Astigmatism: definitions and formulations
THEastigmatism is an optical aberration, that reduces the quality of the image formed by an optical system from a light source. This page is dedicated to the most fundamental aspects of astigmatism, especially eye, and relations between the formulations and the optical characteristics of ocular astigmatism.
Astigmatism: optical consequences
When a light source is punctual, an optical system 'perfect' in shape also one-time image: we're talking about 'rigorous' stigma (in geometrical optics, where we neglect the effect of diffraction, the image of a point source can be a point object). When the optical system has a astigma, the image of the source point is no longer occasional but present a distortion, a remarkable spread which depends on the distance of the plane where the image is collected; ellipse, line, disc, etc... The image of a point is more blurred, and the resolving power of the optical system is reduced (it is more difficult to separate two blurry tasks than two points).
An optical aberration, whatever it is, has to reduce the stigma: what is special about simply called aberration "astigmatism"?
Astigmatism: optical characteristics
Astigmatism is related to the presence of a variation of the refractive power (vergence) between the different meridians of the eye. Astigmatism can be caused by the cornea (toricite), by the lens, or the combined effect of these two structures. This variation of optical power is carried out continuously between two extremes: the meridian of any power to the meridian of greater power. importantly, these extreme power meridians are perpendicular between them (ex: 0 ° - 90 °, 20 ° - 110 °,...). Astigmatism is here implicitly considered to be "regular". When the stigma is abolished by other aberrations that regular astigmatism, the eye doctor speaks readily of "irregular" astigmatism, a term that includes all the optical aberrations of high degree (coma, trefoil, etc.). This distinction is based on the history of the study of the optical aberrations of the eye, and their correction: regular astigmatism is correctable by a glass of bezel, unlike "irregular" said astigmatism
Astigmatism in Ophthalmology:
In ophthalmology, eye astigmatism is an optical defect that meets this definition and is characterized by a variation continuous and regular refractive power between two perpendicular meridians of powers (vergence) extremes. "D astigmatism is often called" cylindrical error. " The origin of this term is the fact that a "cylinder" has an o-ring area, where one of the meridians (next to the axis of the cylinder) is flat, while the perpendicular Meridian has a curvature non-zero.
-Correcting glass 'cylindrical '.
A glass of said essay "cylindrical" allows the ophthalmologist to correct ocular astigmatism during examination of ocular refraction; This glass is similar to a portion of the cylinder; It has a Meridian where the optical power is zero (the rays located in the plane of the Meridian are not deflected), and a Meridian, located at 90 ° from the meridian of power zero, where power is maximum.
To characterize this type of cylindrical glass, just to know the difference of optical power between the most 'powerful' Meridian and the meridian of curvature, and the axis of at least one of them. The optical power varies continuously between these two perpendicular meridians. Regular eye astigmatism by a cylindrical glass correction is obtained through the neutralization of the variation of the optical power linked to eye astigmatism by a variation of the same axis power but of opposite sign (this variation is of course driven by cylindrical glass, with the curvature between the 'flat' axis and the axis the most 'powerful'). For example, the astigmatism noted - 1 × 80 ° is corrected by an astigmatism + 1 × 80 °. It is important to understand what mean this type of formulation: it is crucial to keep in mind that the expression of astigmatism in ophthalmology is above all a formula intended to shape a lens correction and notation conventions do not implicitly match changes in optical power measured for an astigmatic eye.
In ophthalmology, repeating the formulation of astigmatism is historically related to the drafting of optical prescriptions for glasses manufacturing. It differs from astigmatism expression as it is found in other branches of optics. It is a source of some confusion, because in ophthalmology, astigmatism is implicitly formulated so that an optician can make a correction by a glass of bezel.
It logically appeals to a magnitude and an axis:
+ / M x A ° where M is in diopters (M can be positive or negative), and in degree. "" The symbol 'x' is like 'to': ex - 1 × 90 ° reads "less a 90 degree".
This magnitude and this axis can deduct instantly - for man of the art - the way that need to create and position a glass of cylindrical glass correction.
