Vector space of generalized radii of ellipses for quantitative analysis of blur patches and other referred apertures in the astigmatic eye

Evans, Tanya; Harris, W. F.

doi:10.1364/josaa.36.000b93

Cited by 2 publications

(12 citation statements)

References 3 publications

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“…The restricted pencil of rays will form a blur patch at the retina and, similarly, of all the rays incident on the cornea, those that reach the retina are also restricted by the aperture, but referred upstream to the cornea (figure 3). 1 88 89 This effective corneal patch has implications for corneal surgery, such as refractive surgery, corneal inlays and optic zones for contact lenses. In addition, pinhole apertures are available for surgical insertion as a corneal inlay, or a pinhole IOL at the iridial plane.…”

Section: Discussion: Applicationsmentioning

confidence: 99%

“…This restricted pencil can be traced upstream or downstream and its shape, size, orientation and transverse position at a referred plane will be determined by both the geometry of the aperture and the refractive elements upstream or downstream of the aperture. The position, both longitudinally and transversely, of an object referred downstream or an image referred upstream will also have an influence on the geometry of the referred aperture 1…”

Section: Discussion: Applicationsmentioning

confidence: 99%

“…The general equation for aperture referral is boldRnormalR=MboldRnormalP , where boldRnormalP is the generalised radius of the elliptical aperture and boldRnormalR is the generalised radius of the referred aperture. R defines the geometry of an ellipse described by its major a and minor b semidiameters 1 88 89. A circular aperture is a special case of the elliptical aperture where a=b .…”

Section: Discussion: Applicationsmentioning

confidence: 99%

“…A circular aperture is a special case of the elliptical aperture where a=b . M is a generalised linear magnification matrix that may be asymmetric and that depends on the system, longitudinal position of the aperture, object or image position and direction of referral, that is, upstream or downstream 1 18 26 27 88 90. boldRnormalR is defined for all finite ellipses, including degenerate ellipses, that is, point and line segments (or foci).…”

Section: Discussion: Applicationsmentioning

confidence: 99%

“… boldRnormalR is defined for all finite ellipses, including degenerate ellipses, that is, point and line segments (or foci). The referred aperture may be rotated and/or reflected and magnified by different amounts along the diameters 1…”

Section: Discussion: Applicationsmentioning

confidence: 99%

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Linear optics of the eye and optical systems: a review of methods and applications

Evans

Rubin

2022

BMJ Open Ophth

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The purpose of this paper is to review the basic principles of linear optics. A paraxial optical system is represented by a symplectic matrix called the transference, with entries that represent the fundamental properties of a paraxial optical system. Such an optical system may have elements that are astigmatic and decentred or tilted. Nearly all the familiar optical properties of an optical system can be derived from the transference. The transference is readily obtainable, as shown, for Gaussian and astigmatic optical systems, including systems with elements that are decentred or tilted. Four special systems are described and used to obtain the commonly used optical properties including power, refractive compensation, vertex powers, neutralising powers, the generalised Prentice equation and change in vergence across an optical system. The use of linear optics in quantitative analysis and the consequences of symplecticity are discussed.A systematic review produced 84 relevant papers for inclusion in this review on optical properties of linear systems. Topics reviewed include various magnifications (transverse, angular, spectacle, instrument, aniseikonia, retinal blur), cardinal points and axes of the eye, chromatic aberrations, positioning and design of intraocular lenses, flipped, reversed and catadioptric systems and gradient indices. The optical properties are discussed briefly, with emphasis placed on results and their implications. Many of these optical properties have applications for vision science and eye surgery and some examples of using linear optics for quantitative analyses are mentioned.

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Section: Discussion: Applicationsmentioning

confidence: 99%

Section: Discussion: Applicationsmentioning

confidence: 99%

Section: Discussion: Applicationsmentioning

confidence: 99%

Section: Discussion: Applicationsmentioning

confidence: 99%

Section: Discussion: Applicationsmentioning

confidence: 99%

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Linear optics of the eye and optical systems: a review of methods and applications

Evans

Rubin

2022

BMJ Open Ophth

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Matrix optics of artificial intraocular pinhole apertures in astigmatic eyes: modelling depth of field

Evans¹

2023

Biomed. Opt. Express

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This study uses matrix optics to develop a model to predict depth of field in eyes that may have astigmatic elements and apertures that may be elliptical in general. Depth of field is modelled as the visual acuity (VA) as a function of working distance and is illustrated graphically for model eyes that have artificial intraocular pinhole apertures. A small amount of residual myopia is an advantage to increasing the depth of field at near without interfering with distance-vision. A small amount of residual astigmatism is not an advantage to increasing depth of field, without compromising VA at all distances.

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Vector space of generalized radii of ellipses for quantitative analysis of blur patches and other referred apertures in the astigmatic eye

Cited by 2 publications

References 3 publications

Linear optics of the eye and optical systems: a review of methods and applications

Linear optics of the eye and optical systems: a review of methods and applications

Matrix optics of artificial intraocular pinhole apertures in astigmatic eyes: modelling depth of field

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