Geometrical distortion effect in Fizeau interferometry measurements of large-radius tangentially curved optics. Part 1: development, characterization, and first application of bendable URA BPRA test sample

Abstract

Plane wavefront Fizeau interferometry (PWFI) is one of the major metrology techniques for surface characterization of xray optics in the low and middle spatial frequency range. However, PWFI measurements of curved optics are often associated with significant systematic effects arising from complex phenomena, including retrace error, geometrical distortion, image blurring and even sharpening with a tilted surface under test. This paper presents the results of experimental tests and preliminary theoretical modeling to reveal the peculiarities of the geometrical distortion (GD) effect in the PWFI measurements of large-radius tangentially curved surfaces. The tests were performed at the Advanced Light Source (ALS) X-Ray Optics Laboratory (XROL) in the scope of the research and development projects, supported by the DOE SBIR/STTR Program. As a test optical element, we use a specially developed flexible (bendable) test sample with the optical surface patterned as a uniformly redundant array (URA) with the minimum feature size of 730 μm. The inherent binary pseudo-random nature of the URA test patterns allowed us to calibrate the geometric distortions of the Fizeau interferometers available in the ALS XROL laboratory, while avoiding the effect of parasitic interference that occurs when using inherently periodic checkerboard test patterns. We have investigated the GD effect at different curvatures of the URA surface and found a strong (by almost an order of magnitude) increase of the GD error with decrease the surface radius of curvature (ROC) from approximately 250 meters down to 50 meters. To the best of our knowledge, we firstly reveal a significant dependence of the GD error on the interferometer’s defocus. The present investigation in combination of the results of our previous study of other systematic effects in Fizeau interferometry strongly suggests that, for accurate results, the Fizeau interferometers must be thoroughly characterized experimentally, in an arrangement as close as possible to the arrangement used with a particular OUT. Deep understanding of the instrument performance, together with calibration capabilities allowing data reconstruction based on the tool’s calibration, are critical elements of the high accuracy Fizeau interferometry, especially in the stitching mode of measurement.