Caucci Luca, Myers Kyle J, Barrett Harrison H
The University of Arizona, Center for Gamma-Ray Imaging, Department of Medical Imaging, 1609 North Warren Avenue, Tucson, Arizona 85724, United States.
U.S. Food and Drug Administration, Center for Devices and Radiological Health, Division of Imaging and Applied Mathematics, 10903 New Hampshire Avenue, Silver Spring, Maryland 20993, United States.
Opt Eng. 2016 Jan;55(1). doi: 10.1117/1.oe.55.1.013102. Epub 2016 Jan 5.
The statistics of detector outputs produced by an imaging system are derived from basic radiometric concepts and definitions. We show that a fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular, and wavelength variables. We begin the paper by recalling the concept of radiance in geometrical optics, radiology, physical optics, and quantum optics. The propagation and conservation laws for radiance in each of these domains are reviewed. Building upon these concepts, we distinguish four categories of imaging detectors that all respond in some way to the incident radiance, including the new category of photon-processing detectors (capable of measuring radiance on a photon-by-photon basis). This allows us to rigorously show how the concept of radiance is related to the statistical properties of detector outputs and to the information content of a single detected photon. A Monte-Carlo technique, which is derived from the Boltzmann transport equation, is presented as a way to estimate probability density functions to be used in reconstruction from photon-processing data.
成像系统产生的探测器输出统计数据源自基本的辐射度学概念和定义。我们表明，描述光子受限成像系统的一种基本方法是根据空间、角度和波长变量中的泊松随机过程。本文开篇回顾了几何光学、放射学、物理光学和量子光学中的辐射率概念。并对这些领域中辐射率的传播和守恒定律进行了综述。基于这些概念，我们区分了四类成像探测器，它们都以某种方式对入射辐射率做出响应，包括新的光子处理探测器类别（能够逐个光子地测量辐射率）。这使我们能够严格地展示辐射率概念与探测器输出的统计特性以及单个探测光子的信息内容之间的关系。一种源自玻尔兹曼输运方程的蒙特卡罗技术被提出，作为估计用于从光子处理数据进行重建的概率密度函数的方法。
