Non-interferometric X-ray quantitative phase imaging (XQPI), much simpler than the interferometric scheme, has provided high-resolution and reliable phase-contrast images. We report on implementing the volumetric XQPI images using concurrent-bidirectional scanning of the orthogonal plane on the optical axis of the Foucault differential filter; we then extracted data in conjunction with the transport-intensity equation. The volumetric image of the laminate microstructure of the gills of a fish was successfully reconstructed to demonstrate our XQPI method. The method can perform 3D rendering without any rotational motion for laterally extended objects by manipulating incoherent X-rays using the pinhole array.

Enhanced quantitative X-ray phase-contrast (QXPC) imaging is implemented with a Foucault knife-edge array filter (FKAF), which is a real differential spatial filter. The intensities of Foucault differential filtering (FDF) are acquired according to the linear translation of the FKAF along the axes. The FDF using the FKAF scheme for obtaining the QXPC images is demonstrated by a stereoscopic rendering of the quantitative phase images of the tail fin of an anchovy containing soft and hard components in specimen. FDF is a noninterferometric quantitative phase-imaging method that depicts quantitative phase images and renders stereoscopic images.