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Geometrical Optics: Theoretical Achievements and Applications
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Geometrical Optics: Theoretical Achievements and Applications

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Optics and Lasers".

Deadline for manuscript submissions: closed (15 December 2021) | Viewed by 19029

Special Issue Editor

Dr. José Antonio Díaz Navas

E-Mail Website
Guest Editor
Departamento de Óptica, Universidad de Granada, 18071 Granada, Spain
Interests: optical imaging; optical design; hyperspectral imaging; physiological optics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Before the electromagnetism mathematical formalism was established and light was revealed as an electromagnetic wave, Geometrical Optics ruled the propagation of luminous radiation as rays in a geometrical framework for centuries. Thus, rays can be considered as lines carrying electromagnetic energy in a 3D space oriented in all directions, and the wave nature of light can be avoided when the wavelength effects are negligible. When the Fermat Principle was stated, an analogy between ray trajectories and mechanics of point particles was formulated by Hamilton, and Hamiltonian Optics was developed providing useful results, and insights from the application of classical mechanics methods. Nowadays, Geometrical Optics approximation to problems is valuable when designing optical systems in an early stage and diffraction effects are not needed. This requires knowledge of lens surface geometry, refractive index distribution, reliable ray-tracing methods, and aberrations. Further, modern illumination systems design also benefits from Geometrical Optics methods for their successful creation. Last but not least, Hamiltonian Optics formalism, its geometric structure, and underlying symmetries provide methods for introducing wider topics in the quantum theory of light.

The aim of this Special Issue is to attract researchers from all around the world with an active interest in Geometrical Optics to present their latest achievements on the topic, including advances in surfaces and lens geometry knowledge, paraxial-based optical predesign of systems, ray-tracing methods including polarization, inverse problems such as determining refractive index distributions or surface geometries from ray-tracing, aberrations in optical systems, and Hamiltonian Optics methods. The accepted contributions will include theoretical considerations, and applications.

Dr. José Antonio Díaz Navas
Guest Editor

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Keywords

  • Optical systems design
  • Paraxial methods
  • Surface geometry
  • Inverse problems
  • Imaging aberrations
  • Ray-tracing algorithms
  • Eikonals
  • Hamiltonian optics
  • Illumination
  • Polarization ray-tracing.

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Published Papers (6 papers)

