Nyquist-compliant cycloidal computed tomography

Cycloidal computed tomography, by which a lateral sample translation and rotation are combined, is a fully-fly-scan-compatible acquisition scheme for micro-computed-tomography systems using amplitude-modulated beams. Such systems have gained popularity, as they enable x-ray phase-contrast imaging (XPCI) and aperture-driven spatial resolution. The former provides superior contrast for weakly attenuating samples, while the latter allows the resolution of a micro-computed-tomography system to be increased beyond the conventional limit dictated by the source and detector. Such systems initially required time-inefficient step-and-shoot acquisitions, a limitation that has been removed by the development of cycloidal computed tomography. Here we derive cycloidal sampling conditions that are optimal in the sense of the Nyquist-Shannon theorem. Their availability enables the acquisition of well-sampled (i.e., high-resolution) XPCI images in a time-efficient manner, a long-sought outcome with relevance to laboratory implementations, where scan times have traditionally been long, and to synchrotron implementations, where the next frontier is to achieve high-speed (e.g., dynamic) imaging. We make no assumptions on the type of x-ray source used, but demonstrate the optimal conditions with a rotating-anode x-ray tube.