Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system
Abstract
An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.
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Superposition of the original σ-polarized state and the converted (-σ)-polarized state with the exp(2iσφ) vortex generates characteristic 'four-petal' patterns in the first and second Stokes parameters S1 and S2; this effect was observed in diffusive backscattering from microparticle suspensions, scattering by liquid-crystal droplets, and dipole nanoparticle scattering.
“Superposition of the original σ -polarized state and the converted ( -σ )-polarized state with the exp 2 i σφ ( ) vortex generates characteristic 'four-petal' patterns in the first and second Stokes parameters S 1 and S 2 , Fig. 2e. This effect was observed in systems of different nature and scales: diffusive backscattering from microparticle suspensions 109- 111 , scattering by”
From Spin–orbit interactions of light (2015) · cites this paper as [110]
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- Authors
- Richards, B., & Wolf, E.
- Affiliations
- University of Manchester (GB)
- ORCID
- Venue
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1959-12-15
- Volume
- 253
- Issue
- 1274
- Pages
- 358-379
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W2112840649
- Cited by
- 3,095
- References
- 8
- Citations by year
- 2026: 96 · 2025: 127 · 2024: 154 · 2023: 153 · 2022: 144 · 2021: 149 · 2020: 144 · 2019: 182 · 2018: 169 · 2017: 129 · 2016: 130 · 2015: 137 · 2014: 150 · 2013: 134 · 2012: 108
- FWCI
- 1.08
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society of London A Mathematical and Physical Sciences (publishedVersion)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Advanced optical system design
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Keywords
- electromagnetic diffraction, focal plane, linearly polarized light, Poynting vector, energy flow, energy density, unpolarized light, Airy functions, Lommel functions, Struve functions, scalar diffraction theory, resolving power
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