Generalization of the Coddington equations to include hybrid diffractive surfaces

Chunyu Zhao, James H. Burge

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


Coddington Equations are used to calculate the astigmatic images of a small bundle of rays centered on a ray commonly known as the principal ray. Some authors generalize it such that for a refractive or reflective surface of any shape to the 2nd order, and an incident wavefront of any shape to the 2nd order, the refracted or reflected wavefront can be calculated to the 2nd order. We extend it further such that it applies to the diffractive surface as well. The derivation is based on the general Snell's law and differential ray tracing approach. We present these generalized Coddington Equations in two forms: matrix formalism and explicit expressions. The equations are verified with explicit ray tracing using a commercial lens design program. The relations are applied to evaluate the imaging performance for null testing of aspheric surfaces using computer generated holograms.

Original languageEnglish (US)
Title of host publicationInternational Optical Design Conference 2010
StatePublished - 2010
EventInternational Optical Design Conference 2010 - Jackson Hole, WY, United States
Duration: Jun 13 2010Jun 17 2010

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherInternational Optical Design Conference 2010
Country/TerritoryUnited States
CityJackson Hole, WY


  • Aberration
  • Interferometric imaging
  • Optical design
  • Testing

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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