Abstract

We introduce a new algorithm for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The algorithm is based on rewriting the correlation as a counting operation on photon pairs and can be used with arbitrary bin widths and spacing. The flexibility of the algorithm is demonstrated by use of FCS simulations and single-molecule photon antibunching experiments. Execution speed is comparable to the commonly used multiple-tau correlation technique. Wide bin spacings are possible that allow for real-time software calculation of correlations, even for high count rates.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2005

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

Y. Xiao, V. Buschmann, and K. D. Weston, Anal. Chem. 77, 36 (2005).
[CrossRef]

2004

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 108, 3051 (2004).
[CrossRef]

2003

D. Magatti and F. Ferri, Rev. Sci. Instrum. 74, 1135 (2003).
[CrossRef]

M. Wahl, I. Gregor, M. Patting, and J. Enderlein, Opt. Express 11, 3583 (2003).
[CrossRef] [PubMed]

C. W. Hollars, S. M. Lane, and T. Huser, Chem. Phys. Lett. 370, 393 (2003).
[CrossRef]

2002

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

2000

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

J. S. Eid, J. D. Muller, and E. Gratton, Rev. Sci. Instrum. V71, 361 (2000).
[CrossRef]

1998

J. R. Fries, L. Brand, C. Eggeling, M. Kollner, and C. A. M. Seidel, J. Phys. Chem. A 102, 6601 (1998).
[CrossRef]

1995

J. Widengren, U. Mets, and R. Rigler, J. Phys. Chem. 99, 13,368 (1995).
[CrossRef]

1992

1991

K. Schatzel and R. Peters, in Proc. SPIE 1430, 109 (1991).
[CrossRef]

1988

K. Schatzel, M. Drewel, and S. Stimac, J. Mod. Opt. 35, 711 (1988).
[CrossRef]

1985

K. Schatzel, Inst. Phys. Conf. Ser. 77, session 4, 175 (1985).

1972

D. Magde, E. Elson, and W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Balhorn, R.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

Brand, L.

J. R. Fries, L. Brand, C. Eggeling, M. Kollner, and C. A. M. Seidel, J. Phys. Chem. A 102, 6601 (1998).
[CrossRef]

Buschmann, V.

Y. Xiao, V. Buschmann, and K. D. Weston, Anal. Chem. 77, 36 (2005).
[CrossRef]

Chemla, D. S.

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 108, 3051 (2004).
[CrossRef]

Cosman, M.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

Davis, L. M.

Drewel, M.

K. Schatzel, M. Drewel, and S. Stimac, J. Mod. Opt. 35, 711 (1988).
[CrossRef]

Dyck, M.

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

Eggeling, C.

J. R. Fries, L. Brand, C. Eggeling, M. Kollner, and C. A. M. Seidel, J. Phys. Chem. A 102, 6601 (1998).
[CrossRef]

Eid, J. S.

J. S. Eid, J. D. Muller, and E. Gratton, Rev. Sci. Instrum. V71, 361 (2000).
[CrossRef]

Elson, E.

D. Magde, E. Elson, and W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Enderlein, J.

Ferri, F.

D. Magatti and F. Ferri, Rev. Sci. Instrum. 74, 1135 (2003).
[CrossRef]

Fore, S.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

Fries, J. R.

J. R. Fries, L. Brand, C. Eggeling, M. Kollner, and C. A. M. Seidel, J. Phys. Chem. A 102, 6601 (1998).
[CrossRef]

Gratton, E.

J. S. Eid, J. D. Muller, and E. Gratton, Rev. Sci. Instrum. V71, 361 (2000).
[CrossRef]

Gregor, I.

Herten, D. P.

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

Hollars, C. W.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

C. W. Hollars, S. M. Lane, and T. Huser, Chem. Phys. Lett. 370, 393 (2003).
[CrossRef]

Huser, T.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

C. W. Hollars, S. M. Lane, and T. Huser, Chem. Phys. Lett. 370, 393 (2003).
[CrossRef]

Kapanidis, A. N.

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 108, 3051 (2004).
[CrossRef]

Kollner, M.

