Measuring the Height Transfer Function of Phase-Shifting Interferometers

There is an increasing need for accurate measurements of precision surfaces and optical elements over a wide range of spatial frequencies. Ripple in an optical surface, for example, can decrease the performance of demanding optical systems. In characterizing the uncertainty of a surface interferometer, its spatial height transfer function, the dependence of the measured height (or phase) on the spatial frequency content of the measured surface, is rarely considered. In this project we develop test methods for users and manufacturers of surface interferometers to characterize the spatial height transfer function of the interferometer with a specially patterned artifact.

The goal of this project is to characterize the system response of phase-shifting interferometers at different spatial frequencies. In characterizing the uncertainty of a phase-shifting interferometer, its spatial height transfer function, the dependence of the measured height (or phase) on the spatial frequency, is rarely considered. Most conventional applications of surface interferometers are measurements of smoothly polished lenses or mirror surfaces, for which often only relatively low spatial frequencies are of interest. For very demanding applications, the form errors at higher frequencies must also be measured because they can affect the performance of an optical system.

In this project, a mirror with a special height pattern is fabricated using a lithography-based process. The mirror can be used to measure the height transfer function of the interferometer at all frequencies that can be sampled by the camera of the interferometer. The 150 mm diameter mirror has several patterns (reminiscent of moth antennae) with variable spacing in the radial direction. The mirror is applied to evaluate the height transfer characteristics of several types of interferometers under various operating conditions that affect performance, e.g. as a function of the amount of defocus.

• Designed, fabricated, and characterized several test mirrors with different types of radial height relief patterns.
• Evaluated the height transfer function characteristics of several NIST interferometers under various operating conditions (e.g., amount of defocus), and demonstrated that for some interferometers the height response is not uniform over the interferometer aperture.
• In collaboration with NASA, compared experimental results on the height transfer characteristics of an interferometer with analytical predictions.