Abstract

The energy detection of multipulse returns from an optically rough target is considered. A Q-switched laser generates a number of precisely timed giant pulses during a single pumping period. The multipulse signal photoelectron statistics are shown to be negative binomial. The statistical detection performance of single and multipulse systems are compared over a wide range of noise levels. The multipulse range-finder has a power advantage of from 15 dB to over 28 dB under the conditions considered.

© 1967 Optical Society of America

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References

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  1. S. Ackerman, T. S. Morrison, R. L. Iliff, Appl. Opt. 6, 353 (1967).
    [CrossRef] [PubMed]
  2. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
    [CrossRef]
  3. J. W. Goodman, IEEE Trans. AES-2, 526 (1966).
  4. J. W. Goodman, Proc. IEEE 53, 1692 (1965).
  5. J. W. Goodman, Proc. IEEE 53, 1693 (1965).
  6. W. Feller, An Introduction to Probability Theory and Its Applications (John Wiley & Sons, Inc., New York, 1957), 2nd ed., Vol. 1, p. 252.
  7. Ref. 6, p. 253.
  8. Ref. 6, Vol. 1.

1967

1966

J. W. Goodman, IEEE Trans. AES-2, 526 (1966).

1965

J. W. Goodman, Proc. IEEE 53, 1692 (1965).

J. W. Goodman, Proc. IEEE 53, 1693 (1965).

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Ackerman, S.

Feller, W.

W. Feller, An Introduction to Probability Theory and Its Applications (John Wiley & Sons, Inc., New York, 1957), 2nd ed., Vol. 1, p. 252.

Goodman, J. W.

J. W. Goodman, IEEE Trans. AES-2, 526 (1966).

J. W. Goodman, Proc. IEEE 53, 1693 (1965).

J. W. Goodman, Proc. IEEE 53, 1692 (1965).

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Iliff, R. L.

Morrison, T. S.

Appl. Opt.

IEEE Trans.

J. W. Goodman, IEEE Trans. AES-2, 526 (1966).

Proc. IEEE

J. W. Goodman, Proc. IEEE 53, 1692 (1965).

J. W. Goodman, Proc. IEEE 53, 1693 (1965).

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Other

W. Feller, An Introduction to Probability Theory and Its Applications (John Wiley & Sons, Inc., New York, 1957), 2nd ed., Vol. 1, p. 252.

Ref. 6, p. 253.

Ref. 6, Vol. 1.

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Tables (1)

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Table I Comparison of Single and Multipulse Detection for Optically Rough Targets (M = 1).

Equations (15)

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P s ( k ) = [ ( N ¯ s ) k / k ! ] e - N ¯ s ,
P s ( k ) = 0 P s ( k W ) p ( W ) d W ,
P s ( k ) = Γ ( k + M ) Γ ( k + 1 ) Γ ( M ) [ 1 + ( M / N ¯ s ) ] - k [ 1 + ( N ¯ s / M ) ] - M ,
P s ( k ) = [ 1 / ( 1 + N ¯ s ) ] [ N ¯ s / ( 1 + N ¯ s ) ] k .
P s - n ( k ) = ( M M + N ¯ s ) M exp ( - N ¯ n ) ( M - 1 ) ! j = 0 k ( k + M - j - 1 ) ! j ! ( k - j ) ! ( N ¯ n ) j ( N ¯ s M + N ¯ s ) k - j ,
P n ( k ) = [ ( m N ¯ n ) k / k ! ] exp ( - m N ¯ n ) .
F k ( z ) = p / ( 1 - q z ) , ( p + q = 1 ) ,
F k ( m ; z ) = [ p / ( 1 - q z ) ] m .
f ( k ; m , p ) = ( - m k ) p m ( - q ) k , ( - m k ) = ( - m ) ( - m - 1 ) ( - m - k + 1 ) k ! , ( - m 0 ) 1.
m M , p M M + N ¯ s p 0 ,
q N ¯ s M + N ¯ s q 0 , ( - m k ) ( - 1 ) k Γ ( k + M ) Γ ( k + 1 ) Γ ( M ) .
P s ( k ) f ( k ; M , p 0 ) = ( - M k ) ( p 0 ) M ( - q 0 ) k ,
F k ( M ; z ) = [ p 0 / ( 1 - q 0 z ) ] M .
F k ( M m ; z ) = [ p 0 / ( 1 - q 0 z ) ] M m .
f ( k ; M m , p 0 ) = ( - M m k ) ( p 0 ) M m ( - q 0 ) k .

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