J. R. Fries, L. Brand, C. Eggeling, M. Kollner, and C. A. M. Seidel, J. Phys. Chem. A 102, 6601 (1998).
[CrossRef]

Kong, X. X.

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 108, 3051 (2004).
[CrossRef]

Lane, S. M.

C. W. Hollars, S. M. Lane, and T. Huser, Chem. Phys. Lett. 370, 393 (2003).
[CrossRef]

Laurence, T. A.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 108, 3051 (2004).
[CrossRef]

Lounis, B.

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

Magatti, D.

D. Magatti and F. Ferri, Rev. Sci. Instrum. 74, 1135 (2003).
[CrossRef]

Magde, D.

D. Magde, E. Elson, and W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Mets, U.

J. Widengren, U. Mets, and R. Rigler, J. Phys. Chem. 99, 13,368 (1995).
[CrossRef]

Moerner, W. E.

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

Muller, C.

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

Muller, J. D.

J. S. Eid, J. D. Muller, and E. Gratton, Rev. Sci. Instrum. V71, 361 (2000).
[CrossRef]

Patting, M.

Peters, R.

K. Schatzel and R. Peters, in Proc. SPIE 1430, 109 (1991).
[CrossRef]

Rigler, R.

J. Widengren, U. Mets, and R. Rigler, J. Phys. Chem. 99, 13,368 (1995).
[CrossRef]

Sauer, M.

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

Schatzel, K.

K. Schatzel and R. Peters, in Proc. SPIE 1430, 109 (1991).
[CrossRef]

K. Schatzel, M. Drewel, and S. Stimac, J. Mod. Opt. 35, 711 (1988).
[CrossRef]

K. Schatzel, Inst. Phys. Conf. Ser. 77, session 4, 175 (1985).

Seidel, C. A. M.

J. R. Fries, L. Brand, C. Eggeling, M. Kollner, and C. A. M. Seidel, J. Phys. Chem. A 102, 6601 (1998).
[CrossRef]

Shera, E. B.

Soper, S. A.

Stimac, S.

K. Schatzel, M. Drewel, and S. Stimac, J. Mod. Opt. 35, 711 (1988).
[CrossRef]

Tinnefeld, P.

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

Wahl, M.

Webb, W. W.

D. Magde, E. Elson, and W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Weiss, S.

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 108, 3051 (2004).
[CrossRef]

Weston, K. D.

Y. Xiao, V. Buschmann, and K. D. Weston, Anal. Chem. 77, 36 (2005).
[CrossRef]

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

Widengren, J.

J. Widengren, U. Mets, and R. Rigler, J. Phys. Chem. 99, 13,368 (1995).
[CrossRef]

Xiao, Y.

Y. Xiao, V. Buschmann, and K. D. Weston, Anal. Chem. 77, 36 (2005).
[CrossRef]

Yeh, Y.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

Anal. Chem.

K. D. Weston, M. Dyck, P. Tinnefeld, C. Muller, D. P. Herten, and M. Sauer, Anal. Chem. 74, 5342 (2002).
[CrossRef] [PubMed]

Y. Xiao, V. Buschmann, and K. D. Weston, Anal. Chem. 77, 36 (2005).
[CrossRef]

Chem. Phys. Lett.

C. W. Hollars, S. M. Lane, and T. Huser, Chem. Phys. Lett. 370, 393 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. Fore, T. A. Laurence, Y. Yeh, R. Balhorn, C. W. Hollars, M. Cosman, and T. Huser, IEEE J. Sel. Top. Quantum Electron. 11, 873(2005).
[CrossRef]

Inst. Phys. Conf. Ser.

K. Schatzel, Inst. Phys. Conf. Ser. 77, session 4, 175 (1985).

J. Mod. Opt.

K. Schatzel, M. Drewel, and S. Stimac, J. Mod. Opt. 35, 711 (1988).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem.

