Retinal magnification factors at the fixation locus derived from schematic eyes with four individualized surfaces

Abstract

Retinal magnification factors (RMFs) allow the conversion of angles to lengths in retinal images. In this work, we propose paraxial and non-paraxial RMF calculation methods that incorporate the individual topography and separation of the anterior and posterior surfaces of the cornea and crystalline lens, assuming homogeneous ocular media. Across 34 eyes, the two RMF methods differ by 0.1% on average, due to surface tilt, decenter, and lack of rotational symmetry in the non-paraxial modeling, which results in up to 2.2% RMF variation with retinal meridian. Differences with widely used individualized RMF calculation methods are smallest for eyes with ∼24 mm axial length, and as large as 7.5% in a 29.7 mm long eye (15D myope). To better model the capture of retinal images, we propose the tracing of chief rays, instead of the scaling of posterior nodal or principal distances often used in RMF definitions. We also report that RMF scale change is approximately proportional to both refractive error and axial separation between the ophthalmoscope’s exit pupil and the eye’s entrance pupil, resulting in RMF changes as large as 13% for a 1cm displacement in a 15D myopic eye. Our biometry data shows weak correlation and statistical significance between surface radii and refractive error, as well as axial length, whether considering all eyes in the study, or just the high myopes, defined as those with refractive error sphere equivalent ≤ -4D. In contrast, vitreous thicknesses show a strong correlation (r ≤ -0.92) and significance (p ≤ 10−13) with refractive error when considering all eyes or just high myopes (r ≤ -0.95; p ≤ 10−5). We also found that potential RMF change with depth of cycloplegia and/or residual accommodation is smaller than 0.2%. Finally, we propose the reporting of individual ocular biometry data and a detailed RMF calculation method description in scientific publications to facilitate the comparison of retinal imaging biomarker data across studies.