1997A&A...320..799F

We have calibrated optical and near-infrared surface brightness - colour relations for cool giant and supergiant stars using high-precision angular diameters of these stars determined from Michelson interferometry. We find that the giant and supergiant relations are undistinguishable over a wide range of intrinsic colours. We independently determine the slopes of these relations obeyed by Cepheid variables and find that in all the diagrams considered, these agree very well with the slopes derived from the stable giants and supergiants. Forcing the slopes to the values derived from the Cepheids, we determine a very precise value of the zero point of the surface brightness - colour relations valid for Cepheid variables, which is 3.947±0.003. This value is in agreement with the one derived from the Cepheid effective temperature scale of Pel (1978A&A....62...75P), and from the lunar occultation angular diameter of the Cepheid ζ Gem (Ridgway et al. 1982AJ.....87..680R). We apply our newly calibrated surface brightness - colour relations to the cluster Cepheid U Sgr to find its radius and distance from the optical V, V-R_J and the infrared V, V-K and K, J-K Barnes-Evans technique. While the numerical values derived from the three different versions of the technique do agree within 1-σ, the near-infrared distance and radius values are 5-10 times more accurate than the optical one; in particular, the distance and radius of the star derived from the V, V - K solution are 592 ±4 pc and 48.7 ±0.3 solar radii, respectively, with errors less than 1 percent. We briefly discuss the potential of the near-infrared versions of the Barnes-Evans technique to set a very accurate (0.02mag) zero point to Cepheid period-luminosity relations and thus make a very important contribution to the absolute calibration of the extragalactic distance scale.