Numerical Analysis of the Feldkamp–Davis–Kress Effect on Industrial X Ray Computed Tomography for Dimensional Metrology

Abstract

Xray computed tomography (CT) can nondestructively inspect an object and can clearly, accurately, and intuitively display its internal structure, composition, texture, and damage. In industry this technology was initially used for material analysis and nondestructive testing and evaluation. Recently, as an alternative to optical and tactile measurement devices, CT has entered industrial use for dimensional metrology. Unfortunately, industriallevel accuracy is very difficult to attain with CT for various reasons. In this paper we analyze one of the most serious effects, the Feldkamp–Davis–Kress (FDK) effect, which can be observed in most of the common Xray CT scanners with a cone beam. The FDK is the reconstruction algorithm widely accepted as a standard reconstruction method for conebeam type of CT because of its computation efficiency. However, this algorithm merely provides an approximate result. An accurate measurement result can be obtained only in the case of small cone angle. We aim at analyzing the FDK effect independently from other kinds of artifacts. In a practical CT scanning situation, various kinds of artifacts appear in the reconstruction results; thus, we apply a simulation to obtain projection images without noise (scattering, beam hardening, etc.). Then, the FDK algorithm is applied to these projection images to reconstruct CT images so that only the FDK effect can be observed in the reconstructed CT images. Based on this approach, we conducted quantitative analysis on the FDK effect using numerical phantoms of the sphere and stepped cylinders that may be adopted as ISO reference standards for dimensional metrology using Xray CT scanners. This paper describes the evaluation workflow and discusses the cause of the FDK effect on the measurement of the sphere and the stepped cylinders. Particular attention is given to the evaluation of the error distribution feature on different spatial positions. After discussing the error feature, a method for improving measurement accuracy is proposed.