Interferometric apparatus and methodology for precisely measuring the shape of rotationally and non-rotationally symmetric optical surfaces comprising an illumination source with two wavelengths, a transmission flat with a reference surface, a basic optical system for producing a wavefront of predetermined shape, a compensation component having an aspheric wavefront shaping surface and an aspheric reference surface. The aspheric shaping surface modifies the predetermined wavefront so that it impinges on the aspheric reference surface with a shape substantially that same as that of aspheric reference surface. For a given aspheric reference surface, the radius or curvature and spacing of the aspheric shaping surface are optimized so that its aspheric departure is no larger than that of the aspheric reference surface. Precise alignment in six degrees of freedom is provided via feedback control.