A toric lens is a

lens A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements'') ...

with different

optical power In optics, optical power (also referred to as dioptric power, refractive power, focal power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the ...

and

focal length The focal length of an Optics, optical system is a measure of how strongly the system converges or diverges light; it is the Multiplicative inverse, inverse of the system's optical power. A positive focal length indicates that a system Converge ...

in two orientations perpendicular to each other. One of the lens surfaces is shaped like a "cap" from a

torus In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses inclu ...

(see figure at right), and the other one is usually spherical. Such a lens behaves like a combination of a spherical lens and a

cylindrical lens A cylindrical lens is a lens (optics), lens which Focus (optics), focuses light into a line instead of a point as a Lens (optics), spherical lens would. The curved face or faces of a cylindrical lens are sections of a Cylinder (geometry), cylinde ...

. Toric lenses are used primarily in

eyeglass Glasses, also known as eyeglasses (American English), spectacles ( Commonwealth English), or colloquially as specs, are vision eyewear with clear or tinted lenses mounted in a frame that holds them in front of a person's eyes, typically ...

es,

contact lens Contact lenses, or simply contacts, are thin lenses placed directly on the surface of the eyes. Contact lenses are ocular prosthetic devices used by over 150 million people worldwide, and they can be worn to correct vision or for cosmetic ...

es and

intraocular lens An intraocular lens (IOL) is a lens (optics), lens implanted in the human eye, eye usually as part of a treatment for cataracts or for correcting other vision problems such as myopia, near-sightedness (myopia) and farsightedness, far-sightednes ...

es to correct

astigmatism Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. The lens and cornea of an eye without astigmatism are nearly spherical, with only a single radius of curvature, and any refractive errors ...

Torus

A torus is the surface of revolution 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 A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

with radius ''r''. Les trois types de tores

Radius of curvature and optical power

The greatest

radius of curvature In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius ...

of the toric lens surface, , corresponds to the smallest

refractive power In optics, optical power (also referred to as dioptric power, refractive power, focal power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the r ...

, ''S'', given by :

S = \frac

, 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 :

s = \frac

. Since , . The lens behaves approximately like a combination of a spherical lens with optical power ''s'' and a

with power . In

ophthalmology Ophthalmology (, ) is the branch of medicine that deals with the diagnosis, treatment, and surgery of eye diseases and disorders. An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Following a ...

and

optometry Optometry is the healthcare practice concerned with examining the eyes for visual defects, prescribing corrective lenses, and detecting eye abnormalities. In the United States and Canada, optometrists are those that hold a post-baccalaureate f ...

, 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.

Light ray and its refractive power

Light ray In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays ...

s within the (''x'',''y'')-plane of the torus (as defined in the figure above) are

refracted In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenome ...

according to the greatest radius of curvature, , which means that it has the smallest refractive power, ''S''. Light rays within a plane through the axis of revolution (the ''z'' axis) of the torus are refracted according to the smallest radius of curvature, ''r'', which means that it has the greatest refractive power, ''s''. As a consequence, there are two different refractive powers at orientations perpendicular to each other. At intermediate orientations, the refractive power changes gradually from the greatest to the smallest value, or reverse. This will compensate for the astigmatic aberration of the eye.

Atoric lens

With modern computer-controlled design, grinding and polishing techniques, good vision corrections can be achieved for even wider angles of view by allowing certain deviations from the toric shape. This is called an ''atoric lens'' (literally, non-toric lens).Volk, D.: ''Aspheric Lenses''
, in ''Duane's Ophthalmology'', chapter 50 (Lippinkott, Wilkins & Williams / Wolters-Kluwer Health, Chicago, USA) They are related to toric lenses in the same way that

aspheric lens An aspheric lens or asphere (often labeled ''ASPH'' on eye pieces) is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens. ...

es are related to spherical lenses.

Notes

References

{{reflist Geometrical optics Corrective lenses