Modeling of lateral magnification changes due to changes in corneal shape or refraction

Especially after corneal surgery the lateral magnification of the eye providing the retinal image size of an object is a crucial factor influencing visual acuity and binocularity. The purpose of this study is to describe a paraxial computing scheme calculating lateral magnification changes (ratio of the image sizes before and after surgery) due to variation in corneal shape and spectacle refraction.

From the 4 x 4 refraction and translation matrices the system matrix representing the entire 'optical system eye' and the pupil matrix describing the sub-system from the spectacle correction to the aperture stop were defined for the state before and after surgery. As the chief ray is assumed to pass through the centre of the aperture stop, the 2 x 2 matrix of the lateral magnification ratio from preoperative to postoperative is described by the 2 x 2 sub-matrices of the respective pupil matrices. The cardinal meridians can be extracted by calculating the eigenvalues and eigenvectors.

Vertex distance 14 mm, measured distance between corneal apex and aperture stop 3.6mm, keratometry 39 D+6D/0 degrees to 47D+3D/30 degrees and refraction 3.5D-5-5D/5 degrees to -4.0 D-3.5D/25 degrees preoperatively to postoperatively. The matrix of magnification ratio from preop to postop yields (0.8960 -0.0085;0.0074 0.9371) and the eigenvalues decomposition provided a 10.7% minified image at 170.1 degrees and a minified image of 6.1% at 78.7 degrees , which both are clinically relevant.

We presented a straight-forward computer-based strategy for calculation of retinal image size changes using 4 x 4 matrix notation. With this model the meridional changes in lateral magnification from the preoperative to the postoperative stage or between follow-up stages can be estimated from keratometry, refraction, vertex distance and anterior chamber depth, which might be important for binocularity and vision tests in corneal surgery.