Mathematical Construction Of An Optimal Objective Defocus Curve Using Pyramidal Wavefront Aberrometry

To mathematically define and construct an optimal objective defocus curve using pyramidal wavefront aberrometry and to establish a physiologically meaningful mapping between subjective and objective through-focus responses.

This prospective, multicenter, nonrandomized case series enrolled consecutive patients undergoing implantation of the RayOne Galaxy RAO605G and RayOne Galaxy Toric RAO615X IOLs. Surgical procedures were performed by three surgeons at three centers located in Brescia, Italy; Bristol, United Kingdom; and Genoa, Italy between October 2024 and November 2025.

A retrospective dataset of paired subjective and objective defocus curves was analyzed. Each curve consisted of 11 vergence steps from −4.0 D to +1.0 D (0.5 D increments). Fifty paired curves were used for model training and 30 independent curves for validation. Objective metrics were derived from wavefront aberrometry under standardized photopic pupil conditions. The relationship between subjective (x) and objective (y) measurements was modeled using monotonic nonlinear mapping functions. Parameters were estimated using nonlinear least squares (Levenberg–Marquardt). Model performance was assessed by RMSE, correlation analysis, area under the curve (AUC), and curve smoothness metrics.

The rational saturating model demonstrated superior fitting accuracy (lower RMSE) and numerical stability compared to the logarithmic formulation. Strong correlation was observed between predicted and measured objective metrics (r≈0.80–0.85 in validation). Mathematical optimization enabled definition of an objective defocus profile maximizing AUC while minimizing curvature oscillation. Sensitivity simulations revealed that 0.50 D of residual cylinder reduced AUC by approximately 15% and increased curve irregularity.

Objective defocus curves can be mathematically modeled to define an optimal through-focus optical profile. This framework provides a reproducible and computationally efficient method for standardized evaluation of presbyopia-correcting IOL performance.