Determining the power of a thin toric intraocular lens in an astigmatic eye

Astigmatism poses a number of special difficulties when attempting to achieve a desirable refractive outcome during cataract surgery and intraocular lens implantation. One of the most pertinent difficulties is that traditional Gaussian theoretical formulas are simply unable to handle general astigmatic optical systems, that is, systems in which the principal meridians of the refracting interfaces do not lie in two mutually orthogonal planes. This means that the traditional approach falls short when the cornea is treated as bitoric or when other toric optical devices are already present in the eye. In this paper, the modified step-along procedure is utilized in a demonstration of the derivation of the traditional Gaussian theoretical formulas for the determination of intraocular lens power, in a stigmatic eye. Matrices are then used to derive a general formula for the determination of the power of a thin toric intraocular lens in an astigmatic eye. This formula is then modified to allow the user to determine the power of the secondary intraocular lens required to compensate for any residual refraction in a phakic or pseudophakic astigmatic eye. The formulas hold under all conditions, including the case when the cornea is treated as thick and bitoric and when other toric optical devices are already present in the eye. Worked examples are provided.