Axial shift mapping metrology for X-ray telescope mirrors

The next generation of high-resolution X-ray telescopes will require mirror segments characterized to 5 nm uncertainty or better. This is difficult to achieve due to the mirror segment's off-axis hyperbolic and parabolic shape and the challenge of manufacturing and testing a cylindrical null lens. In a typical Fizeau interferometer setup, errors in the assumed perfect null lens will be coupled into the final surface figure, increasing uncertainty. To combat the higher uncertainty of the cylindrical null corrector, we have been developing lateral shift mapping, an absolute metrology technique using a Fizeau interferometer. In this technique, the surface under test is laterally shifted between measurements while the reference surface does not move. Contributions to the interferogram due to the surface under test will move, while contributions due to the reference will stay static. Using this information, we can extract the true surface under test with low uncertainty. There is a quadratic ambiguity that arises due to the extraction method being akin to an integration. We have shown in the past our ability to utilize lateral shift mapping to extract flat surfaces to sub-nanometer uncertainties by comparing our results to a three-flat test. We also demonstrated that we can eliminate the quadratic ambiguity in flats using an external measurement with an autocollimator. We are expanding this method from optical flats to cylindrical surfaces, creating axial shift mapping. We will report on progress toward sub-nanometer measurements of cylindrical mirrors using axial shift mapping.