We present a simple, general approach for ascertaining the aberrations due to rigid body motions that are encountered in optical tests. The expressions used are generally applicable to the displacement of an aspheric optic, relative to the aligned position. However, we apply these expressions to two cases of particular interest in interferometric testing. In the first case, the optic is tested in autocollimation at its focal point. We derive an equation for the wavefront aberrations induced by a small displacement from this focal position. Next we calculate the sensitivity to motion in a center-of-curvature test using nulling optics. We obtain the aberration function for a displacement of the test element from an aligned position. For each case, we analyze the sensitivities to the various degrees of freedom for particular off-axis aspheres of interest. In all such testing situations, in particular for high-precision work, displacements are present to some degree. The key requirement is then to remove the induced errors. We develop an optimum procedure for such removal and we give some example calculations. This procedure allows the metrologist to unambiguously identify surface correction profiles needed in the fabrication of precision, off-axis, aspheric segments.