title: The concept of geodesic curvature applied to optical surfaces.
abstract: OBJECTIVE
  To propose geodesic curvature as a metric to characterise how an optical surface locally differs from axial symmetry. To derive equations to evaluate geodesic curvatures of arbitrary surfaces expressed in polar coordinates.
  
  
  METHODS
  The concept of geodesic curvature is explained in detail as compared to other curvature-based metrics. Starting with the formula representing a surface as function of polar coordinates, an equation for the geodesic curvature is obtained depending only on first and second radial and first order angular derivatives of the surface function. The potential of the geodesic curvature is illustrated using different surface tests.
  
  
  RESULTS
  Geodesic curvature reveals local axial asymmetries more sharply than other types of curvatures such as normal curvatures.
  
  
  CONCLUSIONS
  Geodesic curvature maps could be used to characterise local axial asymmetries for relevant optometry applications such as corneal topography anomalies (keratoconus) or ophthalmic lens metrology.
authors.affiliation: Instituto de Óptica (CSIC), Madrid, Spain.
authors.forename: Sergio
authors.initials: S
authors.lastname: Barbero
mesh_terms: D003315:Cornea / Q000033:anatomy & histology*; D003316:Corneal Diseases / Q000175:diagnosis; D019781:Corneal Topography / Q000379:methods*; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical
keywords: corneal topography; curvature; geodesic curvature; power maps