X-ray 3D Fiber Orientation Tomography via Alternating Optimization of Scattering Coefficients and Directions

Abstract The X-ray Talbot–Lau interferometer (TLI) has been introduced as a device to measure the X-ray interference using an ordinary X-ray source rather than coherent X-ray sources. For nondestructive testing, the advantage of TLI is its capability to obtain darkfield images, where fibers in fiber-reinforced plastics can be distinguished from the matrix. From darkfield images, 3D tomographic reconstruction techniques have been investigated to visualize the distribution of fiber orientations. However, previous approaches assume that X-ray scattering occurs only along the predefined scattering directions that are shared within the entire volume of a test sample. In contrast, a novel technique that we introduce in this paper optimizes the predominant scattering directions independently at each voxel location. The proposed method employs an alternating optimization scheme, where it first calculates the scattering intensities along the scattering directions and then updates these scattering directions, accordingly. Owing to this alternative optimization scheme, our method demonstrates promising performance, particularly when the predominant scattering directions are indeterminate. This advantage of our proposed technique is validated with the sample made of carbon fiber-reinforced plastic (CFRP) and glass fiber-reinforced plastic (GFRP). For these samples, reference fiber orientations are determined in advance using micro-focus CT scanning. To our knowledge, we are the first to optimize both the scattering intensity and scattering directions in reconstructing fiber orientations in industrial-purpose darkfield tomography. The findings presented in this paper potentially contribute to advancing applications in industrial nondestructive testing.