Absolute surface metrology with a phase-shifting interferometer for incommensurate transverse spatial shifts

We consider the detailed implementation and practical utility of a novel absolute optical metrology scheme recently proposed for use with a phase-shifting interferometer (PSI). This scheme extracts absolute phase differences between points on the surface of the optic under test by differencing phase maps made with slightly different transverse spatial shifts of that optic. These absolute phase (or height) differences, which for single-pixel shifts are automatically obtained in the well-known Hudgin geometry, yield the underlying absolute surface map by standard wavefront reconstruction techniques. The PSI by itself maps surface height only relative to that of a separate reference optic known or assumed to be flat. In practice, even relatively high-quality (and expensive) transmission flats or spheres used to reference a PSI are flat or spherical only to a few dozen nanometers peak to valley (P-V) over typical 4 in. apertures. The new technique for removing the effects of the reference surface is in principle accurate as well as simple, and may represent a significant advance in optical metrology. Here it is shown that transverse shifts need not match the pixel size; somewhat counterintuitively, the single-pixel spatial resolution of the PSI is retained even when transverse shifts are much coarser. Practical considerations for shifts not necessarily commensurate with pixel size, and broader applications, are discussed.