Absolute testing of rotationally symmetric surfaces with computer-generated holograms

Extremely high accuracy is demanded for optics working at very short wavelength. Interferometric testing of optical aspheres or freeform surfaces requires null optics, typically computer-generated holograms (CGHs), to balance the wave aberrations. The measurement uncertainty is primarily limited by the accuracy of the test wavefront, which is predominantly influenced by the CGH and the interferometer optics. Absolute testing is fundamental to achieving accuracy much higher than that of the test wavefront through error separation. This paper presents a method for absolute testing of rotationally symmetric surfaces with CGH null optics. The basic assumption is that the off-axis hologram fabricated by raster scanning beam writing has negligible error of rotationally symmetric component due to pattern error of the CGH. Consequently, the wavefront error contributed by the CGH and the transmission flat can be completely separated from the absolute surface shape by combining the N-position method and the shift-rotation method. A theoretical model for absolute testing is proposed under the assumption. Experimental cross test is then presented to validate the method with sub-nanometer uncertainty. The assumption is further confirmed by characterizing the fabrication error of the hologram structures using a white light interferometer. Finally, the effect of noise, translation error, rotation error and eccentricity of rotation on the absolute testing is analyzed.