### 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 2^{nd} order, and an incident wavefront of any shape to the 2^{nd} order, the refracted or reflected wavefront can be calculated to the 2^{nd} 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 language | English (US) |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 7652 |

DOIs | |

State | Published - 2010 |

Event | International Optical Design Conference 2010 - Jackson Hole, WY, United States Duration: Jun 13 2010 → Jun 17 2010 |

### Other

Other | International Optical Design Conference 2010 |
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Country | United States |

City | Jackson Hole, WY |

Period | 6/13/10 → 6/17/10 |

### Fingerprint

### 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

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Generalization of the Coddington equations to include hybrid diffractive surfaces

AU - Zhao, Chunyu

AU - Burge, James H

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Aberration

KW - Interferometric imaging

KW - Optical design

KW - Testing

UR - http://www.scopus.com/inward/record.url?scp=78049407685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78049407685&partnerID=8YFLogxK

U2 - 10.1117/12.871853

DO - 10.1117/12.871853

M3 - Conference contribution

AN - SCOPUS:78049407685

SN - 9780819480828

VL - 7652

BT - Proceedings of SPIE - The International Society for Optical Engineering

ER -