Abstract

We introduce and demonstrate a simple and highly sensitive method for characterizing single-photon detectors. This method is based on analyzing multi-order correlations among time-tagged detection events from a device under calibrated continuous-wave illumination. First- and second-order properties such as detection efficiency, dark count rate, afterpulse probability, dead time, and reset behavior are measured with high accuracy from a single data set, as well as higher-order properties such as higher-order afterpulse effects. While the technique is applicable to any type of click/no-click detector, we apply it to two different single-photon avalanche diodes, and we find that it reveals a heretofore unreported afterpulse effect due to detection events that occur during the device reset.

© 2017 Optical Society of America

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References

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  1. A. L. Migdall, S. V. Polyakov, J. Fan, and J. C. Bienfang, “Single-photon generation and detection, physics and applications,” Single-Photon Generation and Detection, Physics and Applications (2013).
  2. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photon. 3, 696–705 (2009).
    [Crossref]
  3. M. Planck, “Zur theorie des gesetzes der energieverteilung im normalspektrum,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 237–245 (1900).
  4. A. Lienard, “Champ electrique et magnetique produit par une charge electrique concentree en un point et animee d’un mouvement quelconque,” L’Eclairage electrique XVI, 5 (1898).
  5. W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
    [Crossref]
  6. B. Y. Zeldovich and D. N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 9, 40–42 (1969).
  7. A. N. Penin and A. V. Sergienko, “Absolute standardless calibration of photodetectors based on quantum two-pphoton fields,” Appl. Opt. 30, 3582–3588 (1991).
    [Crossref] [PubMed]
  8. A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
    [Crossref]
  9. S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express 15, 1390–1407 (2007).
    [Crossref] [PubMed]
  10. A. G. Stewart, L. Wall, and J. C. Jackson, “Properties of silicon photon counting detectors and silicon photomultipliers,” J. Mod. Opt. 56, 240–252 (2009).
    [Crossref]
  11. A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single-photon detector,” Electron. Lett. 38, 1468–1469 (2002).
    [Crossref]
  12. M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, “Calibrating photon-counting detectors to high accuracy: background and deadtime issues,” J. Mod. Opt. 54, 361–372 (2007).
    [Crossref]
  13. M. Stipcevic, H. Skenderovic, and D. Gracin, “Characterization of a novel avalanche photodiode for single photon detection in vis-nir range,” Opt. Express 18, 17448 (2010).
    [Crossref] [PubMed]
  14. T. F. da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
    [Crossref]
  15. G. Humer, M. Peev, C. Schaeff, S. Ramelow, M. Stipcevic, and R. Ursin, “A simple and robust method for estimating afterpulsing in single photon detectors,” J. Lightwave Technol. 33, 3098 (2015).
    [Crossref]
  16. A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
    [Crossref]
  17. A. Restelli, J. C. Bienfang, and A. L. Migdall, “Time-domain measurements of afterpulsing in ingaas/inp spad gated with sub-nanosecond pulses,” J. Mod. Opt. 59, 1465–1471 (2012).
    [Crossref]

2015 (1)

2012 (1)

A. Restelli, J. C. Bienfang, and A. L. Migdall, “Time-domain measurements of afterpulsing in ingaas/inp spad gated with sub-nanosecond pulses,” J. Mod. Opt. 59, 1465–1471 (2012).
[Crossref]

2011 (1)

T. F. da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[Crossref]

2010 (1)

2009 (3)

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photon. 3, 696–705 (2009).
[Crossref]

A. G. Stewart, L. Wall, and J. C. Jackson, “Properties of silicon photon counting detectors and silicon photomultipliers,” J. Mod. Opt. 56, 240–252 (2009).
[Crossref]

2007 (2)

M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, “Calibrating photon-counting detectors to high accuracy: background and deadtime issues,” J. Mod. Opt. 54, 361–372 (2007).
[Crossref]

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express 15, 1390–1407 (2007).
[Crossref] [PubMed]

2002 (1)

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single-photon detector,” Electron. Lett. 38, 1468–1469 (2002).
[Crossref]

1995 (1)

A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
[Crossref]

1991 (1)

1969 (1)

B. Y. Zeldovich and D. N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 9, 40–42 (1969).

1961 (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

1900 (1)

M. Planck, “Zur theorie des gesetzes der energieverteilung im normalspektrum,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 237–245 (1900).

