title: Compensation of corneal oblique astigmatism by internal optics: a theoretical analysis.
abstract: Oblique astigmatism is a prominent optical aberration of peripheral vision caused by oblique incidence of rays striking the refracting surfaces of the cornea and crystalline lens. We inquired whether oblique astigmatism from these two sources should be expected, theoretically, to have the same or opposite signs across the visual field at various states of accommodation.
  
  
  
  Oblique astigmatism was computed across the central visual field for a rotationally-symmetric schematic-eye using optical design software. Accommodative state was varied by altering the apical radius of curvature and separation of the biconvex lens's two aspheric surfaces in a manner consistent with published biometry. Oblique astigmatism was evaluated separately for the whole eye, the cornea, and the isolated lens over a wide range of surface curvatures and asphericity values associated with the accommodating lens. We also computed internal oblique astigmatism by subtracting corneal oblique astigmatism from whole-eye oblique astigmatism.
  
  
  
  A visual field map of oblique astigmatism for the cornea in the Navarro model follows the classic, textbook description of radially-oriented axes everywhere in the field. Despite large changes in surface properties during accommodation, intrinsic astigmatism of the isolated human lens for collimated light is also radially oriented and nearly independent of accommodation both in theory and in real eyes. However, the magnitude of ocular oblique astigmatism is smaller than that of the cornea alone, indicating partial compensation by the internal optics. This implies internal oblique astigmatism (which includes wavefront propagation from the posterior surface of the cornea to the anterior surface of the lens and intrinsic lens astigmatism) must have tangentially-oriented axes. This non-classical pattern of tangential axes for internal astigmatism was traced to the influence of corneal power on the angles of incidence of rays striking the internal lens.
  
  
  
  Partial compensation of corneal astigmatism by internal optics is due mainly to the highly converging nature of wavefronts incident upon the lens resulting from corneal refraction. The degree of compensation is quadratically dependent on eccentricity but is expected to diminish as the eye accommodates. Neutralising the cornea by index-matching defeats internal compensation, revealing classical, radially-oriented oblique astigmatism in the isolated lens.
authors.affiliation: School of Optometry, Indiana University, Bloomington, Indiana, USA.
authors.forename: Tao
authors.identifier: 0000-0001-9864-3896
authors.initials: T
authors.lastname: Liu
authors.affiliation: School of Optometry, Indiana University, Bloomington, Indiana, USA.
authors.forename: Larry N
authors.initials: LN
authors.lastname: Thibos
mesh_terms: D001251:Astigmatism / Q000175:diagnosis / Q000503:physiopathology / Q000628:therapy*; D003315:Cornea / Q000473:pathology*; D019781:Corneal Topography / Q000379:methods; D006801:Humans; D007910:Lenses, Intraocular; D008962:Models, Theoretical; D055095:Optics and Photonics / Q000379:methods; D012029:Refraction, Ocular / Q000502:physiology*; D014794:Visual Fields
keywords: accommodation; compensation; oblique astigmatism; peripheral vision