Abstract

We implement a simple computer-based photon-counting lock-in that combines the signal-to-noise benefits of photon counting with lock-in detection. We experimentally specify the flatness and the noise characteristics of a flexible software implementation. The noise of amplitude and phase of the small signal is at the limit of photonic shot noise; from 1000 counted photons we reach an amplitude resolution of 4.5% and a phase resolution of 13°. The photon-counting lock-in reduces illumination noise, detector dark count noise, and can suppress background. In particular, phase detection is useful to image the delay characteristics in microscopic systems by use of fluorescent probes that are designed to report membrane potential, temperature, or concentration in a chemical reaction.

© 2002 Optical Society of America

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References

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  1. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic, Dordrecht, The Netherlands, 1999).
    [CrossRef]
  2. K. Carlsson and A. Liljeborg, J. Microsc. (Oxford) 191, 119 (1998).
    [CrossRef]
  3. R. R. Alfonso and N. Ockman, J. Opt. Soc. Am. 58, 90 (1968).
  4. M. K. Murphy, S. A. Clyburn, and C. Veillon, Anal. Chem. 45, 1468 (1973).
    [CrossRef]
  5. F. T. Arecchi, E. Gatti, and A. Sona, Rev. Sci. Instrum. 37, 942 (1966).
    [CrossRef]
  6. B. Pelissier and N. Sadeghi, Rev. Sci. Instrum. 67, 3405 (1996).
    [CrossRef]
  7. Stanford Research Systems, “Signal recovery with photomultiplier tubes,” (1995), http://www.srsys.com .
  8. D. Braun and P. Fromherz, Phys. Rev. Lett. 86, 2905 (2001).
    [CrossRef] [PubMed]
  9. D. Braun (Max Planck Institute of Biochemistry, Am Klopferspitz 18A, D-82152 Martinsried, Germany) and P. Fromherz are preparing a manuscript to be called “Potential imaging with µm and µs resolution reveal seal properties between single cells and planar electrodes.”
  10. D. Braun (Center for Studies in Physics and Biology, Rockefeller University, 1230 York Avenue, New York, N.Y.) A. Libchaber are preparing a manuscript to be called “Lock-in imaging of reaction kinetics.”
  11. Stanford Research Systems Manual, “DSP Lock-in Amplifier SR850,” Chap. 3 (1999), http://www.srsys.com .
  12. Download the LabView source code from http://www.dieterb.de/lockin .

2001 (1)

D. Braun and P. Fromherz, Phys. Rev. Lett. 86, 2905 (2001).
[CrossRef] [PubMed]

1998 (1)

K. Carlsson and A. Liljeborg, J. Microsc. (Oxford) 191, 119 (1998).
[CrossRef]

1996 (1)

B. Pelissier and N. Sadeghi, Rev. Sci. Instrum. 67, 3405 (1996).
[CrossRef]

1973 (1)

M. K. Murphy, S. A. Clyburn, and C. Veillon, Anal. Chem. 45, 1468 (1973).
[CrossRef]

1968 (1)

1966 (1)

F. T. Arecchi, E. Gatti, and A. Sona, Rev. Sci. Instrum. 37, 942 (1966).
[CrossRef]

Alfonso, R. R.

Arecchi, F. T.

F. T. Arecchi, E. Gatti, and A. Sona, Rev. Sci. Instrum. 37, 942 (1966).
[CrossRef]

Braun, D.

D. Braun and P. Fromherz, Phys. Rev. Lett. 86, 2905 (2001).
[CrossRef] [PubMed]

D. Braun (Max Planck Institute of Biochemistry, Am Klopferspitz 18A, D-82152 Martinsried, Germany) and P. Fromherz are preparing a manuscript to be called “Potential imaging with µm and µs resolution reveal seal properties between single cells and planar electrodes.”

D. Braun (Center for Studies in Physics and Biology, Rockefeller University, 1230 York Avenue, New York, N.Y.) A. Libchaber are preparing a manuscript to be called “Lock-in imaging of reaction kinetics.”

Carlsson, K.

K. Carlsson and A. Liljeborg, J. Microsc. (Oxford) 191, 119 (1998).
[CrossRef]

Clyburn, S. A.

M. K. Murphy, S. A. Clyburn, and C. Veillon, Anal. Chem. 45, 1468 (1973).
[CrossRef]

Fromherz, P.

