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  1. R. L. Byer, Opt. Quantum Electron. 7, 147 (1975).
    [CrossRef]
  2. T. Kobayasi, H. Inaba, Opt. Commun. 14, 119 (1975).
    [CrossRef]
  3. B. J. Rye, “Antenna Parameters in Incoherent Backscatter Lidar,” accepted for publication in Appl. Opt.The derivation of Eq. (2) is parallel to that of 〈i2〉 in Appendix A in that paper, following the initial premise that the output charge from the photodetector isqt=e∫−∞∞δ(t−t1)dt∫−∞∞δa−a1)da1.The assumptions made in deriving Eq. (3) are that 〈ΦL〉 ≫ 〈ΦR〉, which should be valid in practical systems using ambient atmospheric backscatter at ranges greater than about 100 m, and that the return field is statistically stationary, i.e., that the return field correlation function gS(t1;t2) = gS(t1 − t2) = gS(τ); strictly this cannot be the case for a lidar system, but it is reasonable to suppose the assumption has approximate validity if the return flux varies only slowly over the sampling time τd.
  4. C. M. Sonnenschein, S. A. Horrigan, Appl. Opt. 10, 1600 (1971).
    [CrossRef] [PubMed]
  5. S. O. Rice, Bell Syst. Tech. J. 23, 282 (1944); Bell Syst. Tech. J. 24, 46 (1945); Bell Syst. Tech. J. 27, 109 (1948).
  6. W. B. Davenport, W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).
  7. H. Z. Cummins, H. L. Swinney, Prog. Opt. 8, 123 (1970).
  8. E. Jakeman, C. J. Oliver, E. R. Pike, Adv. Phys. 24, 349 (1975).
    [CrossRef]

1975 (3)

R. L. Byer, Opt. Quantum Electron. 7, 147 (1975).
[CrossRef]

T. Kobayasi, H. Inaba, Opt. Commun. 14, 119 (1975).
[CrossRef]

E. Jakeman, C. J. Oliver, E. R. Pike, Adv. Phys. 24, 349 (1975).
[CrossRef]

1971 (1)

1970 (1)

H. Z. Cummins, H. L. Swinney, Prog. Opt. 8, 123 (1970).

1944 (1)

S. O. Rice, Bell Syst. Tech. J. 23, 282 (1944); Bell Syst. Tech. J. 24, 46 (1945); Bell Syst. Tech. J. 27, 109 (1948).

Byer, R. L.

R. L. Byer, Opt. Quantum Electron. 7, 147 (1975).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, H. L. Swinney, Prog. Opt. 8, 123 (1970).

Davenport, W. B.

W. B. Davenport, W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Horrigan, S. A.

Inaba, H.

T. Kobayasi, H. Inaba, Opt. Commun. 14, 119 (1975).
[CrossRef]

Jakeman, E.

E. Jakeman, C. J. Oliver, E. R. Pike, Adv. Phys. 24, 349 (1975).
[CrossRef]

Kobayasi, T.

T. Kobayasi, H. Inaba, Opt. Commun. 14, 119 (1975).
[CrossRef]

Oliver, C. J.

E. Jakeman, C. J. Oliver, E. R. Pike, Adv. Phys. 24, 349 (1975).
[CrossRef]

Pike, E. R.

E. Jakeman, C. J. Oliver, E. R. Pike, Adv. Phys. 24, 349 (1975).
[CrossRef]

Rice, S. O.

S. O. Rice, Bell Syst. Tech. J. 23, 282 (1944); Bell Syst. Tech. J. 24, 46 (1945); Bell Syst. Tech. J. 27, 109 (1948).

Root, W. L.

W. B. Davenport, W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Rye, B. J.

B. J. Rye, “Antenna Parameters in Incoherent Backscatter Lidar,” accepted for publication in Appl. Opt.The derivation of Eq. (2) is parallel to that of 〈i2〉 in Appendix A in that paper, following the initial premise that the output charge from the photodetector isqt=e∫−∞∞δ(t−t1)dt∫−∞∞δa−a1)da1.The assumptions made in deriving Eq. (3) are that 〈ΦL〉 ≫ 〈ΦR〉, which should be valid in practical systems using ambient atmospheric backscatter at ranges greater than about 100 m, and that the return field is statistically stationary, i.e., that the return field correlation function gS(t1;t2) = gS(t1 − t2) = gS(τ); strictly this cannot be the case for a lidar system, but it is reasonable to suppose the assumption has approximate validity if the return flux varies only slowly over the sampling time τd.

