Rapid evaluation of vignetting-free high-performance systems

Gregory W. Forbes*, Johannes Ruoff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


System assessment for design often involves averages, such as the standard deviation of the wavefront error, which are estimated by ray tracing through a sample of points within the entrance pupil. General-purpose sampling and weighting schemes are presented, and it is also shown that optical design can benefit from tailored versions of these schemes. It turns out that the type of Gaussian quadrature that has long been recognized for efficiency in this domain requires about 40% to 50% more ray tracing to attain comparable accuracy to generic versions of the new schemes. Even greater efficiency gains can be won, however, by tailoring such sampling schemes to the optical context where azimuthal variation in the wavefront is generally weaker than the radial variation. These new schemes are special cases of what is known in the mathematical world as cubature. Our initial results also led to the consideration of simpler sampling configurations that approximate the newfound cubature schemes. We report on the practical application of a selection of such schemes and make observations that aid in the discovery of cubature schemes relevant to optical design of systems with circular pupils. (C) 2018 Society of Photo-Optical Instrumentation Engineers (SPIE)

Original languageEnglish
Article number101709
Pages (from-to)1-10
Number of pages10
JournalOptical Engineering
Issue number10
Publication statusPublished - 1 Oct 2018


  • cubature
  • numerical methods
  • optical design
  • quadrature
  • system evaluation


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