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Research

13 pages, 327 KiB  
Article
2 × 2 Matrices: Manifolds, Realizations, Applications
by Kenan Uriostegui and Kurt Bernardo Wolf
Appl. Sci. 2021, 11(16), 7479; https://doi.org/10.3390/app11167479 - 14 Aug 2021
Cited by 1 | Viewed by 1869
Abstract
Both geometric and wave optical models, as well as classical and quantum mechanics, realize linear transformations with matrices; for plane optics, these are 2×2 and of unit determinant. Students and some researchers could assume that the structure of this matrix group [...] Read more.
Both geometric and wave optical models, as well as classical and quantum mechanics, realize linear transformations with matrices; for plane optics, these are 2×2 and of unit determinant. Students and some researchers could assume that the structure of this matrix group is fairly evident and hardly interesting. However, the properties and applications even of this lowest 2×2 case are already unexpectedly rich. While in mechanics they cover classical angular momentum, quantum spin, and represent ‘2+1’ relativity, in optical models they lead from the geometrical description of light propagation in the paraxial regime to wave optics via linear canonical transforms requiring a more penetrating view of their manifold structure and multiple covers. The purpose of this review article is to highlight the topological space of 2×2 matrices as it applies to classical versus quantum and wave models, to underline how the latter requires the double cover of the former, thus using 2×2 matrices as an alternative viewpoint of the quantization process, beside the traditional characterization by commutation and non-commutations of position and momentum. Full article
(This article belongs to the Special Issue Geometrical Optics: Theoretical Achievements and Applications)
9 pages, 22039 KiB  
Article
A New Type of Atmospheric Dispersion Corrector Suitable for Wide-Field High-Resolution Imaging and Spectroscopy on Large Telescopes
by Andrew Rakich
Appl. Sci. 2021, 11(14), 6261; https://doi.org/10.3390/app11146261 - 6 Jul 2021
Cited by 3 | Viewed by 3070
Abstract
Atmospheric dispersion produces spectral elongation in images formed by land-based astronomical telescopes, and this elongation increases as the telescope points away from the zenith. Atmospheric Dispersion Correctors (ADCs) produce compensating dispersion that can be adjusted to best cancel out the atmospheric effect. These [...] Read more.
Atmospheric dispersion produces spectral elongation in images formed by land-based astronomical telescopes, and this elongation increases as the telescope points away from the zenith. Atmospheric Dispersion Correctors (ADCs) produce compensating dispersion that can be adjusted to best cancel out the atmospheric effect. These correctors are generally of two basic types: Rotating Atmospheric Dispersion Correctors (R-ADCs), and Linear Atmospheric Dispersion Correctors (L-ADCs). Lately, a third type, the “Compensating Lateral ADC” (CL-ADC) has been proposed. None of these design approaches allow for large corrector systems (with elements greater than 1 m in diameter), in which the secondary spectrum is corrected to small residuals, of the order of tens’ of milliarcseconds. This paper describes a new type of large corrector (>1 m diameter elements), which can achieve the correction of the secondary spectrum to the order of 10 milliarcseconds. This correction is achieved by combining the R-ADC and CL-ADC approaches to dispersion correction. Only glass types readily available in metre diameters are required. Full article
(This article belongs to the Special Issue Geometrical Optics: Theoretical Achievements and Applications)
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13 pages, 1749 KiB  
Article
New Optical Design Method of Floating Type Collimator for Microscopic Camera Inspection
by Seonkoo Chee, Jaemyung Ryu and Hojong Choi
Appl. Sci. 2021, 11(13), 6203; https://doi.org/10.3390/app11136203 - 4 Jul 2021
Cited by 7 | Viewed by 3329
Abstract
Recently released mobile phone cameras are capable of photographing objects at a fairly close distance. In addition, the field angle from the camera has increased. To measure the resolution of a mobile phone camera, the target must be photographed. To measure the resolution [...] Read more.
Recently released mobile phone cameras are capable of photographing objects at a fairly close distance. In addition, the field angle from the camera has increased. To measure the resolution of a mobile phone camera, the target must be photographed. To measure the resolution according to the object distance change from a mobile phone camera with a wide field angle, the target size must be large, whereas the target position must be moved. However, the target size cannot be changed. A virtual object for the target was created using a collimator. Moving a part of the lens group constituting the collimator also changes the virtual object distance. If the amount of change in the virtual object distance is large, the resolution of the collimator may also change. Therefore, a collimator that maintains the resolution even when the distance of the virtual object changes is designed as a floating type in which two lens groups move. Therefore, we propose a new floating collimator optical system that can inspect the resolution of mobile phone cameras from infinity to a close range to compensate for aberrations caused by object distance changes. Full article
(This article belongs to the Special Issue Geometrical Optics: Theoretical Achievements and Applications)
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16 pages, 1990 KiB  
Article
Improved Analytical Theory of Ophthalmic Lens Design
by Eduardo Pascual, José A. Gómez-Pedrero and José Alonso
Appl. Sci. 2021, 11(12), 5696; https://doi.org/10.3390/app11125696 - 19 Jun 2021
Cited by 2 | Viewed by 2741
Abstract
A revisited form of the classic third-order ophthalmic lens design theory that provides a more precise and meaningful use of aspheric surfaces and a generalization of the standard oblique errors is presented. The classical third-order theory follows from the application of the Coddington [...] Read more.
A revisited form of the classic third-order ophthalmic lens design theory that provides a more precise and meaningful use of aspheric surfaces and a generalization of the standard oblique errors is presented. The classical third-order theory follows from the application of the Coddington equations to a ray trace through the lens and the expansion of the incidence angles and the surface sagittas appearing on them up to order two of the radial coordinate. In this work we show that the approximations for surface sagittas and angles can be decoupled, and the lens oblique powers predicted by the proposed theory provides a better fit to the numerical results obtained by exact raytracing and multi-parametric optimization than the classical third-order theory does. Modern ophthalmic lens design uses numerical optimization and exact ray tracing, but the methods presented in this paper provide a deeper understanding of the problem and its limitations. This knowledge and the more general merit functions that are also presented may help guide the numerical approaches. Full article
(This article belongs to the Special Issue Geometrical Optics: Theoretical Achievements and Applications)
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9 pages, 1410 KiB  
Article
Control of Linear Astigmatism Aberration in a Perturbed Axially Symmetric Optical System and Tolerancing
by José Sasián
Appl. Sci. 2021, 11(9), 3928; https://doi.org/10.3390/app11093928 - 26 Apr 2021
Cited by 8 | Viewed by 2736
Abstract
Linear astigmatism aberration is undesirable because it rapidly degrades image quality. We discuss some techniques to control and mitigate this aberration, and provide a comparison of lens systems that have been desensitized for linear astigmatism aberration. Full article
(This article belongs to the Special Issue Geometrical Optics: Theoretical Achievements and Applications)
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11 pages, 2423 KiB  
Article
Focus-Adjustable Head Mounted Display with Off-Axis System
by So Hyun Seo, Jae Myung Ryu and Hojong Choi
Appl. Sci. 2020, 10(21), 7931; https://doi.org/10.3390/app10217931 - 9 Nov 2020
Cited by 8 | Viewed by 2981
Abstract
An off-axis system refers to an optical system in which the optical axis and the normal vector at the vertex of each surface do not match. An off-axis optical system can be applied in order to construct a thin and light optical system. [...] Read more.
An off-axis system refers to an optical system in which the optical axis and the normal vector at the vertex of each surface do not match. An off-axis optical system can be applied in order to construct a thin and light optical system. In particular, the optical system used for a see-through head-mounted display (HMD) must be designed asymmetrically, with respect to the optical axis. Because the vision of a human is different for each individual, HMD requires focus adjustment. The effective focal length (EFL) of the optical system must be calculated to obtain the focus adjustment. However, the off-axis optical system cannot be calculated by conventional methods. In this study, the EFL was calculated by rotating the coordinates of the rays near the optical axis by the angle of reflection or refraction at the intersection of each surface, with the rays coinciding with the optical axis. The magnitude of movement of the micro-display for focus adjustment was obtained from the calculated EFL, for a see-through type HMD. Full article
(This article belongs to the Special Issue Geometrical Optics: Theoretical Achievements and Applications)
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