A toric lens is a lens

Lens (optics)

A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

 with two different powers

Optical power

Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of optical power...

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

Torus

In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...

 (see figure at right), while the other one usually is spherical

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

. Toric lenses are primarily used in eyeglass

Glasses

Glasses, also known as eyeglasses , spectacles or simply specs , are frames bearing lenses worn in front of the eyes. They are normally used for vision correction or eye protection. Safety glasses are a kind of eye protection against flying debris or against visible and near visible light or...

es, contact lens

Contact lens

A contact lens, or simply contact, is a lens placed on the eye. They are considered medical devices and can be worn to correct vision, for cosmetic or therapeutic reasons. In 2004, it was estimated that 125 million people use contact lenses worldwide, including 28 to 38 million in the United...

es and intraocular lens

Intraocular lens

An intraocular lens is an implanted lens in the eye, usually replacing the existing crystalline lens because it has been clouded over by a cataract, or as a form of refractive surgery to change the eye's optical power. It usually consists of a small plastic lens with plastic side struts, called...

es, to correct for astigmatism

Astigmatism (eye)

Astigmatism is an optical defect in which vision is blurred due to the inability of the optics of the eye to focus a point object into a sharp focused image on the retina. This may be due to an irregular or toric curvature of the cornea or lens. There are two types of astigmatism: regular and...

.

Torus

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, an 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

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

 with radius r.

The toric lens

The greatest radius of curvature of the toric lens surface, , corresponds to the smallest refractive power

Optical power

Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of optical power...

, , where n is the index of refraction of the lens material. The smallest radius of curvature, r, corresponds to the greatest refractive power, . Since , . The lens behaves approximately like a combination of a spherical lens with optical power s and a cylindrical lens

Cylindrical lens

A cylindrical lens is a lens which focuses light which passes through on to a line instead of on to a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it onto a line parallel to the intersection of the...

 with power . In ophthalmology

Ophthalmology

Ophthalmology is the branch of medicine that deals with the anatomy, physiology and diseases of the eye. An ophthalmologist is a specialist in medical and surgical eye problems...

 and optometry

Optometry

Optometry is a health care profession concerned with eyes and related structures, as well as vision, visual systems, and vision information processing in humans. Optometrists, or Doctors of Optometry, are state licensed medical professionals trained to prescribe and fit lenses to improve vision,...

  is called the cylinder power of the lens.

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

Spheroid

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters....

.

Working

Light ray

Ray (optics)

In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

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

Refraction

Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

 according to the greatest radius of curvature, , i.e., the smallest refractive power, .

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, i.e., the greatest refractive power, . 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). They are related to toric lenses in the same way that aspheric lens

Aspheric lens

An aspheric lens or asphere 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.