J. Widengren, U. Mets, and R. Rigler, J. Phys. Chem. 99, 13,368 (1995).
[CrossRef]

J. Phys. Chem. A

J. R. Fries, L. Brand, C. Eggeling, M. Kollner, and C. A. M. Seidel, J. Phys. Chem. A 102, 6601 (1998).
[CrossRef]

J. Phys. Chem. B

T. A. Laurence, A. N. Kapanidis, X. X. Kong, D. S. Chemla, and S. Weiss, J. Phys. Chem. B 108, 3051 (2004).
[CrossRef]

Nature

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. Lett.

D. Magde, E. Elson, and W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[CrossRef]

Proc. SPIE

K. Schatzel and R. Peters, in Proc. SPIE 1430, 109 (1991).
[CrossRef]

Rev. Sci. Instrum.

D. Magatti and F. Ferri, Rev. Sci. Instrum. 74, 1135 (2003).
[CrossRef]

J. S. Eid, J. D. Muller, and E. Gratton, Rev. Sci. Instrum. V71, 361 (2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Calculating the cross correlation of photon sequences in two channels, A and B (photon times shown as vertical solid lines), by using our new algorithm. The maximum and minimum limits for M bins in time lag τ ( [ τ 1 min , τ 1 max ) , [ τ 2 min , τ 2 max ) , , [ τ M min , τ M max ) ) are added to the arrival time of each photon in channel A. (a) These limits (arrows for τ 1 min ; lighter dotted lines for other limits) for photon 1 from channel A; (b) these limits for photon 2. In this example, M = 4 , τ 1 min = 0 , τ 2 min = τ 1 max , τ 3 min = τ 2 max , and τ 4 min = τ 3 max . To the left of each limit in (a) is index j of the photon in channel B, such that u j > t 1 + τ curr , where, in turn, τ curr = τ 1 min , τ curr = τ 1 max , etc. Similar indices j are shown in (b). The contribution to correlogram Y k for each time-lag bin k is m k l k . In going from photon 1 to 2 in channel A [comparing (a) and (b)] one makes only small adjustments in the values of l k and m k .

Fig. 2
Fig. 2

Correlations and fits for simulated data of fluorescent molecules diffusing through a Gaussian detection volume. In this case, c = 0.1 , and diffusion time τ D through the detection volume is 300 μ s . The correlation is fitted to C ( τ ) = 1 + 1 [ c ( 1 + τ τ D ) 1 + τ ( 25 τ D ) ] . The correlation calculated with our new algorithm with quasi-logarithmic bin spacings from the multiple-tau correlation algorithm (8 bins per octave, 160 total bins) is shown in black. The dotted light gray curve is a fit with c = 0.099 ± 0.002 and τ D = 294 ± 3 μ s . The dark gray curve is the correlation with wide bin spacings (2 bins per decade, 12 total bins). A fit (not shown) recovered the values N = 0.10 ± 0.01 and 300 ± 100 μ s . The wider spacing sacrifices some accuracy but increases speed of computation.

Fig. 3
Fig. 3

Photon antibunching experiments performed on fluorescently labeled DNA oligomers attached to a glass surface. (a) Image of single surface-immobilized DNA oligomers; image size, 20 μ m × 20 μ m . (b) Long-time-scale correlation over the entire image (bin spacings similar to those in Fig. 2). (c) Short-time scale correlations with linearly spaced bins ( 25 ns bins). The nonnormalized cross correlation for the region with time lags from 1.25 to 1.25 μ s is shown [central plot in (c), dotted curve in (b)], along with the regions within 1.25 μ s of the ± 2 ms time lags [side plot in (c), solid line in (b)]. The spikes in (c) correspond to pulses from the excitation laser. The solid horizontal line is the average peak height in the region 1.25 to 1.25 μ s , and the dotted horizontal line is the average spike height in the regions within 1.25 μ s of ± 2 ms time-lag regions. The peak at 0.2 μ s with low photon pair counts is due to photon antibunching (dark arrow). It is not at 0 time lag owing to a cable delay ( 150 ns ) and a software-adjusted digital delay ( 37.5 ns ) .

Tables (1)

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Table 1 Comparison of Correlation Execution Times

Equations (1)

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C ̂ A B ( τ ) = n ( { ( i , j ) t i = u j τ } ) ( T τ ) n ( { i t i T τ } ) n ( { j u j τ } ) .

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