Math 2.0

Optics, electromagnetic theory Geometrical optics Concept

Keller's geometrical theory of diffraction

Builds on Geometric opticsFermat's principleSommerfeld's half-plane diffraction problem

Summary

Keller's geometrical theory of diffraction is a high-frequency method that adds diffracted rays to the rays of geometrical optics. Diffracted rays start at edges, corners and grazing points of obstacles, and they obey a generalised form of Fermat's principle. The field carried by each diffracted ray is fixed by a diffraction coefficient taken from an exactly solvable model problem, such as Sommerfeld's half-plane problem. It explains how light reaches the geometrical shadow, and its failure at shadow boundaries led to the uniform theory of diffraction.

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Calculus of variations, concept, no evidence levelCalculus of variationsconceptEuler–Lagrange equation, concept, no evidence levelEuler–Lagrange equati…conceptFresnel integrals, concept, no evidence levelFresnel integralsconceptGeodesic, concept, no evidence levelGeodesicconceptGeometric optics, concept, no evidence levelGeometric opticsconceptHelmholtz equation, concept, no evidence levelHelmholtz equationconceptWiener–Hopf method, concept, no evidence levelWiener–Hopf methodconceptFermat's principle, statement, no evidence levelFermat's principlestatementSommerfeld's half-plane diffraction problem, problem, no evidence levelSommerfeld's half-pla…problemKeller's geometrical theory of diffraction, concept, no evidence levelKeller's geometrical …concept
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  • no evidence level
  1. Calculus of variations concept
  2. Euler–Lagrange equation concept
  3. Fresnel integrals concept
  4. Geodesic concept
  5. Geometric optics concept
  6. Helmholtz equation concept
  7. Wiener–Hopf method concept
  8. Fermat's principle statement
  9. Sommerfeld's half-plane diffraction problem problem
  10. Keller's geometrical theory of diffraction concept

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Further reading

  1. Web https://en.wikipedia.org/wiki/Uniform_theory_of_diffraction
About this page
TagES9KPGJAGS
URIm2://ES9KPGJAGS
Kindconcept
WritingW0 stub
MSC78A45, 78M35, 78A05
UsesGeometric optics, Fermat's principle, Sommerfeld's half-plane diffraction problem
Changed3 November 2026

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