In radiography, the brightness of the transmitted light related to the distance of the focal plane from the specimen was used to image a specific inner plane of the laterally extended specimen[1]. Such a method has been renewed as computed laminography using a synchrotron radiation source[2–4] and the phase-contrast imaging method[5] to image transparent laterally extended shapes of objects. Phase imaging principally pertains to interferometric techniques that require high temporal and spatial coherence of the source; however, it is also allowed by non-interferometric methods with low coherence sources. A significant intensity alteration was observed for the transmission of the specimen at a certain distance. It arose from the refraction of X-rays due to the thickness of the specimen. This refraction phenomenon in X-rays leads to the report of the first observation, to the best of our knowledge, of propagation-based phase-contrast imaging in X-rays[6,7]. The images acquired objects located at a different distance inside the specimen, while rotating the specimen provided a reconstruction of quantitative phase images and giving rise to the mapping of 3D images based on the density of a specimen[8]. Non-interferometric methods may offer more stability than the interferometric method and a less technical demanding approach with a low coherence source. The transport-intensity equation (TIE), one of the non-interferometric schemes based on propagation wave field, i.e., the intensity derivative in the direction of wave propagation, has been studied[9,10]. Using the TIE, various studies such as the phase-retrieval method and optical sectioning imaging have been explored in optical spectra[11–15]. Similarly, non-interferometry X-ray phase detection has attempted to take advantage of the TIE[16–20]. Those results in the X-ray region cannot carry the coordinative results compared to the interferometric means until now. Developing non-interferometric phase reconstruction using the TIE and knife-edge scan imaging, especially for 3D X-ray image rendering, has considerable advantages and challenges because those non-interferometric methods are less restricted to the coherency of the source. This work designed the Foucault differential filtering (FDF) setup and performed a concurrent-bidirectional scanning of the Foucault knife-edge array (FKA). The biased derivative filtering (BDF) data were acquired by scanning the FKA for the plane, which was perpendicular to the optical axis at a given distance from the specimen. After that, the BDF data were acquired at every scanning point sequentially along the optical axis. Our imaging algorithm can use a simple arithmetic calculation for phase-retrieval processing because the intensities of BDF are connoted to the Fourier transform (FT). Hence, conventional image reconstruction techniques such as iterative algorithms or filtered back-projection methods do not require applying our volumetric rendering.