title: Superposition of sphero-cylindrical lenses using contour graphs.
abstract: BACKGROUND
  The superposition of thin sphero-cylindrical lenses with arbitrary angles between cylindrical axes is sometimes required in a clinical setting. For example, it may be useful in some instances to perform an overrefraction which, added to the spectacle or toric contact lens in place on the eye, yields a final correcting lens.
  
  
  METHODS
  Computer calculations have been used to create contour graphs allowing a graphical solution to the problem of combining sphero-cylindrical lenses. Although conceptually strightforward, the method has not been presented before.
  
  
  RESULTS
  The use of contour graphs to superpose sphero-cylindrical lenses is shown by examples to be accurate and much simpler than calculational methods.
  
  
  CONCLUSIONS
  Lacking a pre-programmed computer, the method of contour graphs offers a practical method of combining sphero-cylindrical lenses.
authors.affiliation: Southern California College of Optometry, Fullerton 92831, USA.
authors.forename: R P
authors.initials: RP
authors.lastname: Hemenger
mesh_terms: D005139:Eyeglasses; D006801:Humans; D008433:Mathematics; D055656:Prescriptions; D012030:Refractive Errors / Q000503:physiopathology / Q000628:therapy*; D014792:Visual Acuity