Development Of Orthonormal Function Bases For Decomposing Ocular Vergence And Curvature Maps In Dioptric Units

This study introduces novel orthonormal function bases designed to decompose ocular vergence maps (from aberrometers) and corneal power or curvature maps (from topographers) into sums of weighted dioptric coefficients. A key objective is to express variations in optical power or curvature directly in diopters—rather than in microns—thereby providing a more clinically intuitive representation of local refractive changes.

Rothschild Foundation Hospital, CEROV

Optical power and curvature, expressed in diopters (D), are analyzed using data from aberrometers and topographers. Vergence maps (representing local optical power in the pupil plane) and corneal topography maps (expressed in dioptric optical or keratometric power) are decomposed using two proposed bases: a fully orthonormal basis, and a non-totally orthonormal basis (VL-VH) that separates low-degree (VL, n ≤ 2) from high-degree (VH, n > 2) terms without enforcing orthogonality between them. The VL-VH approach ensures that low-degree terms (defocus, astigmatism) remain distinct from higher-order modes, thus simplifying clinical interpretation. 

Using the fully orthonormal basis can yield mean sphero-cylindrical values that may not match paraxial clinical refraction when higher-order aberrations predominate. Conversely, the VL-VH basis isolates clinically relevant low-degree vergence (i.e., paraxial sphero-cylindrical refraction in diopters) from higher-order variations, thus enhancing interpretability. When applied to corneal power maps, VL represents paraxial sphero-toric power, while VH captures localized departures from this baseline. Examples illustrate the computation of coefficients in the dioptric unit and their visualization (e.g., vergence and curvature  “pyramids”) for both total ocular vergence and corneal power distributions.

By focusing on dioptric measures, the proposed  VL-VH approach provides a more straightforward way to capture and interpret optical power or curvature variations that are sometimes less intuitively described in microns. Separating paraxial refraction from higher-order terms offers new avenues for evaluating the refractive impact and topographic variations of ocular pathologies—particularly those involving higher-order aberrations. This framework is broadly applicable to wavefront analysis, corneal topography, and optical system design, offering clinicians and researchers a powerful tool for advancing ophthalmic diagnostics and research.