Axial shift mapping: a self-referencing test for measuring axial figure of near-cylindrical surfaces

Lateral shearing self-referencing interferometry methods shift the surface under test between measurements to extract the surface under test without contributions due to the reference surface. However, rigid body errors occur during shifting which create an ambiguity in the quadratic term of the extracted surfaces. We present axial shift mapping, a lateral shearing self-referencing method for cylinders where we are able to break this quadratic ambiguity through a known artifact mirror in the field of view of the interferometer. We demonstrate how this quadratic ambiguity arises and how a known artifact mirror is used to eliminate the ambiguity. We show extracted one-dimensional surface lines on a flat mirror with 2.8 nm RMS uncertainty. We discuss how we expand axial shift mapping with known artifact mirrors to cylindrical surfaces using a computer generated hologram. We show our ability to use axial shift mapping to do full surface extraction of cylindrical optics along the axial direction with a repeatability of 4.4 nm RMS and demonstrate how the extracted reference surface is within 4.5 nm RMS of agreement with an external measurement source.