Suppose one of the current high angular resolution instruments were capable of measuring the instantaneous angular diameter of a Cepheid throughout its pulsation cycle. By comparing the angular diameter variation to the linear displacement variation, obtained from the integrated radial velocity curve, one could determine both the linear radius and the distance of the variable. This distance would be independent of all other astrophysical distance scales and would be geometric, i.e. independent of the effects of interstellar obscuration.
Although none of the current instruments has this capability, the same result can be accomplished indirectly through use of the stellar surface brightness. Recall that the visual surface brightness can be expressed in terms of the apparent visual magnitude and the stellar angular diameter. At any phase in the Cepheid pulsation, knowledge of the visual surface brightness and the apparent magnitude permits inference of the angular diameter.
From stars with measured angular diameters it is known that the visual surface brightness parameter Fv correlates remarkably well with the Johnson V-R color index (Barnes and Evans 1976; Barnes, Evans and Parsons 1976; Barnes, Evans and Moffett 1978). Johnson VR photometry may thus be used to determine the visual surface brightness and hence the stellar angular diameter. As shown in the referenced works, such angular diameters are essentially independent of the choice of interstellar obscuration corrections. This approach to stellar angular diameters and then to variable star distances is therefore nearly equivalent to direct measurements.