Measurement of a high numerical aperture spherical mirror using a Computer-Generated hologram

• Optical measurement of a NA0.92 spherical concave mirror using a Computer-Generated Hologram (CGH) • CGH fabrication error calibration using the smallest random ball test and its compensation method. • Calibration of interferometric imaging distortion error using a THz wire grid polarizer. • Measurement result comparison between a conventional stitching method and the proposed CGH method. High precision and high numerical aperture (NA) spherical concave mirror is used as a metrology reference for lithography and spectroscopy optics at UV and X-ray wavelengths. We propose to use a computer-generated hologram (CGH) for optical testing of a reference sphere (RS) with an NA of 0.92 as a less time- and effort-intensive alternative to the conventional sub-aperture stitching method. We experimentally obtained the CGH error using the random ball test (RBT) for the first time to our knowledge. We used a spherical ball with a diameter of 3.175 mm, the smallest ball utilized for RBT reported to date. We experimentally verified that the thickness deviation of the CGH substrate due to the fabrication error induces spherical aberration (SA) that can be effectively compensated by defocusing the CGH position at a predefined amount. We also propose to use a THz wire grid polarizer as a distortion reference for the distortion error calibration of an interferometric imaging system. We verified this measurement method for the RS NA 0.92 and compared the result with the conventional stitching method. The results from both testing approaches produced similar surface error maps, thus verifying each approach’s result. But, the single full aperture measurement using a CGH is found to be more efficient for measuring a high NA reference sphere.