The Structure of Fraunhofer Diffraction Patterns of Apertures with N-fold Rotational Symmetry
| Autor: | R.M. Sillitto |
|---|---|
| Rok vydání: | 1983 |
| Předmět: |
Physics
Diffraction Aperture business.industry Zernike polynomials Astrophysics::Instrumentation and Methods for Astrophysics Rotational symmetry Physics::Optics Geometry Invariant (physics) Electronic Optical and Magnetic Materials symbols.namesake Optics Fourier transform Homogeneous space symbols business Bessel function |
| Zdroj: | Optica Acta: International Journal of Optics. 30:1525-1540 |
| ISSN: | 0030-3909 |
| DOI: | 10.1080/713821089 |
| Popis: | The moment theorem is used to show that the innermost part of the Fraunhofer diffraction pattern of any real aperture with higher than two-fold rotational symmetry is rotationally invariant. Then a formalism is presented in which aperture transmission-functions are represented by series of Zernike circle polynomials and diffracted field-amplitudes by series of Bessel functions, from which it is easily shown that the diffraction patterns of such apertures consist of regions, contained between well-defined values of the radius, whose rotational symmetries are integral multiples of that of the aperture. The central region, extending from = 0 to , N ( measures the diffraction angle, and N is the degree of rotational symmetry of the aperture) is rotationally invariant, and successive circumjacent regions have progressively higher rotational symmetries. The diffraction patterns of sectoral apertures and of rings of pinholes are derived and shown to exemplify these general conclusions. Finally it is shown h... |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|