CTmod : Mathematical Foundations

Abstract

CTmod is a set of C++ class libraries primarily designed for the simulation of energy imparted to a CT-scanner detector array using the Monte Carlo method. This report describes mathematical methods and formulas that are used in the code. It is a supplement to the article “CTmod - a toolkit for Monte Carlo simulation of projections including scatter in computed tomography” by A. Malusek, M. Sandborg, and G. Alm Carlsson. In this report, random variables are denoted by a hat. For instance ˆx is a random variable and x is its sample. Points in space are denoted by bold capital letters, e.g. P. Directions are denoted by bold small letters, e.g. u. Inconsistencies in the current notation will be corrected in the next update of this report