Computerized calculation scheme for toric intraocular lenses

While a number of intraocular lens (IOL) power prediction formulae are well established for determination of spherical lenses, no common strategy has been published for the computation of toric IOLs. The purpose of this study is to describe a paraxial computing scheme for tracing an axial pencil of rays through the 'optical system eye' containing astigmatic refractive surfaces with their axes at random. The capabilities of this computing scheme are demonstrated with clinical examples.

Based on a schematic model eye with spherocylindric surfaces, we use two alternative notations for description of vergences or prescriptions: (1) standard notation (refraction in both cardinal meridians and axis), and (2) component notation (spherical equivalent and cylindric component in 0 degrees and 45 degrees. Refractive surfaces are added to the vergence in component notation, whereas the transformation of the vergence through media is performed in the standard notation for both cardinal meridians. For calculation of the toric lens implant, a pencil of rays is traced through the spectacle and the cornea to the estimated lens position as well as backwards from the retina to the estimated lens position. For calculation of residual spectacle refraction, a pencil of rays is traced backwards from the retina through the toric lens implant and the cornea to the spectacle plane.

In example 1 we calculate a 'thin toric lens' for compensation of a corneal astigmatism to achieve a spherical target refraction. In example 2 we compute a 'thick toric lens', which has to compensate for an oblique corneal astigmatism and rotate the spectacle cylinder to the against the rule position to enhance near vision. In example 3 we estimate the residual refraction at the corneal plane after implantation of a thick toric lens, when the cylinder of the lens implant is compensating the corneal cylinder in part and the axis of implantation is not fully aligned with the axis of the corneal astigmatism.

This novel mathematical concept for computation of toric IOLs or prediction of the refractive outcome with a toric implant in place is a straightforward, computer-based approach, which may substitute for more or less empirical methods of determining toric IOL implants.