A Statistical Model of Microscope Resolution

by Gytis Kulaitis
Doctoral thesis
Date of Examination:2020-02-21
Date of issue:2020-07-10
Advisor:Prof. Dr. Axel Munk
Referee:Prof. Dr. Axel Munk
Referee:Prof. Dr. Tatyana Krivobokova
Persistent Address: http://dx.doi.org/10.53846/goediss-8085

 

 

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Abstract

English

A general rule of thumb in imaging is that the resolution of a light microscope depends linearly on the full width at half maximum (FWHM) of its point spread function (psf). In the present work we carefully define a statistical model of resolution by introducing a notion of discernability based on statistical testing whether one or two objects with the same total intensity are present. We consider four common ways of modeling photons detected in a microscopy experiment: as binomial, Poisson, variance stabilized Gaussian (VSG) or homogeneous Gaussian (HG) independent random variables. We show that under the binomial, Poisson and VSG photon models the resolution indeed depends linearly on the FWHM. However, under the HG model, the resolution depends on the FWHM to the power of $5/4$. Thus, at least for microscopy the HG model is too simple and in most experiments the Poisson or the VSG model is preferred, since they are easier to tackle than the binomial model, yet still capture the dependence on the FWHM correctly.
Keywords: microscopy; resolution; minimax; detection boundary; equivalence of experiments
 
Statistik