A Systems Approach to Estimating the Uncertainty Limits of X-Ray Radiographic Metrology

Micro- and nanomanufacturing capabilities have rapidly expanded over the past decade to include complex three-dimensional (3D) structure fabrication; however, the metrology required to accurately assess these processes via part inspection and characterization has struggled to keep pace. X-ray computed tomography (CT) is considered an ideal candidate for providing the critically needed metrology on the smallest scales, especially internal features, or inaccessible regions. X-ray CT supporting micro- and nanomanufacturing often push against the poorly understood resolution and variation limits inherent to the machines, which can distort or hide fine structures. We develop and experimentally verify a comprehensive analytical uncertainty propagation signal variation flow graph (SVFG) model for X-ray radiography in this work to better understand resolution and image variability limits on the small scale. The SVFG approach captures, quantifies, and predicts variations occurring in the system that limit metrology capabilities, particularly in the micro/nanodomain. This work is the first step to achieving full uncertainty modeling of CT reconstructions and provides insight into improving X-ray attenuation imaging systems. The SVFG methodology framework is applied to generate a complete basis set of functions describing the major sources of variation in radiographs. Five models are identified, covering variation in energy, intensity, length, blur, and position. Radiographic system experiments are defined to measure the parameters required by the SVFGs. Best practices are identified for these measurements. The SVFG models are confirmed via direct measurement of variation to predict variation within 30% on average.