Sonnenschein, C. M.

Swinney, H. L.

H. Z. Cummins, H. L. Swinney, Prog. Opt. 8, 123 (1970).

Adv. Phys. (1)

E. Jakeman, C. J. Oliver, E. R. Pike, Adv. Phys. 24, 349 (1975).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

S. O. Rice, Bell Syst. Tech. J. 23, 282 (1944); Bell Syst. Tech. J. 24, 46 (1945); Bell Syst. Tech. J. 27, 109 (1948).

Opt. Commun. (1)

T. Kobayasi, H. Inaba, Opt. Commun. 14, 119 (1975).
[CrossRef]

Opt. Quantum Electron. (1)

R. L. Byer, Opt. Quantum Electron. 7, 147 (1975).
[CrossRef]

Prog. Opt. (1)

H. Z. Cummins, H. L. Swinney, Prog. Opt. 8, 123 (1970).

Other (2)

B. J. Rye, “Antenna Parameters in Incoherent Backscatter Lidar,” accepted for publication in Appl. Opt.The derivation of Eq. (2) is parallel to that of 〈i2〉 in Appendix A in that paper, following the initial premise that the output charge from the photodetector isqt=e∫−∞∞δ(t−t1)dt∫−∞∞δa−a1)da1.The assumptions made in deriving Eq. (3) are that 〈ΦL〉 ≫ 〈ΦR〉, which should be valid in practical systems using ambient atmospheric backscatter at ranges greater than about 100 m, and that the return field is statistically stationary, i.e., that the return field correlation function gS(t1;t2) = gS(t1 − t2) = gS(τ); strictly this cannot be the case for a lidar system, but it is reasonable to suppose the assumption has approximate validity if the return flux varies only slowly over the sampling time τd.

W. B. Davenport, W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

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Equations (15)

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γ p = 1 2 n n σ p Δ r log e [ Φ R ( 1 ) ( r ) Φ R ( 1 ) ( r + Δ r ) Φ R ( 2 ) ( r + Δ r ) Φ R ( 2 ) ( r ) ] ,
( Δ γ ) 2 1 / 2 = 1 / [ 2 n n σ p Δ r ( S / N ) ] ,
q 2 e 2 η Φ L [ τ d + 2 η η h Φ R n 1 τ d τ d | g S ( τ ) | × cos ω τ d t 1 d t 2 ] ,
h d ( t ) = { 1 if τ d / 2 < t < τ d / 2 0 otherwise ,
h d ( t 1 ) h d ( t 2 ) | g S ( τ ) | d t 1 d t 2 = h d ( t 1 ) h d ( t 1 τ ) | g S ( τ ) | d t 1 d τ = τ d g d ( τ ) | g S ( τ ) | d τ ,
m 1 = τ d / [ g d ( τ ) | g S ( τ ) | d τ ]
q 2 = e 2 η N L ( 1 + 2 η η h δ h ) .
δ h = N R / ( m 1 n 1 )
( S N ) = [ i = 1 4 ( S N ) i 2 ] 1 / 2 .
( Δ q 2 ) 2 = q 4 q 2 2 2 q 2 2 .
( S N ) 1 = q 2 q 2 L [ 2 q 2 2 + 2 q 2 L 2 ] 1 / 2 = 2 η η h δ h { 2 [ 1 + ( 1 + 2 η η h δ h ) 2 ] } 1 / 2 ,
( S N ) 1 = { 1 2 if 2 η η h δ h 1 , η η h δ h if 2 η η h δ h 1.
( S / N ) i = [ ( m n M ) / 2 ] 1 / 2 ,
( Δ γ ) 2 1 / 2 = 1 / [ 2 ( 2 m n M ) 1 / 2 n n σ p Δ r ] .
qt=eδ(tt1)dtδaa1)da1.

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