Quantification and compensation of geometry-induced errors in cone-beam X-ray computed tomography

Since the industrial revolution, dimensional metrology has been tasked with meeting the continuously increasing demand for higher accuracy, faster and more comprehensive measuring techniques. X-ray Computed Tomography (CT) is a widely accepted non-destructive three-dimensional characterization technology which employs penetrating electromagnetic radiation and dedicated mathematical algorithms to visualize and analyze the internal structure of an object. While CT has shown significant potential for non-destructive coordinate measurements of external and internal features, there is a need for metrological research to accelerate the acceptance of CT as a measuring instrument.

There is uncertainty in the result of any measurement. Uncertainty is an indication of the quality of a given measurement result and translates into the confidence with which a decision on part conformance can be made. Metrological standards demand that each source of error be determined, if possible, compensated, and residuals after compensation propagated to uncertainty in the measurement result. The major problems complicating characterization and compensation of error sources in CT dimensional measurements are an analytically intractable measurement model i.e. measurement model cannot be written as closed-form analytic expression) and high computational cost associated with simulation of the CT measurement procedure (time, memory and other resources). These problems highlight the need for a framework where uncertainty due to geometrical influence factors is addressed and managed in a computationally efficient way. In this thesis, a framework to handle geometry-induced errors for CT dimensional measurements is developed. The framework consists of three main parts:

1. a method for reducing influence of the Feldkamp artifacts,

2. a method for software-based compensation of misalignments in CT geometry, and

3. a computationally inexpensive model for estimating dimensional measurement uncertainty due to residual misalignments in the CT instrument geometry.

Appearance of Feldkamp artifacts depends on the object itself and its position and orientation during data acquisition. The first method uses a meshed surface, e.g. a Computer-Aided Design (CAD) model of an object and its orientation in the measurement volume to predict where the object's surface will not be reconstructed properly due to Feldkamp artifacts. The method is applied to estimate the object position and orientation that reduces the effects of Feldkamp artifacts.

The second part of the work investigates the capabilities of software-based compensation of CT instrument misalignments as an effective alternative to mechanical adjustment of a CT instrument. Quantitative and qualitative results from computer simulations and experimental study show that a modified conventional reconstruction algorithm with embedded misalignment compensation is an efficient and robust alternative to mechanical adjustment of a CT instrument.

The third part of the proposed framework is a model for estimating dimensional measurement uncertainty due to CT instrument misalignments. The model uses surface points extracted from a CAD-model to calculate discrepancies in the radiographic image coordinates assigned to the projected edges from an aligned system and from a system with misalignments. The proposed method is designed to provide computational benefits in the assessment of coordinate measurement uncertainty when compared to a full Monte Carlo simulation of a CT measurement chain. The efficacy of the proposed method was confirmed on simulated and experimental data in the presence of various geometrical uncertainty contributors.