“Don’t stop me now!”: Stopping rules for iterative reconstruction with dimensional X-ray Computed Tomography

Abstract

X-ray Computed Tomography is regularly exploited in manufacturing, primarily for high-value low-volume cases due to prolonged data acquisition times. For optimal results the Nyquist criterion suggests obtaining 3142 projections for a 2000 pixel width detector reasoning the extended inspection time. Reducing projections enhances speed but the standard FDK reconstruction method suffers a loss in image quality and dimensional accuracy. Iterative reconstruction methods excel with limited data such as fewer projections, offering a promising route forward. However, their application in dimensional measurement has no best practice — particularly when to stop iterating. In this study, a multi-sphere workpiece imaged at $100\mu m$ was reconstructed using SIRT, an iterative reconstruction algorithm, with just 17% (504 projections) of the projection data. The bi-directional measurements of sphere diameters were compared to the FDK reconstruction of the full dataset. In iterative reconstruction, the images improve with each iteration until a point of semi-convergence where it best represents the object, after which unwanted noise from the projections begins to be added. Without a ground truth image the semi-convergence is inferred by semi-convergence of measurement. Here, the difference in the sphere diameter against the FDK measurement is at most 0.0295 voxels ($2.95\mu m$) which is the same magnitude of error as repeated acquisitions with FDK reconstruction of a full dataset. Image metrics are evaluated as a less expensive way to identify the semi-convergence of measurement. In particular anisotropic quality index (AQI) and sharpness are identified candidate rules, as well as highlighting a number of other reasonable stopping rules which were unsuccessful in this scenario. While they cannot identify the precise diameter minima, they are all within 0.008 voxels (0.8 $\mu$m) of the semi-convergence point. Iterative reconstruction is a promising route forward to decrease inspection times with comparably accurate and repeatable measurements if the decision of when to stop iterating is well justified.