Toric

A toric lens is a lens with different optical power and focal length in two orientations perpendicular to each other. One of the lens surfaces is shaped like a "cap" from a torus (see figure at right), while the other one usually is spherical. Toric lenses are primarily used in eyeglasses, contact lenses and intraocular lenses to correct astigmatism.

A torus is the spatial body resulting when a circle with radius r rotates around an axis lying within the same plane as the circle, at a distance R from the circle's centre (see figure at right). If R > r, a ring torus is produced. If R = r, a horn torus is produced, where the opening is contracted into a single point. R < r results in a spindle torus, where only two “dips” remain from the opening; these dips become less deep as R approaches 0. When R = 0, the torus degenerates into a sphere with radius r.

The greatest radius of curvature of the toric lens surface, R + r, corresponds to the smallest refractive power, S, given by

where n is the index of refraction of the lens material.

The smallest radius of curvature, r, corresponds to the greatest refractive power, s, given by

Since R + r > r, S < s. The lens behaves approximately like a combination of a spherical lens with optical power s and a cylindrical lens with power s − S. In ophthalmology and optometry, s − S is called the cylinder power of the lens.

Note that both the greatest and the smallest curvature have a circular shape. Consequently, in contrast with a popular assumption, the toric lens is not an ellipsoid of revolution.

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