Quantitative analysis of eyes and other optical systems in linear optics
| Autor: | William F. Harris, Radboud D. van Gool, Tanya Evans |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Optics and Photonics
02 engineering and technology Eye Space (mathematics) 03 medical and health sciences Imaging Three-Dimensional 0302 clinical medicine 0202 electrical engineering electronic engineering information engineering Humans Point (geometry) Mathematics Basis (linear algebra) Mathematical analysis 020206 networking & telecommunications Models Theoretical Refractive Errors Sensory Systems Symplectic matrix Ophthalmology Eyeglasses Character (mathematics) 030221 ophthalmology & optometry Subspace topology Optometry Vector space Gaussian optics |
| Zdroj: | Ophthalmic and Physiological Optics. 37:347-352 |
| ISSN: | 1475-1313 0275-5408 |
| DOI: | 10.1111/opo.12370 |
| Popis: | PURPOSE To show that 14-dimensional spaces of augmented point P and angle Q characteristics, matrices obtained from the ray transference, are suitable for quantitative analysis although only the latter define an inner-product space and only on it can one define distances and angles. The paper examines the nature of the spaces and their relationships to other spaces including symmetric dioptric power space. METHODS The paper makes use of linear optics, a three-dimensional generalization of Gaussian optics. Symmetric 2 × 2 dioptric power matrices F define a three-dimensional inner-product space which provides a sound basis for quantitative analysis (calculation of changes, arithmetic means, etc.) of refractive errors and thin systems. For general systems the optical character is defined by the dimensionally-heterogeneous 4 × 4 symplectic matrix S, the transference, or if explicit allowance is made for heterocentricity, the 5 × 5 augmented symplectic matrix T. Ordinary quantitative analysis cannot be performed on them because matrices of neither of these types constitute vector spaces. Suitable transformations have been proposed but because the transforms are dimensionally heterogeneous the spaces are not naturally inner-product spaces. RESULTS The paper obtains 14-dimensional spaces of augmented point P and angle Q characteristics. The 14-dimensional space defined by the augmented angle characteristics Q is dimensionally homogenous and an inner-product space. A 10-dimensional subspace of the space of augmented point characteristics P is also an inner-product space. CONCLUSIONS The spaces are suitable for quantitative analysis of the optical character of eyes and many other systems. Distances and angles can be defined in the inner-product spaces. The optical systems may have multiple separated astigmatic and decentred refracting elements. |
| Databáze: | OpenAIRE |
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