Technical report: Calculation and interpretation of corneal transference maps

Transference matrices are interesting tools for optical analysis of an eye alongside ray tracing. To explore possible interpretations of the ABCD entries of the transference, this article applies them to the corneal surfaces to find a surprising link to a corneal biomechanics parameter that may help with keratoconus detection.

The transference matrix used in linear optics has four entries, dilation A, disjugacy B, divergence C, and divarication D. Entry C is the negative of the power of the system. However, the remaining three entries are somewhat difficult to relate to. This work explores how the four fundamental properties of the corneal transference relate to familiar corneal variables such as radii of curvature, thickness, surface powers, and total refractive power.

The cornea is treated as a thick lens, and a transference is obtained for the cornea at approximately 12,000 points, as well as point-by-point corneal maps of A, B, C, and D are obtained based on Scheimpflug tomography data (Pentacam HR, Wetzlar, Germany). The trace of the transference is also obtained.

The four corneal maps of A, B, C, and D resemble familiar clinical maps, albeit at different scales. Pachymetry is represented by B, and total corneal power is represented by C, and A represents a new variable, resembling the corneal contribution to stress (CCS), a new variable used in detecting early keratoconus. D seems to represent a CCS-like variable applied to the posterior corneal surface. In keratoconus, the trace appears as a ring-shaped pattern around the cone.

The A, B, C, and D maps relate information from known clinical maps such as pachymetry, corneal power, and CCS. The trace of the transference provides a new corneal map representing the combination of CCS and a related posterior parameter that may be useful in the detection and follow-up of keratoconus.