Criteria for correction of quadratic field-dependent aberrations

Chunyu Zhao, James H. Burge

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Aberrations of imaging systems can be described by using a polynomial expansion of the dependence on field position, or the off-axis distance of a point object. On-axis, or zero-order, aberrations can be calculated directly. It is well-known that aberrations with linear field dependence can be calculated and controlled by using the Abbe sine condition, which evaluates only on-axis behavior. We present a new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations is derived by using Hamilton's characteristic functions and simplified by evaluating astigmatism in the pupil. The equations, which we call the pupil astigmatism criteria, use on-axis behavior to evaluate and control all aberrations with quadratic dependence on the field and arbitrary dependence on the pupil. These relations are explained and are validated by using several specific optical designs.

Original languageEnglish (US)
Pages (from-to)2313-2321
Number of pages9
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number11
StatePublished - Nov 2002

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition


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