A technique is presented for calculating the aberrations induced by mislocation of a large aspheric optic in an interferometric test. This mislocation can be described by a set of five vectors representing small displacements from an ideal position relative to the interferometer. Two different interferometric test configurations will be analyzed. In one such configuration, the optic is tested in autocollimation at its focal point. In the second such configuration, the optic is tested in retroreflection at its center of curvature. The appropriate aberration function for a displaced but otherwise perfect conic section is developed for each configuration. For testing at focus, this function depends on all five degrees of freedom, but four of them couple in pairs. For center-of-curvature testing, the aberration function depends on translational displacements only, not tilts. We show that even when tight mechanical tolerances are applied to positioning, the aberration effects can still be significant for high precision work. We carry out detailed computations for two optics of typical dimensions to illustrate the importance of these effects. We present a technique to optimally remove errors associated with displacement of an otherwise perfect conic section. The method developed is completely general, including all relevant degrees of freedom. Indeed, the least-squares analysis is carried out on a loss function whose form is independent of testing method and conic constant. Once these mislocation-related errors have been removed, the metrologist can calculate the true aberration function of the optic under test. In this fashion, surface correction contours can be generated for further material removal if required.