BACKGROUND: In the last decades, toric posterior chamber lenses (TPCLs) for cataract surgery and phakic toric lenses (PTLs) for refractive surgery have become more and more popular for correcting high or excessive corneal astigmatism. The purpose of this article is to present a vergence-based calculation scheme for TPCLs and PTLs. METHODS: In Gaussian optics (in the paraxial space), spherocylindrical optical surfaces can be described in a mathematically equivalent formulation as vergences. There are dual notations: The standard notation is used for transforming vergences through a homogeneous optical medium, and the component notation is applied to add up the power of a refractive surface to the vergence. Both notations can be used interchangeably. For calculating TPCLs, the vergences in front of and behind the predicted pseudophakic lens position are determined and subtracted. For calculating PTLs, the anterior vergence at the predicted lens position is estimated for the preoperative and postoperative states, and the difference between the two yields the desired lens power. WORKING EXAMPLES: In the 1(st) example, the power of a thin TPCL is determined step by step by applying the presented calculation scheme, which was designed to be transferred directly to a simple computer program (e.g., Microsoft Excel). In the 2(nd) example, the postoperative refraction is estimated for a simulation in which a TPCL similar to that in example 1 is implanted in a slightly misaligned orientation. In a 3(rd) example, the power of a PTL is determined step by step using the above-mentioned calculation scheme. CONCLUSIONS: The presented calculation scheme allows determination of"thin" TPCLs or PTLs to achieve spherocylindrical target refraction with a cylinder axis at random or to predict the postoperative refraction for any toric lens implanted in any axis. The concept can be easily generalized to"thick" toric intraocular lenses if the geometric data and refraction index of the material are known.
BACKGROUND: In the last decades, toric posterior chamber lenses (TPCLs) for cataract surgery and phakic toric lenses (PTLs) for refractive surgery have become more and more popular for correcting high or excessive corneal astigmatism. The purpose of this article is to present a vergence-based calculation scheme for TPCLs and PTLs. METHODS: In Gaussian optics (in the paraxial space), spherocylindrical optical surfaces can be described in a mathematically equivalent formulation as vergences. There are dual notations: The standard notation is used for transforming vergences through a homogeneous optical medium, and the component notation is applied to add up the power of a refractive surface to the vergence. Both notations can be used interchangeably. For calculating TPCLs, the vergences in front of and behind the predicted pseudophakic lens position are determined and subtracted. For calculating PTLs, the anterior vergence at the predicted lens position is estimated for the preoperative and postoperative states, and the difference between the two yields the desired lens power. WORKING EXAMPLES: In the 1(st) example, the power of a thin TPCL is determined step by step by applying the presented calculation scheme, which was designed to be transferred directly to a simple computer program (e.g., Microsoft Excel). In the 2(nd) example, the postoperative refraction is estimated for a simulation in which a TPCL similar to that in example 1 is implanted in a slightly misaligned orientation. In a 3(rd) example, the power of a PTL is determined step by step using the above-mentioned calculation scheme. CONCLUSIONS: The presented calculation scheme allows determination of"thin" TPCLs or PTLs to achieve spherocylindrical target refraction with a cylinder axis at random or to predict the postoperative refraction for any toric lens implanted in any axis. The concept can be easily generalized to"thick" toric intraocular lenses if the geometric data and refraction index of the material are known.