Centralized inverse-Fano distribution for controlling conversion gain measurement accuracy of detector elements

Abstract

Statistical theory is applied to derive the centralized inverse-Fano distribution as a model for the probability distribution of the photon transfer conversion gain measurement for detector elements. This distribution is confirmed by experiment, thus supporting the theory and enhancing the credibility of the statistical model used. Analysis of the statistical distance between the derived functions and computationally fast approximate forms is carried out to determine the conditions when such approximations are useful. Theoretical results are then applied to develop algorithms for use in live experiments to calculate appropriate sample sizes for measuring the conversion gain given a user-specified acceptable uncertainty.

A practical, effective calculation of gamma difference distributions with open data science tools

“…where γ(a, x) ≡ x 0 t a−1 e −t dt is the lower incomplete gamma function. The same result can be obtained [4] by integrating the joint density…”

“…This important form of f (x), which can also be found in [4], is not only much more economic and comprehensible as (2.2) or mentioned, more "messy" eq. ( 5) in [3], but it contains Tricomi's function (A5), one of the most commonly used hypergeometric functions with a wide variety of applications 2 .…”

“…Another reason consists in the fact that the special functions can have different computer implementations with respect to speed or reliability of computations. Simultaneously we introduce a more compact and readable notation compared to Klar [3], inspired by Hendrickson [4,17].…”

A novel approach to photon transfer conversion gain estimation

“…For sensors that cannot achieve a shot noise limited response one cannot ignore the noise produced by the pixel in the absence of illumination. As such, Hendrickson studied the estimator [13]…”

“…While convenient, the lack of distributional assumptions on the estimator (1.2) is not all that important. Indeed, many authors have shown that most image sensors produce noise that is accurately modeled as normal [16,3,13]. Even in the case where the pixel noise exhibits departures from normality, pt typically requires large samples sizes such that the distributions of the sample statistics ( X, Ȳ , X, Ŷ ) show excellent agreement with what is predicted by a normal model.…”