The inertial confinement fusion program requires the uniformity of multilayered samples to be measured to high accuracy. We currently use a reflection spectroscopy tool to measure optically transparent shells with no more than two layers. The method cannot measure opaque samples such as beryllium shells, low-reflection samples such as foam shells, or any shells with more than two layers such as National Ignition Facility specification Ge-CH shells. We also use a white-light interferometer to measure transparent samples with multiple layers, but only at the North/South Poles for a given orientation. To complement these existing tools, we developed an X-ray technique based on a commercial X-ray microscope (Xradia MicroXCT). MicroXCT is capable of providing high-contrast, high-resolution images and allows the samples to be precision aligned and angular indexed. Dimension accuracy is achieved through the calibration of the projection magnification and the lens distortion. From each X-ray image, a wall thickness trace along the great circle is obtained by converting Cartesian coordinates into cylindrical coordinates, and edge-finding algorithms are developed for a contact radiography project. Three-dimensional reconstruction and wall thickness display allow the visualization of the sample nonuniformity. The method has a 0.3 m measurement precision and, through phase contrast calibration, can achieve 0.3 m accuracy.