Principles of a Non-orthogonal Optical Surface with Potential for Correction of Irregular Astigmatism

PURPOSE: Non-orthogonal lenses, in which the principal meridians of the cylinder surfaces are not perpendicular to each other, can be used to improve vision in the condition of irregular astigmatism. A procedure is developed that allows raytracing and image-quality analysis with such lenses. METHODS: A non-orthogonal surface was developed as a user-defined surface in the programme Ansys Zemax OpticStudio using a bi-cubic meridional mapping function. The function consists of two third-order polynomial sub-functions, each for mapping the actual 'on surface' meridian to an effective meridian that determines the meridional curvature for the two sectors of meridians bounded by the principal meridians. Equations were derived for partial derivatives across the surface, as Zemax requires these for raytracing through a user-defined surface. RESULTS: Examples are shown of tangential and pupil power maps for a thin orthogonal (conventional) +5.00 DS/+2.00 DC × 180 lens and for a non-orthogonal +5.00 DS/+2.00 DC (60) × 180 lens. The orthogonal lens has principal meridians 180° and 90° while the non-orthogonal lens has principal meridians 180° and 60°. For the orthogonal lens, both maps show regular changes in power with meridional angle, and the sagittal power map is rotated by 90° relative to the tangential power map. For the non-orthogonal lens, the sagittal power pattern shows sharp changes in power. The non-orthogonal surfaces were replicated using the 'grid sag' surface of Zemax, and the user-defined surface was verified. Surface fitting using Zernike polynomials returned only a reasonable approximation to a non-orthogonal surface. CONCLUSION: A type of non-orthogonal optical surface based on two third-order polynomials is presented. Aspects of its geometrical optics properties were investigated, including confirming the non-orthogonality of its axes. This type of surface may have utility in the correction of irregular astigmatism, such as occurs in keratoconus.