The relative phase-contrast factor (RPF) represents a quantitative measure of the phase-contrast transfer in x-ray in-line phase-contrast imaging. The larger the modulus of RPF(u, v) is, the more the phase-contrast manifests. In this work we show how the RPF can be determined by measurements of the focal spot size and x-ray spectra for a x-ray imaging system with a micro-focus x-ray tube. The results show the significant effects of x-ray beam hardening on the visibility of phase-contrast, and reveal a new dimension in seeking optimal techniques for x-ray phase-contrast imaging. © 2004 American Association of Physicists in Medicine.