Abstract

We present two new techniques for estimating the autocorrelation function, based on the measurement of the mean number of clipped photocounts and on the calculation of the second-order factorial moment of a series of clipped data. The first procedure has the advantage of simplicity, although it produces a poor signal-to-noise ratio. On the other hand, the second technique gives a very good signal-to-noise ratio, when compared with other known methods.

© 1994 Optical Society of America

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References

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  1. E. Jakeman, E. R. Pike, S. Swain, J. Phys. A 4, 517 (1971).
    [CrossRef]
  2. J. Marron, G. M. Morris, J. Opt. Soc. Am. A 2, 1403 (1985).
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  3. E. Jakeman, J. Phys. A 3, 201 (1970).
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  4. B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), Chap. VII.
  5. C. Aime, E. Aristidi, J. Opt. Soc. Am. A 9, 1812 (1992).
    [CrossRef]
  6. M. P. Cagigal, Opt. Commun. 89, 370 (1992).
    [CrossRef]
  7. P. Prieto, L. Vega, M. P. Cagigal, Opt. Commun. 99, 360 (1993).
    [CrossRef]
  8. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  9. C. L. Mehta, Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. VIII, p. 373.
    [CrossRef]

1993 (1)

P. Prieto, L. Vega, M. P. Cagigal, Opt. Commun. 99, 360 (1993).
[CrossRef]

1992 (2)

1985 (1)

1971 (1)

E. Jakeman, E. R. Pike, S. Swain, J. Phys. A 4, 517 (1971).
[CrossRef]

1970 (1)

E. Jakeman, J. Phys. A 3, 201 (1970).
[CrossRef]

Aime, C.

Aristidi, E.

Bevington, P. R.

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

Cagigal, M. P.

P. Prieto, L. Vega, M. P. Cagigal, Opt. Commun. 99, 360 (1993).
[CrossRef]

M. P. Cagigal, Opt. Commun. 89, 370 (1992).
[CrossRef]

Jakeman, E.

E. Jakeman, E. R. Pike, S. Swain, J. Phys. A 4, 517 (1971).
[CrossRef]

E. Jakeman, J. Phys. A 3, 201 (1970).
[CrossRef]

Marron, J.

Mehta, C. L.

C. L. Mehta, Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. VIII, p. 373.
[CrossRef]

Morris, G. M.

Pike, E. R.

E. Jakeman, E. R. Pike, S. Swain, J. Phys. A 4, 517 (1971).
[CrossRef]

Prieto, P.

P. Prieto, L. Vega, M. P. Cagigal, Opt. Commun. 99, 360 (1993).
[CrossRef]

Saleh, B. E. A.

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

Swain, S.

E. Jakeman, E. R. Pike, S. Swain, J. Phys. A 4, 517 (1971).
[CrossRef]

Vega, L.

P. Prieto, L. Vega, M. P. Cagigal, Opt. Commun. 99, 360 (1993).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. A (2)

E. Jakeman, E. R. Pike, S. Swain, J. Phys. A 4, 517 (1971).
[CrossRef]

E. Jakeman, J. Phys. A 3, 201 (1970).
[CrossRef]

Opt. Commun. (2)

M. P. Cagigal, Opt. Commun. 89, 370 (1992).
[CrossRef]

P. Prieto, L. Vega, M. P. Cagigal, Opt. Commun. 99, 360 (1993).
[CrossRef]

Other (3)

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

C. L. Mehta, Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1970), Vol. VIII, p. 373.
[CrossRef]

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

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Figures (2)

Fig. 1
Fig. 1

SNR of the autocorrelation values obtained from the measurement of the MNCP (solid curve) and from the SOFM (dashed curve) as a function of the mean clipped intensity.

Fig. 2
Fig. 2

SNR of the autocorrelation values obtained from the measurement of the MNCP (squares) and from the SOFM (circles) as a function of the delay value.

Equations (22)

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n ( j X ) = P ( 1 , j X ) + 2 P ( 2 , j X ) ,
n c ( j X ) = P ( 1 , j X ) + P ( 2 , j X ) .
n c ( j X ) = n ( j X ) - P ( 2 , j X ) .
G ( 2 ) ( τ = j X , X ) = P [ 2 , ( j + 1 ) X ] - 2 P ( 2 , j X ) + P [ 2 , ( j - 1 ) X ] ,
G ( 2 ) ( τ = j X , X ) = - n c [ ( j + 1 ) X ] + 2 n c ( j X ) - n c [ ( j - 1 ) X ] .
1 = P ( 0 , j X ) + P ( 1 , j X ) + P ( 2 , j X ) ,
n c ( j X ) = 1 - P ( 0 , j X ) .
Var n c ( j X ) = Var P ( 0 , j X ) .
Var P ( 0 , j X ) = P ( 0 , j X ) [ 1 - P ( 0 , j X ) ] / N .
Var n c ( j X ) n c ( j X ) / N .
Var G ( 2 ) ( j X , X ) = Var n c [ ( j + 1 ) X ] + 4 Var n c ( j X ) + Var n c [ ( j - 1 ) X ] { n c [ ( j + 1 ) X ] + 4 n c ( j X ) + n c [ ( j - 1 ) X ] } / N .
SNR n n c 2 / ( 6 j n c / N ) 1 / 2 = 1 6 j n c 3 / 2 N 1 / 2 ,
W ( X , x ) = x x + X I ( θ ) d θ ,
N ( 2 ) ( X ) = W ( X , x ) 2 ,
N c ( 2 ) ( X ) = 0.
N c ( 2 ) ( j X ) = N ( 2 ) ( j X ) - j N ( 2 ) ( X ) .
G ( 2 ) ( τ = j X , X ) = { N c ( 2 ) [ ( j + 1 ) X ] - 2 N c ( 2 ) ( j X ) + N c ( 2 ) [ ( j - 1 ) X ] } / 2.
N c ( 2 ) ( j X ) 2 P c ( 2 , j X ) .
Var P c ( 2 , j X ) P c ( 2 , j X ) / N ,
Var N c ( 2 ) ( X ) 2 N c ( 2 ) ( X ) / N .
Var G ( 2 ) ( j X , X ) { N c ( 2 ) [ ( j + 1 ) X ] + 4 N c ( 2 ) ( j X ) + N c ( 2 ) [ ( j - 1 ) X ] } / 2 N .
SNR N 1 3 j 2 n c N 1 / 2 ,

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