Generalization of the Coddington equations to include hybrid diffractive surfaces

Chunyu Zhao; James H Burge

doi:10.1117/12.871853

9 September 2010 Generalization of the Coddington equations to include hybrid diffractive surfaces

Chunyu Zhao, James H Burge

Proceedings Volume 7652, International Optical Design Conference 2010; 76522U (2010) https://doi.org/10.1117/12.871853
Event: International Optical Design Conference 2010, 2010, Jackson Hole, WY, United States

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.

Citation Download Citation

Chunyu Zhao and James H Burge "Generalization of the Coddington equations to include hybrid diffractive surfaces", Proc. SPIE 7652, International Optical Design Conference 2010, 76522U (9 September 2010); https://doi.org/10.1117/12.871853

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