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Research Papers

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

[+] Author and Article Information
Lin Xue

RCAST,
The University of Tokyo,
7-3-1, Hongo, Bunkyo,
Tokyo 1538904, Japan
e-mail: mechanicalautomaticxue@gmail.com

Hiromasa Suzuki, Yutaka Ohtake

RCAST,
The University of Tokyo,
7-3-1, Hongo, Bunkyo,
Tokyo 1538904, Japan

Hiroyuki Fujimoto, Makoto Abe, Osamu Sato, Toshiyuki Takatsuji

National Metrology Institute of Japan,
National Institute of Advanced Industrial
Science and Technology (AIST),
Tsukuba, Ibaraki 305-8563, Japan

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received September 26, 2014; final manuscript received October 5, 2014; published online April 8, 2015. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 15(2), 021008 (Jun 01, 2015) (8 pages) Paper No: JCISE-14-1301; doi: 10.1115/1.4028942 History: Received September 26, 2014; Revised October 05, 2014; Online April 08, 2015

X-ray 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, industrial-level 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 X-ray CT scanners with a cone beam. The FDK is the reconstruction algorithm widely accepted as a standard reconstruction method for cone-beam 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 X-ray 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.

Copyright © 2015 by ASME
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References

Figures

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Fig. 2

Test object and 2D projection image: (a) sphere; (b) stepped cylinders; (c) projection image of sphere; and (d) projection image of stepped cylinders

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Fig. 3

Projection trajectory of fan beam scanning and cone-beam scanning

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Fig. 4

CT coordinate system with a sphere

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Fig. 5

Deviation generation for a sphere (r = 25, voxel size = 0.2): (a) reconstructed CT model; (b) reconstructed slice (XZ slice); and (c) CT value profile along the Z axis

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Fig. 6

Positional effects for a sphere: (a) deviation distribution of movement along the Z axis and (b) deviation distribution of movement along the X axis

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Fig. 7

Plot of radius error along the Z axis

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Fig. 8

Position parameters

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Fig. 9

Curve of radius error for the case of movement along the X axis

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Fig. 10

Curve of radius error for the case of movement along the Z axis (a = 50, b = 300, r = 10, voxel size = 0.1)

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Fig. 11

CT coordinate system with a cylinder

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Fig. 12

Deviation generation for a cylinder (r = 25, h = 50, voxel size = 0.3): (a) reconstructed CT model; (b) CT value profile along line a; (c) projection image; and (d) reconstructed slice (XZ slice)

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Fig. 13

Position parameters

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Fig. 14

Movement along the X axis: (a) curve of height error and (b) curve of radius error

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Fig. 15

Movement along the Z axis (a = 50, b = 200, r = 10, h = 30, voxel size = 0.15): (a) curve of height error and (b) curve of radius error

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Fig. 16

Position parameters for analyzing positional effects for a cylinder slanted around the Y axis

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Fig. 17

Positional effects for a cylinder slanted around the Y axis: (a) curve of max deviation on the top and (b) curve of max deviation on the cylindrical surface

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Fig. 18

Slant angles of a cylinder: (a) case 1 φ < β; (b) case 2 β < φ < γ; and (c) case 3 φ > γ

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Fig. 19

Positional effects for a cylinder slanted around the Y axis: (a) curve of height error and (b) curve of radius error

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Fig. 20

Position parameters for analyzing positional effects for a stepped cylinders

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Fig. 21

Positional effects on the measurement of a stepped cylinders: (a) curve of max deviation on the cylindrical surface and (b) curve of radius error

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