Rayleigh-Sommerfield Diffraction vs Fresnel-Kirchhoff, Fourier Propagation and Poisson's Spot

Abstract

The boundary conditions imposed on the diffraction problem in order to obtain the Fresnel-Kirchhoff (FK) solution are well-known to be mathematically inconsistent and to be violated by the solution when the observation point is close to the diffracting screen 1-3. These problems are absent in the Rayleigh- Sommerfeld (RS) solution. The difference between RS and FK is in the inclination factor and is usually immaterial because the inclination factor is approximated by unity. But when this approximation is not valid, FK can lead to unacceptable answers. Calculating the on-axis intensity of Poisson s spot provides a critical test, a test passed by RS and failed by FK. FK fails because (a) convergence of the integral depends on how it is evaluated and (b) when the convergence problem is xed, the predicted amplitude at points near the obscuring disk is not consistent with the assumed boundary conditions.

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Document Details

Document Type
Technical Report
Publication Date
Dec 30, 2004
Accession Number
ADA429355

Entities

People

  • Robert L. Lucke

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Sensors

DTIC Thesaurus Topics

  • Acoustic Waves
  • Acoustics
  • Amplitude
  • Boundaries
  • Computer Programs
  • Differential Equations
  • Diffraction
  • Equations
  • Fourier Series
  • Helmholtz Equations
  • Integrals
  • Intensity
  • Jet Propulsion
  • Plane Waves
  • Three Dimensional
  • Two Dimensional
  • Waves

Readers

  • Calculus or Mathematical Analysis
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering