Generalized sine condition

Tamer T. Elazhary, Ping Zhou, Chunyu Zhao, James H. Burge

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The classic Abbe sine condition relates pupil distortion to aberrations with linear field dependence such as coma. This paper provides a fully generalized form of the sine condition that does not use any symmetry. It accurately predicts the change in aberration in the presence of field independent and pupil aberrations. The definitions of the image, object, and coordinate system are completely arbitrary. The relationship is verified using ray trace simulations of a number of systems that have varying degrees of complexity. The potential applications are discussed.

Original languageEnglish (US)
Pages (from-to)5037-5049
Number of pages13
JournalApplied optics
Issue number16
StatePublished - Jun 1 2015

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering


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