title: Approximating lens power.
abstract: OBJECTIVE
  To provide a scalar measure of refractive error, based on geometric lens power through principal, orthogonal and oblique meridians, that is not limited to the paraxial and sag height approximations.
  
  
  METHODS
  A function is derived to model sections through the principal meridian of a lens, followed by rotation of the section through orthogonal and oblique meridians. Average focal length is determined using the definition for the average of a function.
  
  
  RESULTS
  Average univariate power in the principal meridian (including spherical aberration), can be computed from the average of a function over the angle of incidence as determined by the parameters of the given lens, or adequately computed from an integrated series function. Average power through orthogonal and oblique meridians, can be similarly determined using the derived formulae.
  
  
  CONCLUSIONS
  The widely used computation for measuring refractive error, the spherical equivalent, introduces non-constant approximations, leading to a systematic bias. The equations proposed provide a good univariate representation of average lens power and are not subject to a systematic bias. They are particularly useful for the analysis of aggregate data, correlating with biological treatment variables and for developing analyses, which require a scalar equivalent representation of refractive power.
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: D006801:Humans; D007909:Lenses; D008962:Models, Theoretical; D055095:Optics and Photonics / Q000295:instrumentation* / Q000379:methods*; D012030:Refractive Errors / Q000175:diagnosis*