Grazing incidence interferometry using diffractive optical elements for the shape measurement of the mantle surface of rod-shaped objects I: measuring principle and theory

摘要

Grazing incidence interferometry can be used to measure the shape of technical surfaces having a rod geometry which means that arbitrary cross sections are allowed while this cross section is kept through the length of the rod in a first approximation. In the first part of the paper the principle and the theoretical background are discussed. For beam splitters and beam shaping suitable diffractive optical elements (DOE) are used. The interferometer is due to the diffractive beam splitters achromatic, i.e., the effective wavelength is equal to the pitch of the DOE. The structures of the DOE are parallel curves to the meridian of the sample under test. The design principle for the calculation of the DOE structures is derived. The interference patterns of ideal typical test pieces like cylinders or more general mathematically convex surfaces can be calculated in a linear approximation as a function of the alignment parameters. This functional is used to remove the alignment aberrations by lsq-fitting to the measured phase values. By axial movements of one DOE the phase of the interference pattern can be varied allowing for phase shift evaluations of the shape of the surface under test.