Share Email Print

Optical Engineering

Finite element area and line integral transforms for generalization of aperture function and geometry in Kirchhoff scalar diffraction theory
Author(s): Hal G. Kraus
Format Member Price Non-Member Price
PDF $20.00 $25.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper Abstract

Two finite element-based methods for calculating Fresnel region and near-field region intensities resulting from diffraction of light by two-dimensional apertures are presented. The first is derived using the Kirchhoff area diffraction integral and the second is derived using a displaced vector potential to achieve a line integral transformation. The specific form of each ofthese formulations is presented for incident spherical waves and for Gaussian laser beams. The geometry of the twodimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define apertures of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s), which may be of continuous or discontinuous form. The finite element transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is illustrated in several examples which include secondary obstructions, secondary spider supports, multiple mirror arrays, synthetic aperture arrays, apertures covered by screens, apodization, phase plates, and off-axis apertures. Typically, the finite element line integral transform results in significant gains in computational efficiency over the finite element Kirchhoff transform method, but is also subject to some loss in generality.

Paper Details

Date Published: 1 February 1993
PDF: 16 pages
Opt. Eng. 32(2) doi: 10.1117/12.60856
Published in: Optical Engineering Volume 32, Issue 2
Show Author Affiliations
Hal G. Kraus, Idaho National Engineering Lab. (United States)

© SPIE. Terms of Use
Back to Top