On Certain Mathematical Problems in Two-Photon Laser Scanning Microscopy. Issue 5 (3rd September 2017)

• Record Type: Journal Article
• Authors: Simsek, Burcin; Iyengar, Satish
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 5(2017)
• Page Start: 587
• Page End: 600
• Publication Date: 2017-09-03
• Subjects: dead period -- finite horizon -- inhomogeneous Poisson process -- polynomial identities -- waiting time; 60G55 -- 12D99 -- 78A60; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1336123
• Languages: English
• ISSNs: 1392-6292

Abstract

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.