D. Braun and P. Fromherz, Phys. Rev. Lett. 86, 2905 (2001).
[CrossRef] [PubMed]

D. Braun (Max Planck Institute of Biochemistry, Am Klopferspitz 18A, D-82152 Martinsried, Germany) and P. Fromherz are preparing a manuscript to be called “Potential imaging with µm and µs resolution reveal seal properties between single cells and planar electrodes.”

Gatti, E.

F. T. Arecchi, E. Gatti, and A. Sona, Rev. Sci. Instrum. 37, 942 (1966).
[CrossRef]

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic, Dordrecht, The Netherlands, 1999).
[CrossRef]

Libchaber, A.

D. Braun (Center for Studies in Physics and Biology, Rockefeller University, 1230 York Avenue, New York, N.Y.) A. Libchaber are preparing a manuscript to be called “Lock-in imaging of reaction kinetics.”

Liljeborg, A.

K. Carlsson and A. Liljeborg, J. Microsc. (Oxford) 191, 119 (1998).
[CrossRef]

Murphy, M. K.

M. K. Murphy, S. A. Clyburn, and C. Veillon, Anal. Chem. 45, 1468 (1973).
[CrossRef]

Ockman, N.

Pelissier, B.

B. Pelissier and N. Sadeghi, Rev. Sci. Instrum. 67, 3405 (1996).
[CrossRef]

Sadeghi, N.

B. Pelissier and N. Sadeghi, Rev. Sci. Instrum. 67, 3405 (1996).
[CrossRef]

Sona, A.

F. T. Arecchi, E. Gatti, and A. Sona, Rev. Sci. Instrum. 37, 942 (1966).
[CrossRef]

Veillon, C.

M. K. Murphy, S. A. Clyburn, and C. Veillon, Anal. Chem. 45, 1468 (1973).
[CrossRef]

Anal. Chem. (1)

M. K. Murphy, S. A. Clyburn, and C. Veillon, Anal. Chem. 45, 1468 (1973).
[CrossRef]

J. Microsc. (Oxford) (1)

K. Carlsson and A. Liljeborg, J. Microsc. (Oxford) 191, 119 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. Lett. (1)

D. Braun and P. Fromherz, Phys. Rev. Lett. 86, 2905 (2001).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (2)

F. T. Arecchi, E. Gatti, and A. Sona, Rev. Sci. Instrum. 37, 942 (1966).
[CrossRef]

B. Pelissier and N. Sadeghi, Rev. Sci. Instrum. 67, 3405 (1996).
[CrossRef]

Other (6)

Stanford Research Systems, “Signal recovery with photomultiplier tubes,” (1995), http://www.srsys.com .

D. Braun (Max Planck Institute of Biochemistry, Am Klopferspitz 18A, D-82152 Martinsried, Germany) and P. Fromherz are preparing a manuscript to be called “Potential imaging with µm and µs resolution reveal seal properties between single cells and planar electrodes.”

D. Braun (Center for Studies in Physics and Biology, Rockefeller University, 1230 York Avenue, New York, N.Y.) A. Libchaber are preparing a manuscript to be called “Lock-in imaging of reaction kinetics.”

Stanford Research Systems Manual, “DSP Lock-in Amplifier SR850,” Chap. 3 (1999), http://www.srsys.com .

Download the LabView source code from http://www.dieterb.de/lockin .

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic, Dordrecht, The Netherlands, 1999).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Implementation of the photon-counting lock-in. Projections of time-binned counts Nraw to sinusoidal reference RX and cosinusoidal reference RY are time averaged to yield the small IX and IY signals of the lock-in.

Fig. 2
Fig. 2

Flatness of the photon-counting lock-in checked from 1 Hz to 10 kHz with a modulated LED. Each point is the lock-in output from 2×105 counted photons within 2-s measurement time.

Fig. 3
Fig. 3

Noise performance. The photon-counting lock-in operates at the shot-noise limit of photon counting. The relative error of photon counts I, relative amplitude A, and phase φ is inversely proportional to the square root of the number of counted photons I as given by Eqs. (4) and (5).

Equations (5)

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x=1Nn=0N-1xtn.
ΔII=Ix+iIyI=2NrawNRxRx2+iNRyRy2.
ΔIkI=mtn=kNtnNrawmtn=k1.
σI/I=100%/Nraw,
σA=100%/Nraw,  σφ=360°/Nraw.

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