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), and the other one is usually spherical. Such a lens behaves like a combination of a spherical lens and a cylindrical lens. Toric lenses are used primarily in eyeglasses, contact lenses and intraocular lenses to correct astigmatism.
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 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 [lower-alpha 1] .
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 rays within the (x,y)-plane of the torus (as defined in the figure above) are refracted according to the greatest radius of curvature, R + r, 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.
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). [1] [2] They are related to toric lenses in the same way that aspheric lenses are related to spherical lenses.
In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.
A lens is a transmissive optical device which 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), usually arranged along a common axis. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a desired shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called lenses, such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses.
A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.
In geometry, a torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
A corrective lens is a lens that is typically worn in front of the eye to improve daily vision. The most common use is to treat refractive errors: myopia, hypermetropia, astigmatism, and presbyopia. Glasses or "spectacles" are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye. Intraocular lenses are surgically implanted most commonly after cataract removal but can be used for purely refractive purposes.
In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems.
An eyeglass prescription is an order written by an eyewear prescriber, such as an optometrist, that specifies the value of all parameters the prescriber has deemed necessary to construct and/or dispense corrective lenses appropriate for a patient. If an eye examination indicates that corrective lenses are appropriate, the prescriber generally provides the patient with an eyewear prescription at the conclusion of the exam.
An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. The term comes from the Greek α- (a-) meaning "without" and στίγμα (stigma), "a mark, spot, puncture".
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
Refractive error, also known as refraction error, is a problem with focusing light accurately on the retina due to the shape of the eye and or cornea. The most common types of refractive error are near-sightedness, far-sightedness, astigmatism, and presbyopia. Near-sightedness results in far away objects being blurry, far-sightedness and presbyopia result in close objects being blurry, and astigmatism causes objects to appear stretched out or blurry. Other symptoms may include double vision, headaches, and eye strain.
A spherometer is an instrument used for the precise measurement of the radius of curvature of a sphere or a curved surface. Originally, these instruments were primarily used by opticians to measure the curvature of the surface of a 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.
A keratometer, also known as an ophthalmometer, is a diagnostic instrument for measuring the curvature of the anterior surface of the cornea, particularly for assessing the extent and axis of astigmatism. It was invented by the German physiologist Hermann von Helmholtz in 1851, although an earlier model was developed in 1796 by Jesse Ramsden and Everard Home.
Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis. The distance from the vertex to the center of curvature is the radius of curvature of the surface.
Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance. Other symptoms can include eyestrain, headaches, and trouble driving at night. Astigmatism often occurs at birth and can change or develop later in life. If it occurs in early life and is left untreated, it may result in amblyopia.
In optics, vergence is the angle formed by rays of light that are not perfectly parallel to one another. Rays that move closer to the optical axis as they propagate are said to be converging, while rays that move away from the axis are diverging. These imaginary rays are always perpendicular to the wavefront of the light, thus the vergence of the light is directly related to the radii of curvature of the wavefronts. A convex lens or concave mirror will cause parallel rays to focus, converging toward a point. Beyond that focal point, the rays diverge. Conversely, a concave lens or convex mirror will cause parallel rays to diverge.
A cylindrical lens is a lens which focuses light into a line instead of 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 into a line parallel to intersection of the surface of the lens and a plane tangent to it along the cylinder's axis. The lens converges or diverges the image in the direction perpendicular to this line, and leaves it unaltered in the direction parallel to its cylinder's axis.
The eye, like any other optical system, suffers from a number of specific optical aberrations. The optical quality of the eye is limited by optical aberrations, diffraction and scatter. Correction of spherocylindrical refractive errors has been possible for nearly two centuries following Airy's development of methods to measure and correct ocular astigmatism. It has only recently become possible to measure the aberrations of the eye and with the advent of refractive surgery it might be possible to correct certain types of irregular astigmatism.
Subjective Refraction is a technique to determine the combination of lenses that will provide the best corrected visual acuity (BCVA). It is a clinical examination used by orthoptists, optometrists and ophthalmologists to determine a patient's need for refractive correction, in the form of glasses or contact lenses. The aim is to improve current unaided vision or vision with current glasses. Glasses must also be comfortable visually. The sharpest final refraction is not always the final script the patient wears comfortably.
The Jackson cross cylinder (JCC) is an instrument used by ophthalmologists, orthoptists and optometrists in their routine eye examination, particularly in determination of corrective lens power in patients with astigmatism. It is also used for testing near point of the eye.
