Surface shape measurement of mirrors in the form of rotation figures by using point diffraction interferometer

Abstract

The paper deals with the use of a point diffraction interferometer (PDI) to study the surface shape of rotation figures. The relations are given for the correspondence of the coordinates on the surfaces of an ellipsoid, a paraboloid and a hyperboloid as well as on an interferogram. Using PDI and Zygo white-light interferometer (WLI), we experimentally investigated the surface shape of the grazing incidence ellipsoid with the multilayer reflective coating on a wavelength of 0.154 nm with the following parameters: length is 55 mm, half-axis are 6 and 235 mm. The results coincided with an accuracy of 73 nm (RMS) without taking into account the PDI lateral resolution, and with an accuracy of 50 nm (RMS) with taking it into account, which ensures the local angles measurement accuracy of the ellipsoid-shaped reflecting surface at a level of 3 μrad. We think that this difference may be attributed to the limited lateral resolution of PDI and errors of frames stitching of WLI; nevertheless, we do believe that the PDI measurement accuracy is in the range of sub-μrad.