Test optics error removal

Wave-front or surface errors may be divided into rotationally symmetric and nonrotationally symmetric terms. It is shown that if either the test part or the reference surface in an interferometric test is rotated to N equally spaced positions about the optical axis and the resulting wave fronts are averaged, then errors in the rotated member with angular orders that are not integer multiples of the number of positions will be removed. Thus if the test piece is rotated to N equally spaced positions and the data rotated back to a common orientation in software, all nonrotationally symmetric errors of the interferometer except those of angular order kN theta are completely removed. It is also shown how this method may be applied in an absolute test, giving both rotationally symmetric and nonsymmetric components of the surface. A general proof is given that assumes only that the surface or wave-front information can be described by some arbitrary set of orthognal polynomials in a radial coordinate r and terms in sin theta and cos theta. A simulation, using Zernike polynomials, is also presented.