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On Certain Mathematical Problems in Two-Photon Laser Scanning Microscopy

    Burcin Simsek Affiliation
    ; Satish Iyengar Affiliation

Abstract

In an earlier paper, we derived the distribution of the number of photons detected in two-photon laser scanning microscopy when the counter has a dead period. We assumed a Poisson number of emissions, exponential waiting times, and an infinite time horizon, and used an equivalent inhomogeneous Poisson process formulation. We then used that result to improve image quality as measured by the signal-to-noise ratio. Here, we extend that study in two directions. First, we treat the finite-horizon case to assess the accuracy of the simpler infinite-horizon approximation. Second, we use a direct approach by conditioning on the Poisson count for the infinite-horizon case to derive several polynomial identities.

Keyword : dead period, finite horizon, inhomogeneous Poisson process, polynomial identities, waiting time

How to Cite
Simsek, B., & Iyengar, S. (2017). On Certain Mathematical Problems in Two-Photon Laser Scanning Microscopy. Mathematical Modelling and Analysis, 22(5), 587-600. https://doi.org/10.3846/13926292.2017.1336123
Published in Issue
Sep 21, 2017
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