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

Lateral shearing self-referencing interferometry methods shift the surface under test between measurements to separate its topography from that of the reference surface. However, rigid body errors occur during shifting, creating an ambiguity in the quadratic term of the extracted surfaces. We present axial shift mapping, a lateral shearing self-referencing interferometry method for cylinders, in which the quadratic ambiguity is resolved by measuring the rigid body errors using known artifact mirrors residing in the interferometer's field of view. First, one-dimensional lines of a flat mirror are measured with 2.8 nm RMS difference compared to a three flat test. Then, axial shift mapping is extended to cylindrical surfaces using a computer generated hologram. We find that axial shift mapping results in full surface extraction of cylindrical optics, along the axial direction, with a repeatability of 4.4 nm RMS. We also find that the reference surface extracted through axial shift mapping is within 4.5 nm RMS of the transmitted wavefront error of the computer generated hologram substrate, which was expected to be the largest contribution of reference wavefront error.