Radii and Distances of Cepheids. I. Method and Measurement Errors

We develop a formulation of the Baade-Wesselink method which uses the Fourier coefficients of the observables. We derive an explicit, analytic expression to determine the mean radius from each Fourier order. The simplicity of this method allows us to derive the uncertainty in the mean radius due to measurement errors. Using simulations and a recent data set we demonstrate that the precision of the radius measurement with optical magnitudes is in most cases limited by the accuracy of the measurement of the phase difference between the light and the color index curve. In this case it is advantageous to determine the inverse radius, because it has normal errors.