Monte Carlo approximation of partial volume effect for synthetic X-ray computed tomography of spheroidal particles

Abstract X-ray computed tomography is commonly used to investigate the morphology of particles in granular materials, yet the accuracy of the image analysis algorithms that extract these quantities is rarely characterised. A central obstacle is the lack of synthetic ground-truth images that reproduce the partial volume effect (PVE) at particle boundaries, for which analytical solutions exist only for few regular shapes. We present a Monte Carlo method that approximates the PVE for spheroids of arbitrary size, aspect ratio, and orientation.Because the estimate is a binomial proportion, its uncertainty is known in closed form and decreases as N -1/2 MC . The volumetric error is unbiased and below 0.01% across all cases tested, and the orientation error below 0.04 • away from the near-spherical limit. Requiring only an inside/outside test, the method extends to any implicitly defined particle shape, providing a practical basis for benchmarking image analysis algorithms in granular measurement.