| This project was inspired by the need for a remote method to accurately measure radius of curvature of mirrors tested under the NASA Advanced Mirror System Demonstrator program. Under this program, off axis parabolas (subscale candidates for James Webb Space Telescope optical elements) were tested under cryo-vac conditions. A remote, differential interferometric method is presented for measuring the shape parameters of general aspheric mirrors. The result of measurement is the assignment of best-fit values to a set of parameters that characterize the shape of the surface. If the mirror is nominally a conic of rotation, for example, the measurement yields the radius of curvature and conic constant. The method involves testing the optic in an interferometric center-of-curvature null configuration but can easily be extended to include conjugate null tests. During the measurement, known translational misalignments are introduced and the effects on the optical path length function are measured using a phase-shifting interferometer. Based on the nominal mirror shape, a model function is defined, up to a set of free shape parameters. The mirror shape parameters are regressed, based on the interferometric data, from this model. This differential measurement method works for on- and off-axis mirrors of all shapes and can be applied remotely as long as the mirror is mounted on an actuated stage. Hence, this measurement method would work well in a cryogenic testing situation. We have successfully applied the method to the case of an off-axis parabola with a nominal radius of curvature of 304.8 mm, a diameter of 76.17 mm, and a pupil offset of -89.40 mm. |