1898 (1)

A. Lienard, “Champ electrique et magnetique produit par une charge electrique concentree en un point et animee d’un mouvement quelconque,” L’Eclairage electrique XVI, 5 (1898).

Bienfang, J. C.

A. Restelli, J. C. Bienfang, and A. L. Migdall, “Time-domain measurements of afterpulsing in ingaas/inp spad gated with sub-nanosecond pulses,” J. Mod. Opt. 59, 1465–1471 (2012).
[Crossref]

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, “Calibrating photon-counting detectors to high accuracy: background and deadtime issues,” J. Mod. Opt. 54, 361–372 (2007).
[Crossref]

A. L. Migdall, S. V. Polyakov, J. Fan, and J. C. Bienfang, “Single-photon generation and detection, physics and applications,” Single-Photon Generation and Detection, Physics and Applications (2013).

Carpenter, R.

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

da Silva, T. F.

T. F. da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[Crossref]

Datla, R.

A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
[Crossref]

Fan, J.

A. L. Migdall, S. V. Polyakov, J. Fan, and J. C. Bienfang, “Single-photon generation and detection, physics and applications,” Single-Photon Generation and Detection, Physics and Applications (2013).

Gracin, D.

Hadfield, R. H.

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photon. 3, 696–705 (2009).
[Crossref]

Hershman, B.

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

Humer, G.

Jackson, J. C.

A. G. Stewart, L. Wall, and J. C. Jackson, “Properties of silicon photon counting detectors and silicon photomultipliers,” J. Mod. Opt. 56, 240–252 (2009).
[Crossref]

Kaji, R.

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single-photon detector,” Electron. Lett. 38, 1468–1469 (2002).
[Crossref]

Klyshko, D. N.

B. Y. Zeldovich and D. N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 9, 40–42 (1969).

Lienard, A.

A. Lienard, “Champ electrique et magnetique produit par une charge electrique concentree en un point et animee d’un mouvement quelconque,” L’Eclairage electrique XVI, 5 (1898).

Louisell, W. H.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Ma, L.

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

Migdall, A.

M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, “Calibrating photon-counting detectors to high accuracy: background and deadtime issues,” J. Mod. Opt. 54, 361–372 (2007).
[Crossref]

A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
[Crossref]

Migdall, A. L.

A. Restelli, J. C. Bienfang, and A. L. Migdall, “Time-domain measurements of afterpulsing in ingaas/inp spad gated with sub-nanosecond pulses,” J. Mod. Opt. 59, 1465–1471 (2012).
[Crossref]

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express 15, 1390–1407 (2007).
[Crossref] [PubMed]

A. L. Migdall, S. V. Polyakov, J. Fan, and J. C. Bienfang, “Single-photon generation and detection, physics and applications,” Single-Photon Generation and Detection, Physics and Applications (2013).

Mink, A.

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

Orszak, J. S.

A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
[Crossref]

Peev, M.

Penin, A. N.

Planck, M.

M. Planck, “Zur theorie des gesetzes der energieverteilung im normalspektrum,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 237–245 (1900).

Polyakov, S. V.

S. V. Polyakov and A. L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express 15, 1390–1407 (2007).
[Crossref] [PubMed]

M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, “Calibrating photon-counting detectors to high accuracy: background and deadtime issues,” J. Mod. Opt. 54, 361–372 (2007).
[Crossref]

A. L. Migdall, S. V. Polyakov, J. Fan, and J. C. Bienfang, “Single-photon generation and detection, physics and applications,” Single-Photon Generation and Detection, Physics and Applications (2013).

Ramelow, S.

Restelli, A.

A. Restelli, J. C. Bienfang, and A. L. Migdall, “Time-domain measurements of afterpulsing in ingaas/inp spad gated with sub-nanosecond pulses,” J. Mod. Opt. 59, 1465–1471 (2012).
[Crossref]

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

Schaeff, C.

Sergienko, A.

A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
[Crossref]

Sergienko, A. V.

Shih, Y. H.

A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
[Crossref]

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Skenderovic, H.

Stewart, A. G.

