Abstract

The effect of the detector nonlinearity on the statistics of a fluctuating signal is evaluated. The input signal is assumed to be log-normally distributed, which is of interest in the study of the laser propagation through the turbulent atmosphere. Both detector threshold and saturation effects are taken into account.

© 1978 Optical Society of America

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References

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  1. M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Fluctuations of Laser Radiation (Akad. Nauk, Moscow, 1973) (in Russian).
  2. M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).
  3. V. I. Tatarski, Wave Propagation in Turbulent Atmosphere (Nauka, Moscow, 1967) (in Russian).
  4. P. Ciolli, A. Consortini, F. Pasqualetti, L. Ronchi, R. Vanni, Appl. Opt. 16, 1128 (1977).
    [CrossRef]

1977

1974

M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).

Chrupin, A. S.

M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).

Ciolli, P.

Consortini, A.

Gracheva, M. E.

M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Fluctuations of Laser Radiation (Akad. Nauk, Moscow, 1973) (in Russian).

Gurvich, A. S.

M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Fluctuations of Laser Radiation (Akad. Nauk, Moscow, 1973) (in Russian).

Kashkarov, S. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Fluctuations of Laser Radiation (Akad. Nauk, Moscow, 1973) (in Russian).

Lomades, S. O.

M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).

Pasqualetti, F.

Pokasov, V. V.

M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Fluctuations of Laser Radiation (Akad. Nauk, Moscow, 1973) (in Russian).

Ronchi, L.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in Turbulent Atmosphere (Nauka, Moscow, 1967) (in Russian).

Vanni, R.

Appl. Opt.

Radiofisika

M. E. Gracheva, A. S. Gurvich, S. O. Lomades, V. V. Pokasov, A. S. Chrupin, Radiofisika 17, 105 (1974) (in Russian).

Other

V. I. Tatarski, Wave Propagation in Turbulent Atmosphere (Nauka, Moscow, 1967) (in Russian).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. V. Pokasov, Similarity Correlations and Their Experimental Verification in the Case of Strong Fluctuations of Laser Radiation (Akad. Nauk, Moscow, 1973) (in Russian).

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Figures (5)

Fig. 1
Fig. 1

Output signal z vs input signal αS for some values of the parameter αSo.

Fig. 2
Fig. 2

Probability distribution P(z) plotted vs z (dashed lines) for different values of the log-amplitude variance γ of the input signal. Dashed lines refer to the equivalent log-normal distributions: (a) αSo = 1, L′ = 0; (b) αSo = 1, L′ = ln3; (c) αSo = 3, L′ = 0; (d) αSo = 3, L′ = ln3.

Fig. 3
Fig. 3

Log-amplitude variance γz of the detected signal z, plotted vs γ for some values of L'.

Fig. 4
Fig. 4

Skewness coefficient γ1V and excess coefficient γ2V of the detected signal plotted vs γ in the cases αSo = 1 [Figs. 2(a) and 2(b)] and αSo = 3 [Figs. 2(c) and 2(d)]. Dashed lines refer to log-normal distribution.

Fig. 5
Fig. 5

Excess coefficient γ2V plotted vs skewness coefficient γ1V of the detected signal, in the cases (a) αSo = 1; and (b) αSo = 3. Each curve is labeled by the value of γ of the input signal. The dashed line refers to log-normal distribution.

Equations (10)

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V = V ¯ arctan [ α ( S S o ) ] + V o ,
V th = V o 1 2 π V ¯ V sat = V o + 1 2 π V ¯ ,
z = arctan α S o + [ ( V V o ) / V ¯ ]
p ( S ) = 1 ( 2 π ) 1 / 2 γ 1 S exp [ 1 2 γ 2 ( ln S L ) 2 ] ,
P ( z ) = p [ S = 1 α ( α S o + tan y ) ] dS dz ,
y = [ ( V V o ) / V ¯ ] = z arctan α S o .
P ( z ) = 1 ( 2 π ) 1 / 2 γ 1 α S o + tan y 1 cos 2 y × exp { 1 2 γ 2 [ ln ( α S o + tan y ) L ] 2 } ,
L = L + ln α .
γ 1 V = m 3 V m 2 V 3 / 2 , γ 2 V = m 4 V m 2 V 2 3 ,
m n V = ( V V ) n

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