Absolute surface metrology by differencing spatially shifted maps from a phase-shifting interferometer

Surface measurements of precision optics are commonly made with commercially available phase-shifting Fizeau interferometers that provide data relative to flat or spherical reference surfaces whose unknown errors are comparable to those of the surface being tested. A number of ingenious techniques provide surface measurements that are "absolute," rather than relative to any reference surface. Generally, these techniques require numerous measurements and the introduction of additional surfaces, but still yield absolute information only along certain lines over the surface of interest. A very simple alternative is presented here, in which no additional optics are required beyond the surface under test and the transmission flat (or sphere) defining the interferometric reference surface. The optic under test is measured in three positions, two of which have small lateral shifts along orthogonal directions, nominally comparable to the transverse spatial resolution of the interferometer. The phase structure in the reference surface then cancels out when these measurements are subtracted in pairs, providing a grid of absolute surface height differences between neighboring resolution elements of the surface under test. The full absolute surface, apart from overall phase and tip/tilt, is then recovered by standard wavefront reconstruction techniques.