Perturbation methods in optics: application to the interferometric measurement of surfaces

Manufacturing and misalignment errors are present in every optical system. Usually these errors lead to intolerable wavefront deviations and system inaccuracies if they are not characterized and taken into consideration. In the interferometric measurement of surfaces, the characterization of the interferometer aberrations plays a central role, since unknown phase contributions lead to an erroneous assessment of the test surface and therefore an incorrect estimation of the performance of an optical system. In this work, we present a method for the interferometric characterization of surfaces based on the principles of Hamilton's characteristic functions and perturbation theory. The application of the proposed method to an interferometer for the measurement of aspherical surfaces is shown.