Scaling the Retinal Image of the Wide-Angle Eye Using the Nodal Point

Optical modeling of the entire visual field of the eye

Vision is rarely evaluated scientifically at very large visual angles, despite being used continuously in everyday life. Furthermore, raytrace calculations indicate that peripheral optical properties are different for a pseudophakic eye, and even though this is rarely noted by patients, it is probably the cause of bothersome "negative dysphotopsia." Simplified paraxial parameters that characterize the basic properties of phakic and pseudophakic eyes are collected together here as a baseline, and then raytracing is used to show that input angles of about 60°, which correspond to obstruction by the nose, eyebrow, and cheek, illuminate a retinal hemisphere. At larger angles in the temporal direction, the image with an intraocular lens (IOL) reaches a limit due to vignetting at about a 90° input angle to the optical axis, in comparison to 105° with the Gullstrand-Emsley eye model, and 109° for the most realistic gradient index crystalline lens model. Scaling the far peripheral vision region more accurately may lead to benefits relating to intraocular lenses, diseases of the peripheral retina, widefield fundus images, and myopia prevention.

Focal length, EFL, and the eye

The focal length is often called the effective focal length, or efl instead, and although this is acceptable for a lens in air, it is not otherwise correct. The eye is used as an example here for an optical system where the object is in air and the image is in fluid. Welford, Aberrations of Optical Systems (1986) has paraxial equations that are consistent with historical use while also clearly defining efl. These are based on power at a surface having to be the same for light traveling in both directions (n ^'/f ^'). The focal length f ^' is the actual physical distance from the 2nd principal point to the paraxial focus, and the equivalent focal length, or efl, is the focal length divided by the image index (f ^'/n ^'). Separately, when the object is in air, the efl is shown to act at the nodal point, with the lens system represented by either an equivalent thin lens at the principal point with a focal length or a different equivalent thin lens in air at the nodal point with an efl. The rationale for using effective instead of equivalent for efl is unclear, but efl is used more as a symbol than as an acronym.

Widefield and Ultra-Widefield Retinal Imaging: A Geometrical Analysis

Diabetic retinopathy (DR) often causes a wide range of lesions in the peripheral retina, which can be undetected when using a traditional fundus camera. Widefield (WF) and Ultra-Widefield (UWF) technologies aim to significantly expand the photographable retinal field. We conducted a geometrical analysis to assess the field of view (FOV) of WF and UWF imaging, comparing it to the angular extension of the retina. For this task, we shot WF images using the Zeiss Clarus 500 fundus camera (Carl Zeiss Meditec, Jena, Germany). Approximating the ocular bulb to an ideal sphere, the angular extension of the theoretically photographable retinal surface was 242 degrees. Performing one shot, centered on the macula, it was possible to photograph a retinal surface of ~570 mm², with a FOV of 133 degrees. Performing four shots with automatic montage, we obtained a retinal surface area of ~1100 mm² and an FOV of 200 degrees. Finally, performing six shots with semi-automatic montage, we obtained a retinal surface area of ~1400 mm² and an FOV of 236.27 degrees, which is close to the entire surface of the retina. WF and UWF imaging allow the detailed visualization of the peripheral retina, with significant impact on the diagnosis and management of DR.

Radial and Tangential Retinal Magnifications as Functions of Visual Field Angle Across Spherical, Oblate, and Prolate Retinal Profiles

Purpose

To provide a tool for calculating radial and tangential retinal magnifications as functions of field angle and retinal shape and to articulate patterns of magnification across the retina for monocular and binocular combinations of prolate-, oblate-, and spherical-shaped retinas.

Methods

Formulae were derived to calculate radial and tangential retinal magnifications (mm/deg) from field angle (degrees), retinal asphericity (unitless conic constant), retinal vertex radius of curvature (mm), and nodal point position (mm). Monocular retinal magnifications were determined for eyes with prolate, spherical, and oblate retinas as functions of field angle. Bilateral differences in magnifications were examined for combinations of those eyes.