A. G. Stewart, L. Wall, and J. C. Jackson, “Properties of silicon photon counting detectors and silicon photomultipliers,” J. Mod. Opt. 56, 240–252 (2009).
[Crossref]

Stipcevic, M.

Tang, X.

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

Tsuchida, H.

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single-photon detector,” Electron. Lett. 38, 1468–1469 (2002).
[Crossref]

Ursin, R.

von der Weid, J. P.

T. F. da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[Crossref]

Wall, L.

A. G. Stewart, L. Wall, and J. C. Jackson, “Properties of silicon photon counting detectors and silicon photomultipliers,” J. Mod. Opt. 56, 240–252 (2009).
[Crossref]

Ware, M.

M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, “Calibrating photon-counting detectors to high accuracy: background and deadtime issues,” J. Mod. Opt. 54, 361–372 (2007).
[Crossref]

Xavier, G. B.

T. F. da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[Crossref]

Yariv, A.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Yoshizawa, A.

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single-photon detector,” Electron. Lett. 38, 1468–1469 (2002).
[Crossref]

Zeldovich, B. Y.

B. Y. Zeldovich and D. N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 9, 40–42 (1969).

Appl. Opt. (1)

Electron. Lett. (1)

A. Yoshizawa, R. Kaji, and H. Tsuchida, “Quantum efficiency evaluation method for gated-mode single-photon detector,” Electron. Lett. 38, 1468–1469 (2002).
[Crossref]

IEEE J. Quantum Electron. (1)

T. F. da Silva, G. B. Xavier, and J. P. von der Weid, “Real-time characterization of gated-mode single-photon detectors,” IEEE J. Quantum Electron. 47, 1251–1256 (2011).
[Crossref]

J. Lightwave Technol. (1)

J. Mod. Opt. (3)

A. Restelli, J. C. Bienfang, and A. L. Migdall, “Time-domain measurements of afterpulsing in ingaas/inp spad gated with sub-nanosecond pulses,” J. Mod. Opt. 59, 1465–1471 (2012).
[Crossref]

M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, “Calibrating photon-counting detectors to high accuracy: background and deadtime issues,” J. Mod. Opt. 54, 361–372 (2007).
[Crossref]

A. G. Stewart, L. Wall, and J. C. Jackson, “Properties of silicon photon counting detectors and silicon photomultipliers,” J. Mod. Opt. 56, 240–252 (2009).
[Crossref]

L’Eclairage electrique (1)

A. Lienard, “Champ electrique et magnetique produit par une charge electrique concentree en un point et animee d’un mouvement quelconque,” L’Eclairage electrique XVI, 5 (1898).

Metrologia (1)

A. Migdall, R. Datla, A. Sergienko, J. S. Orszak, and Y. H. Shih, “Measuring absolute infrared spectral radiance with correlated visible photons: Technique verification and measurement uncertainty,” Metrologia 32, 479–483 (1995).
[Crossref]

Nat. Photon. (1)

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photon. 3, 696–705 (2009).
[Crossref]

New J. Phys. (1)

A. Mink, J. C. Bienfang, R. Carpenter, L. Ma, B. Hershman, A. Restelli, and X. Tang, “Programmable instrumentation and gigahertz signaling for single-photon quantum communication systems,” New J. Phys. 11, 045016 (2009).
[Crossref]

Opt. Express (2)

Phys. Rev. (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[Crossref]

Sov. Phys. JETP Lett. (1)

B. Y. Zeldovich and D. N. Klyshko, “Statistics of field in parametric luminescence,” Sov. Phys. JETP Lett. 9, 40–42 (1969).

Verhandlungen der Deutschen Physikalischen Gesellschaft (1)

M. Planck, “Zur theorie des gesetzes der energieverteilung im normalspektrum,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 237–245 (1900).

Other (1)

A. L. Migdall, S. V. Polyakov, J. Fan, and J. C. Bienfang, “Single-photon generation and detection, physics and applications,” Single-Photon Generation and Detection, Physics and Applications (2013).

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Figures (5)

Fig. 1
Fig. 1 Schematic of the characterization setup.

