title: Simplified mathematics for customized refractive surgery.
abstract: OBJECTIVE
  To describe a simple mathematical approach to customized corneal refractive surgery or customized intraocular lens (IOL) design that allows "hypervision" and to investigate the accuracy limits.
  
  
  METHODS
  University eye hospital, Mainz, Germany.
  
  
  METHODS
  Corneal shape and at least 1 IOL surface are approximated by the well-known Cartesian conic section curves (ellipsoid, paraboloid, or hyperboloid). They are characterized by only 2 parameters, the vertex radius and the numerical eccentricity. Residual refraction errors for this approximation are calculated by numerical ray tracing. These errors can be displayed as a 2-dimensional refraction map across the pupil or by blurring the image of a Landolt ring superimposed on the retinal receptor grid, giving an overall impression of the visual outcome.
  
  
  RESULTS
  If the eye is made emmetropic for paraxial rays and if the numerical eccentricities of the cornea and lens are appropriately fitted to each other, the residual refractive errors are small enough to allow hypervision. Visual acuity of at least 2.0 (20/10) appears to be possible, particularly for mesopic pupil diameters. However, customized optics may have limited application due to their sensitivity to misalignment errors such as decentrations or rotations.
  
  
  CONCLUSIONS
  The mathematical approach described by Descartes 350 years ago is adequate to calculate hypervision optics for the human eye. The availability of suitable mathematical tools should, however, not be viewed with too much optimism as long as the accuracy of the implementation in surgical procedures is limited.
authors.affiliation: Universitäts-Augenklinik, Mainz, Germany.
authors.forename: Paul Rolf
authors.initials: PR
authors.lastname: Preussner
authors.forename: Jochen
authors.initials: J
authors.lastname: Wahl
mesh_terms: D003315:Cornea / Q000601:surgery*; D006801:Humans; D007910:Lenses, Intraocular; D008433:Mathematics; D008954:Models, Biological; D055095:Optics and Photonics; D011474:Prosthesis Design; D054140:Refractive Surgical Procedures; D014792:Visual Acuity