Self-referenced technique for the determination of meridional figure errors of a toroidal mirror with a Sagnac interferometer.

A simple, self-referenced technique for the determination of meridional surface slope errors of toroidal mirrors (TMs) used in synchrotron radiation is presented. An expanded, collimated, linearly polarized laser beam is allowed to fall on a TM, and the reflected toric wavefront from the TM is allowed to enter a Sagnac interferometer based lateral shearing interferometer setup, which duplicates the beam into identical wavefront components having orthogonal linear polarizations, i.e., p and s polarizations, and introduces appropriate lateral shear between the identical pair of wavefronts along the meridional direction. The laterally sheared identical wavefronts interfere when brought to the same state of polarization. The optical path difference (OPD) variation along the direction of the lateral shear in the interference field is a map of the slope variation. Polarization phase shifting interferometery has been applied to find the OPD variation and thus the slope distribution and errors. Results obtained for a TM of moderately long average radius of curvature along the central meridional section and a relatively shorter radius of curvature along the sagittal section are presented and compared with that obtained with a long trace profiler.