A Sampling Theorem for Computational Diffraction

2013/01/29 by Daniel J. Merthe, Merthe, Daniel J.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Optics (physics.optics) #math-ph #math.MP #physics.optics

paper · pdf · doi:10.48550/arxiv.1301.6814

arxiv created 2013/02/01 · arxiv updated 2013/02/04

Abstract

A major challenge of many diffraction calculations, using some form of the Rayleigh-Sommerfeld formulas, is the integration of a highly oscillatory integrand. Here we derive a potentially useful alternative form of solution to the Helmholtz equation, which implies a sampling theorem for the evaluation of a diffracted scalar field. This alternative solution bears close resemblance to the Rayleigh-Sommerfeld diffraction formulas, but instead incorporates the boundary conditions digitally. Hence, the integration is replaced by a simple summation. This formulation may be more efficient for accurate computer-based calculation of the diffracted scalar field.

Related

• Line-Integral Representations of the Diffraction of Scalar Fields
• Some computational aspects of using Huygens-Fresnel-Kirchoff diffraction theory
• Geometrical Theory of Diffraction*
• Diffraction to De-Diffraction
• Algorithmics of Diffraction