Absolute spherical test towards an accuracy of one-hundredth of the wavelength

Two dominant systematic errors in the absolute interferometric test of high numerical-aperture sphericals are discussed and measured experimentally in pursuit of an accuracy of λ=100. Gravitational sag deformation of a 4-inch spherical concave surface was measured in a vertical phase-shifting Fizeau interferometer. The surface shapes of two identical transmission spherical concaves were measured via the two-surface comparison method using three positional measurements. One of the surfaces was then rotated around the optical axis and the interference phases were averaged to extract a rotationally symmetric component of the aberration. The gravitational sag was then determined by the aberration component independent of the rotation. The geometrical error in the phase shift is also estimated theoretically and corrected in the experiment. Experimental results show that the both errors amount to 6 to 7 nm peak-to-valley lengths, the magnitudes of which are comparable to that of the total aberration of the spherical surface.