In ophthalmology, the vertical and horizontal planes are identified as tangential and sagittal meridians, respectively. Ophthalmic astigmatism is a refraction error of the eye in which there is a difference in degree of refraction in different meridians. It is typically characterized by an aspherical, non-figure of revolution cornea in which the corneal profile slope and refractive power in one meridian is greater than that of the perpendicular axis.
Astigmatism causes difficulties in seeing fine detail. In some cases vertical lines and objects such as walls may appear to the patient to be leaning over like the Tower of Pisa. Astigmatism can be often corrected by glasses with a lens that has different radii of curvature in different planes (a cylindrical lens), contact lenses, or refractive surgery.
Astigmatism is quite common. Studies have shown that about one in three people suffers from it . The prevalence of astigmatism increases with age . Although a person may not notice mild astigmatism, higher amounts of astigmatism may cause blurry vision, squinting, asthenopia, fatigue, or headaches.
There are a number of tests used by ophthalmologists and optometrists during eye examinations to determine the presence of astigmatism and to quantify the amount and axis of the astigmatism. A Snellen chart or other eye chart may initially reveal reduced visual acuity. A keratometer may be used to measure the curvature of the steepest and flattest meridians in the cornea’s front surface. A corneal topographer may also be used to obtain a more accurate representation of the cornea’s shape . An autorefractor or retinoscopy may provide an objective estimate of the eye’s refractive error and the use of Jackson cross cylinders in a phoropter may be used to subjectively refine those measurements. An alternative technique with the phoropter requires the use of a “clock dial” or “sunburst” chart to determine the astigmatic axis and power.
Astigmatism due to misaligned or malformed lenses and mirrors
Grinding and polishing of precision optical parts, either by hand or machine, typically employs significant downward pressure, which in turn creates significant frictional side pressures during polishing strokes that can combine to locally flex and distort the parts. These distortions generally do not possess figure-of-revolution symmetry and are thus astigmatic, and slowly become permanently polished into the surface if the problems causing the distortion are not corrected. Astigmatic, distorted surfaces potentially introduce serious degradations in optical system performance.
Surface distortion due to grinding or polishing increases with the aspect ratio of the part (diameter to thickness ratio). To a first order, glass strength increases as the cube of the thickness. Thick lenses at 4:1 to 6:1 aspect ratios will flex much less than high aspect ratio parts, such as optical windows, which can have aspect ratios of 15:1 or higher. The combination of surface or wavefront error precision requirements and part aspect ratio drives the degree of back support uniformity required, especially during the higher down pressures and side forces during polishing. Optical working typically involves a degree of randomness that helps greatly in preserving figure-of-revolution surfaces, provided the part is not flexing during the grind/polish process.