Results

Retinal shape substantially affects magnification profiles even for eyes with the same axial length. Greatest magnification changes across a retina and between eyes, as well as greatest increase in radial-tangential differences (distortion), occur with prolate retinas. Binocular magnification differences were smallest for oblate retinas. Nodal points anterior to the vertex center of curvature and oblate asphericity both cause field-dependent reductions in magnification relative to the fovea (barrel distortion), whereas nodal points posterior to vertex center of curvature and prolate asphericity cause the opposite (pincushion distortion). Retinal magnification differences due to eye shape are much greater than aniseikonia thresholds and chromatic differences in magnification. A spreadsheet tool implements the magnification calculations.

Conclusions

Local retinal magnifications as functions of field angle have substantial effects on objective applications (imaging retinal anatomy) and subjective experiences (aniseikonia) and quantify an ocular property that differs across eye shapes and refractive errors.

Translational Relevance

Methods are provided to customize the calculation of radial and tangential magnifications across the retina for individual eyes, which will bolster the multifactorial study of the effects of foveal and peripheral optics across eye shapes and refractive errors.

Editorial to the Special Issue on “Ocular Imaging for Eye Care”

The need for fast, inexpensive, and robust medical technology is now more crucial than ever [...]

Nodal points and the eye

Nodal points are defined using parallel object and image rays at very small angles to the optical axis, and Johann Listing described them when characterizing the eye in 1845. They are only distinct from principal points when there is a refractive index difference, but Reginald Clay used the term "nodal slide" in 1904 for equipment that uses lens rotation when measuring a lens focal length in air. Over time, sketches of nodal rays at large angles have become common, and these perhaps appear to support observations that input angles to the eye match image angles measured to the nodal point. Raytrace calculations confirm that this is correct for very large angles, but the relationship comes from the cornea curving around, towards incoming light, angles being rescaled at the exit pupil by a constant factor, and then the retina curving around to meet the image rays. The eye has high linearity, with 1:1 angular scaling occurring at approximately the nodal point, but ray bundles passing through the pupil center, rather than paraxial nodal rays, define the optical properties.

Effect of a 7.0 mm intraocular lens optic on peripheral retinal illumination with implications for negative dysphotopsia

PURPOSE

To use optical modeling to compare a 6.0 mm and 7.0 mm intraocular lens (IOL) optic diameters on peripheral retinal illumination with implications for negative dysphotopsia.

SETTING

Mayo Clinic, Rochester, Minnesota, and Simpson Optics LLC, Arlington, Texas.

DESIGN

Model eye.

METHODS

Ray-tracing software was used to simulate retinal illumination from an extended light source for a pseudophakic eye with in-the-bag biconvex IOLs (refractive index [n] = 1.46 and 1.55) and a 2.5 mm pupil. Ray-tracing diagrams and simulated retina illumination profiles were compared using the 6.0 mm and 7.0 mm optic diameter IOLs. Retinal locations were scaled to relative visual angles from 70 to 110 degrees horizontally.

RESULTS

A 7.0 mm optic (n = 1.46) expands the image field by 2.8 degrees compared with a 6.0 mm optic. High-angle input light misses a 7.0 mm optic at a larger visual angle than a 6.0 mm optic, shifting illumination of the peripheral retina by this light anteriorly by 5.6 degrees. Consequently, a region of nonilluminated peripheral nasal retina is enlarged and shifted peripherally using a 7.0 mm optic (visual angle, 86.3 to 96.3 degrees) compared with a 6.0 mm optic (visual angle, 83.5 to 90.7 degrees). Similar illumination changes were seen modeling a 1.55 n IOL.

CONCLUSIONS

A narrow dark region in the nasal retina when using a 6.0 mm optic is changed to a broader, more peripheral dark region when using a 7.0 mm optic. An extended, more peripheral dark nasal region may make a temporal shadow less bothersome and explain lower negative dysphotopsia rates using a 7.0 mm optic.