Abstract

A Poisson point process presents a series of characteristics that may be used to define functions with a good signal-to-noise ratio. This research describes a statistical function obtained by handling the measured intervals between photopulses and containing the same information about the signal to be analyzed as the triple correlation. This function can be successfully applied to the analysis of low-light-level signals or images.

© 1991 Optical Society of America

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References

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  1. M. P. Cagigal, Opt. Lett. 13, 262 (1988).
    [CrossRef] [PubMed]
  2. D. Newman, A. A. Canas, J. C. Dainty, Appl. Opt. 24, 4210 (1985).
    [CrossRef] [PubMed]
  3. J. C. Dainty, M. J. Northcott, Opt. Commun. 58, 11 (1986).
    [CrossRef]
  4. M. P. Cagigal, C. Camara, Proc. Soc. Photo-Opt. Instrum. Eng. 1027, 204 (1988).
  5. C. Camara, M. P. Cagigal, F. Moreno, F. Gonzalez, J. Phys. D 23, 1015 (1990).
    [CrossRef]
  6. B. E. A. Saleh, B. K. Selinger, Appl. Opt. 16, 1408 (1977).
    [CrossRef] [PubMed]
  7. B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).
  8. P. R. Bebington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

1990 (1)

C. Camara, M. P. Cagigal, F. Moreno, F. Gonzalez, J. Phys. D 23, 1015 (1990).
[CrossRef]

1988 (2)

M. P. Cagigal, Opt. Lett. 13, 262 (1988).
[CrossRef] [PubMed]

M. P. Cagigal, C. Camara, Proc. Soc. Photo-Opt. Instrum. Eng. 1027, 204 (1988).

1986 (1)

J. C. Dainty, M. J. Northcott, Opt. Commun. 58, 11 (1986).
[CrossRef]

1985 (1)

1977 (1)

Bebington, P. R.

P. R. Bebington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Cagigal, M. P.

C. Camara, M. P. Cagigal, F. Moreno, F. Gonzalez, J. Phys. D 23, 1015 (1990).
[CrossRef]

M. P. Cagigal, C. Camara, Proc. Soc. Photo-Opt. Instrum. Eng. 1027, 204 (1988).

M. P. Cagigal, Opt. Lett. 13, 262 (1988).
[CrossRef] [PubMed]

Camara, C.

C. Camara, M. P. Cagigal, F. Moreno, F. Gonzalez, J. Phys. D 23, 1015 (1990).
[CrossRef]

M. P. Cagigal, C. Camara, Proc. Soc. Photo-Opt. Instrum. Eng. 1027, 204 (1988).

Canas, A. A.

Dainty, J. C.

Gonzalez, F.

C. Camara, M. P. Cagigal, F. Moreno, F. Gonzalez, J. Phys. D 23, 1015 (1990).
[CrossRef]

Moreno, F.

C. Camara, M. P. Cagigal, F. Moreno, F. Gonzalez, J. Phys. D 23, 1015 (1990).
[CrossRef]

Newman, D.

Northcott, M. J.

J. C. Dainty, M. J. Northcott, Opt. Commun. 58, 11 (1986).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, B. K. Selinger, Appl. Opt. 16, 1408 (1977).
[CrossRef] [PubMed]

B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).

Selinger, B. K.

Appl. Opt. (2)

J. Phys. D (1)

C. Camara, M. P. Cagigal, F. Moreno, F. Gonzalez, J. Phys. D 23, 1015 (1990).
[CrossRef]

Opt. Commun. (1)

J. C. Dainty, M. J. Northcott, Opt. Commun. 58, 11 (1986).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. P. Cagigal, C. Camara, Proc. Soc. Photo-Opt. Instrum. Eng. 1027, 204 (1988).

Other (2)

B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).

P. R. Bebington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

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Figures (2)

Fig. 1
Fig. 1

Relative error in percent involved in determining F as a function of the number of channels used for N2 = 103, Ī = 0.01, and F = 0.75 from the measurement of G(3)(τ, τ′) (solid curve) and from M(τ, τ′) (dotted curve).

Fig. 2
Fig. 2

Relative error in percent involved in determining F as a function of the mean intensity for N2 = 103, Nc = 20, and F = 0.95 from the measurement of G(3)(τ, τ′) (solid curve) and from M(τ, τ′) (dotted curve).

Equations (19)

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ω n = W [ ( n - 1 ) T , T ] = ( n - 1 ) T n T I ( θ ) d θ ,
G ( 3 ) ( τ , τ , T ) = W ( θ , T ) W ( θ + τ , T ) W ( θ + τ , T ) ,
P f ( t 1 ) = I ( t 1 ) exp [ - W ( 0 , t 1 ) ] ,
P f ( t 1 ) I ( t 1 ) .
P f ( t 1 , t 2 , t 3 ) = I ( t 1 ) I ( t 2 ) I ( t 3 ) exp [ - W ( 0 , t 3 ) ] .
P f ( t 1 , t 2 , t 3 ) I ( t 1 ) I ( t 2 ) I ( t 3 ) ,
P f ( t 1 , t 2 , t 3 ) P f ( t 1 ) P f ( t 2 ) P f ( t 3 ) .
P f ( K Δ T ) = ( K - 1 ) Δ T K Δ T P f ( t i ) d t i .
M ( J Δ T , L Δ T ) = ( 1 / N c ) K = 1 N c P f ( K Δ T ) P f [ ( K + J ) Δ T ] × P f [ ( K + L ) Δ T ] ,
Var P f ( t , t , t ) P f ( t , t , t ) 6 / N c 3 .
Var M ( τ , τ ) M ( τ , τ ) 6 / N c 4 ,
SNR M = [ M ( τ , τ ) N c 4 / 6 ] 1 / 2 .
Var G ( 3 ) ( τ , τ ) = G ( 3 ) ( τ , τ ) / N 2
SNR G = [ G ( 3 ) ( t , t ) N 2 ] 1 / 2 .
Var α = { i = 1 L [ f ( α , t i ) / α ] 2 / Var f ( α , t i ) } - 1 ,
I ( t ) = I ¯ [ 1 + F cos ( ω t ) ] ,
P f ( K Δ T ) = I ¯ Δ T { 1 + A cos [ ( K + 0.5 ) Δ T ω ] } ,
A = F sin ( ω Δ T / 2 ) / ( ω Δ T / 2 ) ,
M ( J Δ T , L Δ T ) = 1 + A 2 ( C τ + C τ + C τ - τ ) / 2 ,

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