The Cherenkov Telescope Array (CTA) is a forthcoming international ground-based observatory for very high-energy gamma rays. Its goal is to reach sensitivity five to ten times better than existing Cherenkov telescopes such as VERITAS, H.E.S.S. or MAGIC and extend the range of observation to energies down to few tens of GeV and beyond 100 TeV. To achieve this goal, an array of about 100 telescopes is required, meaning a total reflective surface of several thousands of square meters. Thence, the optimal technology used for CTA mirrors' manufacture should be both low-cost (~1000 euros/m2) and allow high optical performances over the 300-550 nm wavelength range. More exactly, a reflectivity higher than 85% and a PSF (Point Spread Function) diameter smaller than 1 mrad. Surface roughness can significantly contribute to PSF broadening and limit telescope performances. Fortunately, manufacturing techniques for mirrors are now available to keep the optical scattering well below the geometrically-predictable effect of figure errors. This paper determines first order surface finish tolerances based on a surface microroughness characterization campaign, using Phase Shift Interferometry. That allows us to compute the roughness contribution to Cherenkov telescope PSF. This study is performed for diverse mirror candidates (MAGIC-I and II, ASTRI, MST) varying in manufacture technologies, selected coating materials and taking into account the degradation over time due to environmental hazards.