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Direct diameter observations of Cepheid variables are used to calibrate theBarnes-Evans Cepheid surface brightness relation. Fifty-nine separate Cepheiddiameter measurements from four different optical interferometers are used tocalculate surface brightnesses as a function of magnitude and color. The linearfit to Cepheid surface brightness versus color is in excellent agreement withfunctions in the literature found using interferometric observations ofnon-variable giant and supergiant stars (Fouque & Gieren 1997). Using theserelations the distance is calculated to delta Cephei, for which an independentdistance is known from trigonometric parallax. The distance from the relationin this paper differs from that derived by the previously published relation by4% but is still marginally within the combined errors. Both distances are wellwithin the errors of the distance derived from trigonometric parallax.Comment: 30 pages, 8 figures, accepted for publication in A

Calibration of the Barnes-Evans Relation Using Interferometric Observations of Cepheids