# Spectral methods in edge-diffraction theories

## Abstract

Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries and caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are throughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [Proc. IEEE 62, 1468 (1974)] for circular apertures is deduced. 34 refs., 1 fig.

- Authors:

- (Univ. of Glasgow (United Kingdom))

- Publication Date:

- OSTI Identifier:
- 7059226

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of the Optical Society of America, Part A: Optics and Image Science; (United States); Journal Volume: 9:12

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; DIFFRACTION; THEORETICAL DATA; ELECTROMAGNETIC PULSES; INTEGRALS; ASYMPTOTIC SOLUTIONS; MAGNETOACOUSTIC WAVES; GEOMETRY; SPECTRA; COHERENT SCATTERING; DATA; ELECTROMAGNETIC RADIATION; HYDROMAGNETIC WAVES; INFORMATION; MATHEMATICS; NUMERICAL DATA; PULSES; RADIATIONS; SCATTERING; 664200* - Spectra of Atoms & Molecules & their Interactions with Photons- (1992-)

### Citation Formats

```
Arnold, J.M..
```*Spectral methods in edge-diffraction theories*. United States: N. p., 1992.
Web. doi:10.1364/JOSAA.9.002192.

```
Arnold, J.M..
```*Spectral methods in edge-diffraction theories*. United States. doi:10.1364/JOSAA.9.002192.

```
Arnold, J.M.. Tue .
"Spectral methods in edge-diffraction theories". United States. doi:10.1364/JOSAA.9.002192.
```

```
@article{osti_7059226,
```

title = {Spectral methods in edge-diffraction theories},

author = {Arnold, J.M.},

abstractNote = {Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries and caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are throughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [Proc. IEEE 62, 1468 (1974)] for circular apertures is deduced. 34 refs., 1 fig.},

doi = {10.1364/JOSAA.9.002192},

journal = {Journal of the Optical Society of America, Part A: Optics and Image Science; (United States)},

number = ,

volume = 9:12,

place = {United States},

year = {Tue Dec 01 00:00:00 EST 1992},

month = {Tue Dec 01 00:00:00 EST 1992}

}