An optical method for deriving the anterior and posterior curvatures of intraocular lenses using dual back-vertex power measurements

Abstract

We present a theoretical framework to estimate the anterior and posterior radii of curvature of a thick intraocular lens (IOL) by measuring its back-vertex power in two orientations. Armed with the lens thickness, refractive index, and a potential axial offset d from haptic angulation, one can determine the individual surface powers and, thus, the geometry of the implant. Using paraxial optics, we derive the back-vertex power in normal and flipped orientations. We consider two cases: d  = 0 (no haptic-induced offset) and d ≠ 0 (finite shift). In the d  = 0 case, using standard paraxial relations (y– ν method), we obtain compact expressions that allow direct recovery of the surface powers from the dual back-vertex powers. For d ≠ 0 , the measured powers are first mapped back to the lens vertex (Eq 11), after which the same closed-form retrieval as for d  = 0 applies. When d  = 0, a closed-form solution yields the surface powers ( P 1 , P 2 ) and radii ( R ia , R ip ) . If the lens is shifted by d, we first correct to the vertex plane (Eq 11) and then apply the same closed-form relations. Though lens nominal power alone does not reveal geometry, our dual-orientation approach recovers how much power resides on each surface, benefiting thick-lens IOL power formulas and refining predictions in cataract surgery planning.