It has been brought to the authors' attention (Hanes, personal communication) that the results obtained for the limiting precision in a scanning optical interferometer (Hill and Bruce 1U62) are invalid for the particular conditions examined. Although there does exist a photon noise distinct from the shot noise in the photodetector its effect is very small. The transmittance of the Fabry-Perot interferometer was incorrectly evaluated and when allowance is made for this the limiting precisions of the Michelson and Fabry-Perot interferometers are about equal.