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.
Highlights
Two-photon laser scanning microscopy (TPLSM) is a valuable tool for imaging living tissues
In our earlier work [13], the distribution of D was derived by using inhomogeneous Poisson approach under the infinite time period assumption
We obtain the distribution of D using an equivalent approaches by using lengthy analysis of the order statistics formula
Summary
Two-photon laser scanning microscopy (TPLSM) is a valuable tool for imaging living tissues. In an earlier paper [13], we used standard model assumptions [7]: Poisson with mean α for the number of photons emitted, exponential emission waiting times (fluorescence lifetimes), and a fixed (standardized) dead period δ upon registration of a photon. In [13] we used this inhomogeneous Poisson process approach to obtain the exact distribution of the number of photons detected, D, for an infinite time horizon.
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