Finite element Fourier and Abbe transform methods for generalization of aperture function and geometry in Fraunhofer diffraction theory
- Idaho National Engineering Lab., EG and G Idaho, Inc., Idaho Falls, ID (US)
This paper discusses methods for calculating Fraunhofer intensity fields resulting from diffraction through one- and two-dimensional apertures are presented. These methods are based on the geometric concept of finite elements and on Fourier and Abbe transforms. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define aperture(s) 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 transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is most evident in two dimensions, where several examples are presented which include secondary obstructions, straight and curved secondary spider supports, multiple-mirror arrays, synthetic aperture arrays, segmented mirrors, apertures covered by screens, apodization, and phase plates. Typically, the finite element Abbe transform method results in significant gains in computational efficiency over the finite element Fourier transform method, but is also subject to some loss in generality.
- DOE Contract Number:
- AC07-76ID01570
- OSTI ID:
- 7114269
- Journal Information:
- Optical Engineering; (United States), Vol. 30:8; ISSN 0091-3286
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
47 OTHER INSTRUMENTATION
DIFFRACTION
FRAUNHOFER LINES
APERTURES
CALCULATION METHODS
EFFICIENCY
FINITE ELEMENT METHOD
FOURIER TRANSFORMATION
GAUSS FUNCTION
INTEGRALS
NUMERICAL ANALYSIS
ONE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
COHERENT SCATTERING
FUNCTIONS
INTEGRAL TRANSFORMATIONS
MATHEMATICS
NUMERICAL SOLUTION
OPENINGS
SCATTERING
TRANSFORMATIONS
661300* - Other Aspects of Physical Science- (1992-)
440600 - Optical Instrumentation- (1990-)