Optimal local shape description for rotationally non-symmetric optical surface design and analysis

Opt Express. 2008 Feb 4;16(3):1583-9. doi: 10.1364/oe.16.001583.


A local optical surface representation as a sum of basis functions is proposed and implemented. Specifically, we investigate the use of linear combination of Gaussians. The proposed approach is a local descriptor of shape and we show how such surfaces are optimized to represent rotationally non-symmetric surfaces as well as rotationally symmetric surfaces. As an optical design example, a single surface off-axis mirror with multiple fields is optimized, analyzed, and compared to existing shape descriptors. For the specific case of the single surface off-axis magnifier with a 3 mm pupil, >15 mm eye relief, 24 degree diagonal full field of view, we found the linear combination of Gaussians surface to yield an 18.5% gain in the average MTF across 17 field points compared to a Zernike polynomial up to and including 10th order. The sum of local basis representation is not limited to circular apertures.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Computer Simulation
  • Computer-Aided Design*
  • Equipment Design / methods*
  • Equipment Failure Analysis / methods*
  • Lenses*
  • Models, Theoretical*