Parametric mid-spatial frequency surface error synthesis

Timothy Hefferan, Logan Graves, Isaac Trumper, Soojong Pak, Daewook Kim

Research output: Contribution to journalArticlepeer-review


Standard mid-spatial frequency tooling mark errors were parameterized into a series of characteristic features and systematically investigated. Diffraction encircled and ensquared energy radii at the 90% levels from an unpowered optical surface were determined as a function of the root-mean-square surface irregularity, characteristic tooling mark parameters, fold mirror rotation angle, and incident beam f-number. Tooling mark frequencies on the order of 20 cycles per aperture or less were considered. This subset encompasses small footprints on single-point diamond turned optics or large footprints on sub-aperture tool polished optics. Of the characteristic features, off-axis fabrication distance held the highest impact to encircled and ensquared energy radii. The transverse oscillation of a tooling path was found to be the second highest contributor. Both impacts increased with radial tooling mark frequency.

Original languageEnglish (US)
Article number584
Issue number12
StatePublished - Dec 2021


  • Encircled energy
  • Fabrication
  • Metrology
  • Periodic structure
  • Tooling marks

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Instrumentation
  • Radiology Nuclear Medicine and imaging


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