Abstract

Triple-correlation values are obtained as a combination of second-order factorial moments of the triggered photocount distribution. The signal-to-noise ratio obtained from this kind of measurement is smaller than that obtained from direct calculation of the triple correlation for small time-delay values.

© 1992 Optical Society of America

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References

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  1. L. Mandel, Proc. Phys. Soc. 84, 435 (1964).
    [CrossRef]
  2. B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).
  3. L. Bassano, P. Otonello, Appl. Opt. 21, 3677 (1983).
    [CrossRef]
  4. T. Yoshimura, T. Nakajima, N. Wakabayashi, Appl. Opt. 20, 2993 (1981).
    [CrossRef] [PubMed]
  5. M. P. Cagigal, T. Ariste, Spectrosc. Lett. 22, 279 (1989).
    [CrossRef]
  6. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  7. M. P. Cagigal, Opt. Commun. 61, 1 (1987).
    [CrossRef]

1989 (1)

M. P. Cagigal, T. Ariste, Spectrosc. Lett. 22, 279 (1989).
[CrossRef]

1987 (1)

M. P. Cagigal, Opt. Commun. 61, 1 (1987).
[CrossRef]

1983 (1)

1981 (1)

1964 (1)

L. Mandel, Proc. Phys. Soc. 84, 435 (1964).
[CrossRef]

Ariste, T.

M. P. Cagigal, T. Ariste, Spectrosc. Lett. 22, 279 (1989).
[CrossRef]

Bassano, L.

Bevington, P. R.

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

Cagigal, M. P.

M. P. Cagigal, T. Ariste, Spectrosc. Lett. 22, 279 (1989).
[CrossRef]

M. P. Cagigal, Opt. Commun. 61, 1 (1987).
[CrossRef]

Mandel, L.

L. Mandel, Proc. Phys. Soc. 84, 435 (1964).
[CrossRef]

Nakajima, T.

Otonello, P.

Saleh, B. E. A.

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

Wakabayashi, N.

Yoshimura, T.

Appl. Opt. (2)

Opt. Commun. (1)

M. P. Cagigal, Opt. Commun. 61, 1 (1987).
[CrossRef]

Proc. Phys. Soc. (1)

L. Mandel, Proc. Phys. Soc. 84, 435 (1964).
[CrossRef]

Spectrosc. Lett. (1)

M. P. Cagigal, T. Ariste, Spectrosc. Lett. 22, 279 (1989).
[CrossRef]

Other (2)

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

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

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Figures (2)

Fig. 1
Fig. 1

Triple-correlation variances involved in direct measurement (solid curve) and in triggered delayed factorial moment measurement (dashed curve) as a function of the mean intensity per counting time 〈W〉.

Fig. 2
Fig. 2

Triple-correlation signal-to-noise ratio (SNR) obtained by direct measurement (solid curve) and by triggered delayed factorial moment measurement (dashed curve) as a function of the second time delay.

Equations (29)

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P ( n , t ) = [ W ( t , t + T ) ] n exp [ - W ( t , t + T ) ] / n ! ,
W ( t , t + T ) = t t + T I ( θ ) d θ
P 1 ( m , t , t + T ) = I ( t ) W ( t , t + T ) m × exp [ - W ( t , t + T ) ] / [ I ( t ) m ! ] ,
N ( r ) ( T ) = n ( t , T ) [ n ( t , T ) - 1 ] [ n ( t , T ) - r + 1 ] .
N ( r ) ( T ) = W ( t , t + T ) r .
N 1 ( r ) ( T ) = 0 P ( 1 , t , t + Δ ) W ( t + Δ , t + Δ + T ) r d t 0 P ( 1 , t , t + Δ ) d t ,
P ( 1 , t , t + Δ ) = Δ I ( t ) ,
N 1 ( r ) ( T ) = 0 P I ( t ) W ( t , t + T ) r d t I ( t ) ,
I ( t ) = 0 P I ( t ) d t .
P ( n , θ , t ) = I ( t ) [ W ( t + θ , t + θ + T ) ] n × exp [ - W ( t + θ , t + θ + T ) ] / [ I ( t ) n ! ] .
N 1 ( 2 ) ( T , θ ) = I ( t ) W 2 ( t + θ , t + θ + T ) I ( t ) .
G ( 3 ) ( τ , τ ) = I ( t ) I ( t + τ ) I ( t + τ ) .
G ( 3 ) ( τ , τ ) = W ( t , t + T ) W ( t + τ , t + τ + T ) × W ( t + τ , t + τ + T ) .
N 1 ( 2 ) ( T , θ ) = G ( 3 ) ( θ , θ ) / W ,
N 1 ( 2 ) ( T , θ ) = W ( t ) W 2 ( t , + θ , t + θ + 2 T ) / W ,
W 2 ( t + θ , t + θ + 2 T ) = [ W ( t + θ , t + θ + T ) + W ( t + θ + T , t + θ + 2 T ] 2 = ( W 1 + W 2 ) 2 = W 1 2 + 2 W 1 W 2 + W 2 2 .
G ( 3 ) ( θ , θ + n T ) = W 2 { N 1 ( 2 ) [ ( n + 1 ) T , θ ] - N 1 ( 2 ) ( n T , θ ) - N 1 ( 2 ) ( n T , θ + T ) + N 1 ( 2 ) [ ( n - 1 ) T , θ + T ] } .
G ( 3 ) ( θ , θ + n T ) = W 2 T ( / T ) × [ T ( / T ) N 1 ( 2 ) ( n T , θ ) ] | θ + n T = constant
Var G ( 3 ) ( θ , θ + n T ) = ( W 2 ) 2 { Var N 1 ( 2 ) [ ( n + 1 ) T , θ ] + Var N 1 ( 2 ) ( n T , θ ) + Var N 1 ( 2 ) ( n T , θ + T ) + Var N 1 ( 2 ) [ ( n - 1 ) T , θ + T ] } + [ G ( 3 ) ( θ , θ + n T ) / W ] 2 Var W .
Var N 1 ( 2 ) ( n T , θ ) N 1 ( 2 ) ( n T , θ ) / N ,
Var G ( 3 ) ( θ , θ + n T ) ( 1 / N ) ( W 2 ) 2 { N 1 ( 2 ) [ ( n + 1 ) T , θ ] + N 1 ( 2 ) ( n T , θ ) + N 1 ( 2 ) ( n T , θ + T ) + N 1 ( 2 ) [ ( n - 1 ) T , θ + T ] } ,
Var G D ( 3 ) ( θ , θ + n T ) G ( 3 ) ( θ , θ + n T ) / N .
2 n 2 < W - 1 .
I ( t ) = I ( 1 + M cos ω t ) ,
W ( t , t + T ) = I T { 1 + A cos [ ( t + T / 2 ) ω ] } ,
A = M sin ( ω T / 2 ) / ( ω T / 2 ) ,
G ( 3 ) ( τ , τ ) = ( I T ) 3 ( 1 + ½ A 2 { cos ( ω τ ) + cos ( ω τ ) + cos [ ω ( τ - τ ) ] } ) ,
N 1 ( 2 ) ( n T , θ ) = n 2 ( I T ) 2 ( 1 + ½ A n T 2 + A T A n T ) × cos { ω [ θ + ½ ( n - 1 ) T ] } ) ,
A n T = M sin ( n T ω / 2 ) / ( n T ω / 2 ) .

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