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Fig. 2
Fig. 2 Typical second-order measurements on detectors A (a through c) and B (d through f) at an average count-rate of ≈500000 s−1. (a, d) High count rate start-multistop histogram, C(2). Main features are the recovery time, afterpulsing peak. (b, e) Start-single stop histograms of the same experiment as above. Histograms of first, second, third and fourth detection are shown and marked by color. (c, f) Afterpulsing profile of a detector, obtained under low-average count-rate conditions, with photon counts and dark counts subtracted, therefore the effect of higher-order detections not associated with the laser source is negligible.

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Fig. 3
Fig. 3 Afterpulsing seen as second-order correlation features for a range of input powers for detector A (a) and B (b).

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Fig. 4
Fig. 4 The two-step detector recovery calculations. A plot of observed afterpulse counts at different input powers with true electronic afterpulses subtracted. Detector A exhibits a rise in apparent afterpulsing whereas detector B exhibits their suppression. Dots: measured values. Solid lines: linear fits based on low count rates. Dashed lines: extrapolation of linear fits. Deviation of the measured data from these extrapolations shows saturation effects at higher count rates.

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Fig. 5
Fig. 5 Third-order measurements on detectors A (a through c) and B (d through f). (a, d) Raw third-order start-multistop histogram, C(3). Surface cuts (marked with horizontal lines) represent the second afterpulsing peak, and are plotted separately. (b, e) Test of a second-order detector model. Difference between expected and actual histograms expressed as a logarithm of the ratio of the measured and expected histograms, see Eq. (5). The second-order model is correct except for times immediately following the inactive time, indicating that more than one prior detection affects the detector’s behavior. (c, f) Structure of second afterpulses, i.e. afterpulses that occur immediately after an earlier afterpulse, and a transition to the steady-state. A significant change in the second afterpulse shape with respect to that of the typical afterpulse is seen for detector A. A significant decrease in the afterpusing events is seen for detector B.

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Tables (1)

Tables Icon

Table 1 Summary of SPAD parameters found under a second-order detector model, see text.

View Table

Equations (11)

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C ( 2 ) ( Δ t ) = ∫ − ∞ ∞ f ( t + Δ t ) f ( t ) d t ,
f ( t ) = ∑ i = 0 N δ ( t − t i ) .
C ( 2 ) ( Δ t j ) = ∫ Δ t j Δ t j + 1 C ( 2 ) ( τ ) d τ
C ( 2 ) ( Δ t j ) = ∑ i = 0 N ∑ k = 0 N δ Δ t j , t k − t i ,
Ξ = ∑ Δ t j = t recovery 2 t recovery [ C ( 2 ) ( Δ t j ) − C theor ( 2 ) ( Δ t j ) ] ,
C theor ( 2 ) ( Δ t j ) = C afterpulse ( 2 ) ( Δ t j ) + ( N − ∑ Δ t k = t j − t recovery t j − 1 C theor ( 2 ) ( Δ t k ) ) r corrected
C ( 3 ) ( Δ t ( 12 ) , Δ t ( 13 ) ) = ∫ − ∞ ∞ f ( t + Δ t ( 12 ) ) f ( t + Δ t ( 13 ) ) f ( t ) d t ,
C ( 3 ) ( Δ t j ( 12 ) , Δ t m ( 13 ) ) = ∑ i = 0 N ∑ k = 0 N ∑ n = 0 N δ Δ t j ( 12 ) , t k − t i δ Δ t m ( 13 ) , t n − t i .
C theor ( 3 ) ( Δ t ( 12 ) , Δ t ( 13 ) ) = α C ( 2 ) ( Δ t ( 12 ) ) C ( 2 ) ( Δ t ( 13 ) − Δ t ( 12 ) ) ,
R ( Δ t ( 12 ) , Δ t ( 13 ) ) = ln ( C ( 3 ) ( Δ t ( 12 ) , Δ t ( 13 ) ) + 1 C theor ( 3 ) ( Δ t ( 12 ) , Δ t ( 13 ) ) + 1 ) .
C B ( 2 ) ( Δ t j ) = C afterpulse ( 2 ) ( Δ t j ) + ( N ( 1 − ℱ ) − N t reset r connected − ∑ Δ t k = t j − t recovery t j − 1 C B ( 2 ) ( Δ t k ) ) r corrected .

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