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Original Articles

On Certain Mathematical Problems in Two-Photon Laser Scanning Microscopy

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Pages 587-600 | Received 19 Feb 2017, Published online: 21 Sep 2017

References

  • D.L. Bentley. A contribution to counter theory. Journal of the Royal Statistical Society. Series B, 25(7):169–178, 1963.
  • D.R. Cox and D.V. Hinkley. Theoretical Statistics. Chapman and Hall, London, 1979.
  • D.J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes: volume II: general theory and structure. Springer, New York, 1988.
  • W. Denk, J.H. Strickler and W.W. Webb. Two-photon laser scanning fluorescence microscopy. Science, 248(4951):73–76, 1990. doi: 10.1126/science.2321027
  • J.D. Driscoll, A.Y. Shih, S. Iyengar, J.J. Field, G.A. White, J.A. Squier, G. Cauwenberghs and D. Kleinfeld. Photon counting, censor corrections, and lifetime imaging for improved detection in two-photon microscopy. Journal of Neurophysiology, 105(6):3106–3113, 2011. https://doi.org/10.1152/jn.00649.2010.
  • W. Feller. An Introduction to Probability Theory and its Applications. Wiley, New York, 1968.
  • M. Oheim, D.J Micheal, M. Geisbauer, D. Madsen and R.H. Chow. Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches. Advanced Drug Delivery Reviews, 58(7):788–808, 2006. https://doi.org/10.1023/A:1021167932414.
  • F.W.J. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark. NIST Handbook of Mathematical Functions. Cambridge University Press, New York, 2010.
  • K. Omote. Dead-time effects in photon counting distributions. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 293(3):582–588, 1990. https://doi.org/10.1016/0168-9002(90)90327-3.
  • R. Pyke. On renewal processes related to type i and type ii counter models. The Annals of Mathematical Statistics, 29(3):737–754, 1958. doi: 10.1214/aoms/1177706533
  • A. Sharma and J.G. Walker. Paralyzable and nonparalyzable deadtime analysis in spatial photon counting. Review of Scientific Instruments, 63(12):5784–5793, 1992. https://doi.org/10.1063/1.1143364.
  • B. Simsek. Applications of point process models to imaging and biology. PhD Dissertation, Statistics Department, University of Pittsburgh, 2016.
  • B. Simsek and S. Iyengar. On the distribution of photon counts with censoring in two-photon laser scanning microscopy. Journal of Mathematical Imaging and Vision, 58(1):47–56, 2017. https://doi.org/10.1007/s10851-016-0690-4.
  • L. Takacs. On a probability problem arising in the theory of counters. Proceedings of the Cambridge Philosophical Society, 52(3):488–498, 1956. https://doi.org/10.1017/S0305004100031480.
  • D.F. Yu and J.A. Fessler. Mean and variance of single photon counting with deadtime. Physics in Medicine and Biology, 45(7):2043–2056, 2000. doi: 10.1088/0031-9155/45/7/324

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