Showing papers by "Stuart T. Smith published in 2020"

Empirical approaches to uncertainty analysis of X-ray computed tomography measurements: A review with examples

Abstract: The substitution method—an empirical approach for uncertainty assessment (adapted from the ISO 15530-3 guidelines) that is based on a comparison between repeated measurements of a calibrated standard workpiece and measurements of a test (uncalibrated) sample—has been the approach most adopted over the past decade for estimation of measurement uncertainties in dimensional metrology with X-ray computed tomography (CT). However, questions about how to apply the substitution (or use calibrated workpieces) for X-ray CT metrology persist because the substitution method does not always encompass all the most relevant CT measurement influencing factors. This paper discusses some issues with the direct application of the ISO 15530 series for the estimation of CT measurement uncertainties and reviews other empirical methods that can be applied in uncertainty analyses in CT metrology. Special attention is placed to the treatment of uncertainties in the case of ‘uncorrected’ measurement results (i.e., not compensated for bias), which for X-ray CT has traditionally been limited to the use of the root-sum-of-squares of standard uncertainties (RSSu) approach. This article investigates other possibilities for uncertainty estimation of ‘uncorrected’ results that could be applied to CT measurements, namely the root-sum-of-squares of expanded uncertainties (RSSU), the algebraic sum of expanded uncertainty with the signed bias (SUMU), the enlargement of the expanded uncertainty by adding the absolute value of the bias (SUMUMAX), and the so-called Ue method that sums the expanded uncertainty with the absolute value of the bias scaled by a factor e assigned for a 95% distribution coverage. In addition, the alternative of using a maximum permissible error ( M P E ) statement—typically specified by the manufacturer of the CT instrument—to generate a rough estimate of the expanded uncertainties of CT measurements is considered. Through two examples using dimensional X-ray CT data, these possibilities are analyzed. From all the possibilities for estimation of uncertainties associated with CT dimensional measurements that are not compensated for bias, the RSSu method produced the largest uncertainty estimates and thus seems to be the most conservative approach. For dimensioning geometric features mostly ranging between 10 mm and 60 mm, the expanded uncertainties ( k = 2 ) computed with the RSSu method ranged from 0.6 μm up to 72.7 μm. It was with the asymmetrical SUMU approach that the smaller uncertainty intervals were generated. On the other hand, uncertainty bounds estimated with the M P E based approach changed little from a constant value (around ±9.5 μm), and, therefore, risk creating significant under- or over-estimation of the uncertainty intervals.

Effect of the number of projections on dimensional measurements with X-ray computed tomography

Abstract: In X-ray computed tomography (CT) reducing the number of projections (Np) acquired for data reconstruction will reduce the measurement acquisition time and, thereby, the cost of the measuring process. However, reducing Np can also reduce reconstruction quality and the accuracy of dimensional information provided by the CT measurement. This paper assesses changes in dimensional accuracy of X-ray CT data as a function of Np. The variance of CT dimensional measurements, with respect to reference data obtained from tactile coordinate measurement machines (CMMs), is studied. Two cheese-like hole-cubes made of aluminum material and nylon (a polyamide thermoplastic) are used as measuring workpieces. It is determined that using Np between 600 and 2000 does not produce major changes in accuracy for size measurements (lengths and diameters), for which absolute deviations between CT and reference data were mainly within the range of 5–10 μm. This range reflects sub-voxel accuracies of CT measurement (the voxel size for CT data reconstruction was 73 μm) when determining component size dimensions. However, for Np ≥ 2000) is preferable. Although the accuracy of measurements of size also deteriorates with reducing Np the accuracy loss is less severe, particularly if averaging over several data points. When measuring size, a loss of image quality can be tolerated as a trade-off for time optimization in CT data collection. Assessments of image quality further complement the conclusions presented in this paper.

Amplitude-wavelength maps for X-ray computed tomography systems

Abstract: Amplitude–wavelength (AW) maps or “Stedman diagrams” are often used to provide a graphical representation of the limitations and capabilities of surface measuring instruments. This paper presents an approach for setting the parameter constraints of X-ray computed tomography (CT) in terms of resolution and measuring range for the purpose of representing the performance of industrial CT systems on an AW map. Such AW map will allow instrument users to quickly compare the CT instrument performance to other measuring systems. Examples of the construction of AW maps for different working capabilities of X-ray CT systems, and based on experimental data, are provided. Polypropylene, aluminum, and steel are three workpiece materials considered for determining some of the limitations of measuring capability for the maps developed in this paper. Although the limiting boundaries of the AW plots presented in this paper set a generalized measure of performance for comparisons with other measuring instruments, they may evolve with more comprehensive models of the limiting factors in X-ray CT.