Generalization of the Coddington equations to include hybrid diffractive surfaces

Chunyu Zhao, James H Burge

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

3 Citations (Scopus)

Abstract

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 publicationProceedings of SPIE - The International Society for Optical Engineering
Volume7652
DOIs
StatePublished - 2010
EventInternational Optical Design Conference 2010 - Jackson Hole, WY, United States
Duration: Jun 13 2010Jun 17 2010

Other

OtherInternational Optical Design Conference 2010
CountryUnited States
CityJackson Hole, WY
Period6/13/106/17/10

Fingerprint

Half line
rays
Ray Tracing
Ray tracing
Wavefronts
ray tracing
Wave Front
Lens Design
Aspheric Surface
lens design
Hologram
Holograms
Generalized Equation
bundles
Null
Lenses
Bundle
derivation
Imaging
formalism

Keywords

  • Aberration
  • Interferometric imaging
  • Optical design
  • Testing

ASJC Scopus subject areas

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

Cite this

Zhao, C., & Burge, J. H. (2010). Generalization of the Coddington equations to include hybrid diffractive surfaces. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 7652). [76522U] https://doi.org/10.1117/12.871853

Generalization of the Coddington equations to include hybrid diffractive surfaces. / Zhao, Chunyu; Burge, James H.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7652 2010. 76522U.

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

Zhao, C & Burge, JH 2010, Generalization of the Coddington equations to include hybrid diffractive surfaces. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 7652, 76522U, International Optical Design Conference 2010, Jackson Hole, WY, United States, 6/13/10. https://doi.org/10.1117/12.871853
Zhao C, Burge JH. Generalization of the Coddington equations to include hybrid diffractive surfaces. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7652. 2010. 76522U https://doi.org/10.1117/12.871853
Zhao, Chunyu ; Burge, James H. / Generalization of the Coddington equations to include hybrid diffractive surfaces. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7652 2010.
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