title: Average focal length and power of a section of any defined surface.
abstract: OBJECTIVE
  To provide a method to allow calculation of the average focal length and power of a lens through a specified meridian of any defined surface, not limited to the paraxial approximations.
  
  
  METHODS
  University of Liverpool, Liverpool, United Kingdom.
  
  
  METHODS
  Functions were derived to model back-vertex focal length and representative power through a meridian containing any defined surface. Average back-vertex focal length was based on the definition of the average of a function, using the angle of incidence as an independent variable.
  
  
  RESULTS
  Univariate functions allowed determination of average focal length and power through a section of any defined or topographically measured surface of a known refractive index. These functions incorporated aberrations confined to the section.
  
  
  CONCLUSIONS
  The proposed method closely approximates the average focal length, and by inference power, of a section (meridian) of a surface to a single or scalar value. It is not dependent on the paraxial and other nonconstant approximations and includes aberrations confined to that meridian. A generalization of this method to include all orthogonal and oblique meridians is needed before a comparison with measured wavefront values can be made.
authors.affiliation: St. Paul's Eye Unit, Royal Liverpool University Hospital, Liverpool, United Kingdom. s.b.kaye@liverpool.ac.uk
authors.forename: Stephen B
authors.initials: SB
authors.lastname: Kaye
mesh_terms: D001699:Biometry / Q000379:methods; D007910:Lenses, Intraocular; D008433:Mathematics; D055095:Optics and Photonics