. J. Glauber, Phys. Rev. 130, 2529 (1963).
  7. L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965). See Sec. 5.6, pp. 261–264.
  8. Ref. 3, Ch. II, Sec. 5, pp. 50–55.
  9. L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
  10. Ref. 7, Sec. 3.1, pp. 235–242, and Sec. 5.5, pp. 260–261.
  11. P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).
  12. The moment-generating function of a random variable x is the expected value 〈expzx〉. It differs from the familiar characteristic function only by a factor i in the exponent.
  13. Ref. 3, Ch. V, Sec. 2, pp. 142–149.
  14. H. Morawitz, Phys. Rev. 139, A1072 (1965).
  15. H. Gamo, J. Opt. Soc. Am. 56, 441 (1966).
  16. Ref. 3, Ch. V, pp. 129–165,
  17. If the background radiation is thought of as turning the aperture into an incoherent source of luminance proportional to |τ(ξ)|2, this is just the van Cittert—Zernike theorem. See M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Sec. 10.4.2, pp. 505–511.
  18. B. Oliver, Proc. IRE 49, 1960 (1961).
  19. Ref. 3, p. 91.
  20. E. Parzen, Modern Probability Theory and Its Applications (John Wiley & Sons, Inc., New York, 1960). See p. 399, p. 407.
  21. Ref. 3, p. 177.
  22. S. O. Rice, Bell System Tech. J. 23, 282 (1944). See Sec. 1.5.
  23. M. Kac and A. J. F. Siegert, J. Appl. Phys. 18, 383 (1947).
  24. D. A. Darling and A. J. F. Siegert, Trans. IRE IT-3, 32, 38 (1957).

Born, M.

If the background radiation is thought of as turning the aperture into an incoherent source of luminance proportional to |τ(ξ)|2, this is just the van Cittert—Zernike theorem. See M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Sec. 10.4.2, pp. 505–511.

Darling, D. A.

D. A. Darling and A. J. F. Siegert, Trans. IRE IT-3, 32, 38 (1957).

Forrester, A. T.

A. T. Forrester, J. Opt. Soc. Am. 51, 253 (1961).

Gamo, H.

H. Gamo, J. Opt. Soc. Am. 56, 441 (1966).

Glauber, R. J.

R. J. Glauber, Phys. Rev. 130, 2529 (1963).

Helstrom, C. W.

C. W. Helstrom, Statistical Theory of Signal Detection (Pergamon Press, Oxford, 1960), Ch. IV, Sec. 2, pp. 91–95.

Kac, M.

M. Kac and A. J. F. Siegert, J. Appl. Phys. 18, 383 (1947).

Kelley, P. L.

P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).

Kleiner, W. H.

P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).

Mandel, L.

L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).

L. Mandel, Proc. Phys. Soc. (London) 81, 1104 (1963).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965). See Sec. 5.6, pp. 261–264.

Morawitz, H.

H. Morawitz, Phys. Rev. 139, A1072 (1965).

Oliver, B.

B. Oliver, Proc. IRE 49, 1960 (1961).

Parzen, E.

E. Parzen, Modern Probability Theory and Its Applications (John Wiley & Sons, Inc., New York, 1960). See p. 399, p. 407.

Rice, S. O.

S. O. Rice, Bell System Tech. J. 23, 282 (1944). See Sec. 1.5.

Ross, M.

M. Ross, Laser Receivers (John Wiley & Sons, Inc., New York, 1966).

Siegert, A. J. F.

M. Kac and A. J. F. Siegert, J. Appl. Phys. 18, 383 (1947).

D. A. Darling and A. J. F. Siegert, Trans. IRE IT-3, 32, 38 (1957).

Wolf, E.

If the background radiation is thought of as turning the aperture into an incoherent source of luminance proportional to |τ(ξ)|2, this is just the van Cittert—Zernike theorem. See M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Sec. 10.4.2, pp. 505–511.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965). See Sec. 5.6, pp. 261–264.

Other (24)

A. T. Forrester, J. Opt. Soc. Am. 51, 253 (1961).

M. Ross, Laser Receivers (John Wiley & Sons, Inc., New York, 1966).

C. W. Helstrom, Statistical Theory of Signal Detection (Pergamon Press, Oxford, 1960), Ch. IV, Sec. 2, pp. 91–95.

L. Mandel, Proc. Phys. Soc. (London) 81, 1104 (1963).

Ref. 3, Ch. I, Sec. 3, pp. 11–15

R. J. Glauber, Phys. Rev. 130, 2529 (1963).

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965). See Sec. 5.6, pp. 261–264.

Ref. 3, Ch. II, Sec. 5, pp. 50–55.

L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).

Ref. 7, Sec. 3.1, pp. 235–242, and Sec. 5.5, pp. 260–261.

P. L. Kelley and W. H. Kleiner, Phys. Rev. 136, A316 (1964).

The moment-generating function of a random variable x is the expected value 〈expzx〉. It differs from the familiar characteristic function only by a factor i in the exponent.

Ref. 3, Ch. V, Sec. 2, pp. 142–149.

H. Morawitz, Phys. Rev. 139, A1072 (1965).

H. Gamo, J. Opt. Soc. Am. 56, 441 (1966).

Ref. 3, Ch. V, pp. 129–165,

If the background radiation is thought of as turning the aperture into an incoherent source of luminance proportional to |τ(ξ)|2, this is just the van Cittert—Zernike theorem. See M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Sec. 10.4.2, pp. 505–511.

B. Oliver, Proc. IRE 49, 1960 (1961).

Ref. 3, p. 91.

E. Parzen, Modern Probability Theory and Its Applications (John Wiley & Sons, Inc., New York, 1960). See p. 399, p. 407.

Ref. 3, p. 177.

S. O. Rice, Bell System Tech. J. 23, 282 (1944). See Sec. 1.5.

M. Kac and A. J. F. Siegert, J. Appl. Phys. 18, 383 (1947).

D. A. Darling and A. J. F. Siegert, Trans. IRE IT-3, 32, 38 (1957).

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