title: Toric intraocular lenses--theory, matrix calculations, and clinical practice.
abstract: To describe 1) how to determine toric (posterior chamber) intraocular lenses (IOLs) with standard formulas, 2) a matrix-based calculation scheme for determining toric IOLs using 4x4 matrices, 3) a method to determine residual refraction after implantation of an arbitrary toric lens, and 4) to address clinical aspects.
  
  
  
  Formulas and metrics are reviewed for determining IOL power and residual refraction after toric IOL implantation.
  
  
  
  From 4x4 refraction and translation matrices characterizing refractive surfaces and interspaces between refractive surfaces, a system matrix is determined characterizing the entire optical system paraxially. Toric posterior chamber IOLs are determined by solving a linear equation system. In a second step, the same methodology is used for estimation of the residual refraction at the spectacle plane after implantation of an arbitrary toric lens. The methodology is applied to working examples, and the calculation procedure is described in a step-by-step approach.
  
  
  
  A straight-forward en bloc concept is demonstrated for determination of toric IOLs and estimation of the residual refraction. The applicability is shown in working examples, and clinical aspects such as rotation of the lens implant are addressed.
authors: Institute of Medical Physics and Optics, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany. achim.langenbucher@imp.uni-erlangen.de
authors: Achim
authors: A
authors: Langenbucher
authors: Anja
authors: A
authors: Viestenz
authors: Nóra
authors: N
authors: Szentmáry
authors: Wolfgang
authors: W
authors: Behrens-Baumann
authors: Arne
authors: A
authors: Viestenz
mesh_terms: D006801:Humans; D007910:Lenses, Intraocular; D008433:Mathematics; D055620:Optical Phenomena; D055095:Optics and Photonics; D019591:Pseudophakia / Q000503:physiopathology; D012029:Refraction, Ocular