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.