Vergence-based ocular wavefront expansions in diopters: orthogonal functions, clinical metrics, and visualization tools

We introduce two families of vergence functions to express ocular wavefront aberrations in diopters, bridging aberrometry, and clinical refraction. First, we build a fully orthogonal vergence basis (<i>V</i>~), analogous to Zernike polynomials, which preserves mode orthogonality and supports unbiased coefficient statistics. In our VL-VH basis (<i>V</i>), a clear separation between low-degree and high-degree prevents the intrusion of low-degree terms into high-degree modes, which could otherwise hinder direct clinical interpretation. The vergence function expansions in both bases are derived from wavefront slopes through radial differentiation. We demonstrate their clinical utility through three cases: a normal eye, a keratoconic eye, and a post-myopic LASIK eye. The VL-VH basis provides stable refraction estimates across pupil sizes by fitting low-degree terms over central regions, closely matching subjective refraction. In contrast, the orthogonal <i>V</i>~ basis shows pupil-dependent refraction due to peripheral wavefront influence. In eyes with significant spherical aberration, the bases yield markedly different refractive predictions, with VL-VH better aligning with clinical measurements. Pyramid plots, dioptric maps, and coefficient histograms facilitate aberration visualization and diagnosis. These vergence-based tools enhance the integration of advanced aberrometry into clinical practice.