Quantitative analysis of scaling error compensation methods in dimensional X-ray computed tomography

• We present different methods for scale error correction in dimensional X-ray computed tomography.
• We explain the difference between scaling factor and scaling error using mathematical formulas.
• The influence of three different methods for scaling error compensation is quantitatively documented on a case study.
• Uncertainty estimation is used to quantitatively assess each method.
• Results of CT measurements are compared to CMM measurements, taking into account the uncertainty of the correction method.

X-ray Computed Tomography (CT) has become an important technology for quality control of industrial components. As with other technologies, e.g., tactile coordinate measurements or optical measurements, CT is influenced by numerous quantities which may have negative impact on the accuracy and repeatability of dimensional and geometrical measurements. The aim of this paper is to discuss different methods for the correction of scaling errors and to quantify their influence on dimensional measurements. Scaling errors occur first and foremost in CT systems with no built-in compensation of positioning errors of the manipulator system (magnification axis). This article also introduces a new compensation method for scaling errors using a database of reference scaling factors and discusses its advantages and disadvantages. In total, three methods for the correction of scaling errors – using the CT ball plate, using calibrated features measured by CMM and using a database of reference values – are presented and applied within a case study. The investigation was performed on a dose engine component of an insulin pen, for which several dimensional measurands were defined. The component has a complex geometry and is made of brass, which makes its measurements with CT challenging. It is shown that each scaling error correction method results in different deviations between CT measurements and reference measurements from a CMM. Measurement uncertainties were estimated for each method, taking into consideration the contributions related to the applied correction method. The newly suggested approach using the database appeared to work well, indicating, that if the properties of a CT system under investigation are monitored using a reference object (ball bar in our case), a correction factor based on individual selected magnification factors can be applied for scaling error correction of any object, and thus no additional scanning of a reference object is needed.