Using a white noise reference object to determine the depth of field of the instrument transfer function for Fizeau interferometers

Fizeau interferometers are a common tool for the measurement of precision surfaces because they offer subnanometer height resolution over large areas. However, the optical system of the interferometer is typically limiting the lateral resolution. To quantify this for interferometers, the ITF (instrument transfer function) is defined as the ratio of measured structure height over actual structure height over the spatial frequency spectrum. The commercial availability of wavelength shifting Fizeau interferometers enables the measurement of multiple objects at different distances from the interferometer against each other. The lateral resolution is then dependent on which plane is in focus, the optical path difference of the objects and the out-of-focus ITF. In order to determine the latter, this report uses a lithographically manufactured reference object which was designed to achieve a constant PSD (power spectral density) over a wide spatial frequency range including the common lateral resolution cut-offs of most Fizeau interferometers. This enables simple and reliable measurements of the ITF for Fizeau interferometers with different aperture sizes.