Relative peripheral refractive error under single-vision spectacle correction in a GRIN ray-tracing pediatric eye: lens-form and material dependence

Model-output data for the single-vision (monofocal) spectacle-corrected eye — how the peripheral defocus of a corrected eye depends on the lens form, the lens material/index, the prescription, the pupil, the eccentricity and the accommodative state — accompanying the manuscript on peripheral defocus and myopia. Generated by the open grin-defocus-eye engine v1.3.1 (software record DOI 10.5281/zenodo.20891318). Each row is a direct engine readout — no post-processing. Model. AVOCADO gradient-index crystalline lens (Sheil & Goncharov) in an aspheric pediatric eye (age 10); own conic tracer and RK4 GRIN integrator (a homogeneous Le Grand eye on Optiland is a validation oracle only). The retina is an Atchison conicoid coupled to axial elongation. The spectacle is traced as two real surfaces in air (front: base curve, carries the asphericity; back: carries the prescription) at a 12 mm back-vertex distance ahead of the cornea, read with the same wavefront pipeline as the bare eye (a plano lens reproduces the uncorrected-eye refraction exactly), so spectacle RPRE is on the same validated footing as the bare-eye readout. The uncorrected eye (form = none) is included as the per-state baseline, so corrected and uncorrected peripheries are directly comparable within this record. Every lens is solved to central emmetropia (M(0)=0 at distance). Accommodation for near33 is solved through the lens for a 33 cm object, so spectacle effectivity is captured. Conventions. Dioptres (D); sign clinical (myopia < 0, hyperopia > 0); RPRE(θ) = M(θ) − M(0) (relative peripheral refractive error; >0 = relative peripheral hyperopia, myopiagenic); J0 > 0 = with-the-rule astigmatism. Viewing states: distance (relaxed, A=0, lens corrects to central emmetropia) and near33 (33 cm, accommodation solved through the lens). Grid: lens form × material/index × prescription SR ∈ {−6,−3,+3,+6} D (the emmetrope needs no spectacle and is omitted) × pupils 2/4/6 mm × eccentricity 10/20/30°. One reader throughout: 5 rings × 14 spokes, exit-pupil normalisation matched to each analysis pupil (Thibos/ANSI), so the 4 mm pupil is the reference for cross-table statements. Peripheral readout validated against the homogeneous oracle to ≤ 0.03 D out to ~20°; 30° reported with a caveat; the 6 mm column is the least reliable. License: CC–BY–4.0. Lens forms (all corrected forms solved to M(0)=0, so the comparison isolates the surface form): none — the uncorrected eye, written per state as the baseline (M0 = eye_M0; material and design columns blank). trial — symmetric equiconvex / equiconcave sphere (front_R = −back_R), trial-frame / cheapest single-vision lens; not corrected for oblique astigmatism. sphere — best-form (Vogel / Tscherning, Ostwalt branch): steep base curve, spherical both sides. asphere_stock — a realistic off-the-shelf front-aspheric lens (Essilor Ormix / Hoya / Rodenstock convention): base curve from a fixed manufacturable nomogram (bc_family), front conic solved to minimise the field-RMS foveal oblique astigmatism of the rotating eye (chief ray through the centre of rotation, gaze 0–35°) — decoupled from the peripheral measurement by construction. asphere_ideal — an idealised upper bound: modest conic plus a solved even-aspheric A4 (then A6) on the front surface, designed point-focal against the eye's own peripheral oblique astigmatism. Not a stock product; it bounds the achievable form effect. A bi-aspheric / atoric form is deliberately not included: it has no canonical stock recipe (such lenses are free-form-optimised per prescription, not built to a single base-curve rule), so a single defensible preset does not exist. Materials (a three-index dispensed-plastic ladder, run identically across all powers so the material effect is isolated): cr39 (ne 1.502, standard), mid156 (1.563, mid-index volume leader), hi167 (1.674, high-index thin). The engine's full material registry lives in the software record. Files. data/spectacle_lensform.csv — tidy long format, one row per (SR, form, material, cond, pupil, angle), with the designed lens geometry per cell. Columns: SR, eye_M0, form, material, n_e, cond, A_acc, Pf, conic, A4, A6, tc, front_R, back_R, bc_family, design_criterion, gaze_field_deg, cor_mm, pupil, angle, M0, RPRE, J0. data/spectacle_pivot.csv — the same readings in wide format, forms side by side, one row per (SR, material, cond, pupil, angle). Columns: SR, material, cond, pupil, angle, RPRE_none, RPRE_trial, RPRE_sphere, RPRE_asphere_stock, RPRE_asphere_ideal, J0_none, J0_trial, J0_sphere, J0_asphere_stock, J0_asphere_ideal. data/spectacle_undercorrection_accom.csv (added in v1.1.0) — a focused clinical case study: a hyperope (SR = +6 D) under-corrected by a +3 D spectacle (residual U = +3 D), the residual carried by accommodation (ideal central compensation — the macula is focused, no lag — so the whole effect lands in the periphery and the pupil), against full correction (+6 D lens, U = 0) and no lens (U = +6, context). Forms none/trial/sphere/asphere_stock, materials cr39/hi167, at distance and near33. One accommodation per state is solved so the min-RMS central refraction is nulled at the 3 mm reference pupil through the lens (first-downward-crossing to 16 D). Adds columns lens_power, U and the absolute peripheral powers M_abs = M0+RPRE, M_tan = M_abs+J0, M_sag = M_abs−J0; M0 is the object-referenced macular control (≈0 near the 3 mm solve pupil, drifting at 2/6 mm by accommodative spherical aberration). Columns: SR, lens_power, U, form, material, cond, A_acc, pupil, angle, M0, RPRE, J0, M_abs, M_tan, M_sag. Results and analysis are reported in the accompanying manuscript; this record provides the underlying model-output data only. Provenance. Numpy-only, deterministic. Generating scripts (in the software record): experiments/run_lensform_sweep.py (the sweep; designs each lens via experiments/grin_lensform_presets.py and reads the periphery with the same refract_grin reader as the uncorrected series; the wide pivot is derived from the long table) and experiments/run_under3_accom.py (the undercorrection-with-accommodation case study). Please cite both this dataset and the software record (DOI 10.5281/zenodo.20891318). See DATA_README.md for the full data dictionary.