For example, in the expression of a plan eye astigmatism (-1 x 90 °), the magnitude is-1 D, and the axis of 90 °. "Plan" means that there is no need a glass "spherical" (correcting myopia or hyperopia) in the realization of the final glass of bezel. Expression - 1 × 90 ° can be understood as "there are maximally a diopter and less between the meridians of extreme power, and this difference of 1 d is along the Meridian 90 °". Or, more simply: ' there is a diopter and less at the level of the Meridian 90 °. Yet, we should not deduce that it would suffice to add a diopter of optical power at 90 ° to correct the astigmatism... It would be fairer to interpret the wording (-1 x 90 °) in reverse, IE as a surfeit of power of a diopter at 0 °.
Correct the astigmatism expressed as - 1 × 90 °, to actually place a corrector device that will actually remove the optical power equal to the maximum to 1 d next to the Meridian located at... 0 °! (it's the case of the cylindrical glass right in the preceding figure). There is no error, this lack of obvious logic is related to the conventions and formulations adopted in physiological optics. Indeed, the sign "-" in front of the 1 in the expression - 1 × 90 ° expresses the presence of myopia by convention, IE excess of optical power (rays converge in front of the retina). In the case of an astigmatism "-1 × 90 °", the axis Meridian 0 ° has an excess of vergence of a diopter adjustment, and the Meridian located at 90 ° has a proper vergence (rays refracted in the vertical plane are the only ones to be focused on the retina). The cylindrical glass correction is concave, and its axis of power no is placed according to the axis 90 °. Glass - 1 × 90 ° maximum well removes a diopter to... 0 ° (and less and less until the axis at 90 ° where the glass has no optical effect).
Another example: that of an astigmatism + 1 × 0 °. This formulation can be understood as "there is a diopter more at 0 °. This is true, but a finalist point of view, it is preferable to consider that missing a diopter at 90 °. The sign '+' is by convention as the default 'hypermetropique '; missing so power (from a remote source rays are focused behind the retina, except those located in the plane of the axis Meridian 0 °).
In the end, it could be argued as follows:
-a formulation such as: m x A ° (so-called "negative cylinder") means that there is an excess of M diopter next to the axis at A + 90 °. To correct the astigmatism, the cylindrical glass will be concave in axis A + 90 ° and 'flat' in the axis has (), which will have the effect of "reducing" m diopter optical power next to the Meridian A + 90 °
-a formulation such as: + M x A ° (so-called "positive cylinder") means that there is a lack of M diopter next to the axis at A + 90 °. "" To correct the astigmatism, cylindrical glass will be convex in the A + 90 ° axis and 'flat' in the a-axis (), which will have the effect of "increase" m diopter optical power next to the Meridian A + 90 °
In case of defocus partner (or "sphere"), the formulation of astigmatism joins that of the sphere. We're talking about compound astigmatism (it may be myopic, or hypermetropique, or even joint). The formulation - 2 (-1 x 90 °) translated the presence of myopia associated with astigmatism (compound myopic astigmatism). Please understand this formulation as the presence of an excess of power 3 dioptres at 0 °, and 90 ° 2 diopter. The average defocus is equal to-2.50 D, around which is a fluctuation of magnitude 1 d. all of the light rays converge in front of the retina.
Astigmatism direct or reverse
Astigmatism said "direct" or "consistent with the rule" ("with the rule" in English: WTR) corresponds to situations where the vertical meridians (60 ° / 120 °) are more powerful than the horizontal Meridian (0 ° / 30 ° and 150 ° / 180 °). This situation can be caused by a pronounced camber from vertical meridians of the cornea.
Astigmatism says 'reverse' or 'no-rule' ('against the rule' in English: ATR) corresponds to the situations where the vertical meridians are less powerful than the horizontal Meridian.
Oblique astigmatism corresponds to the intermediate situations (extreme curvature meridians located between 30 ° / 60 ° and 120 ° / 150 °).
Some diseases are accompanied by a direction of astigmatism that they generate. For example, the astigmatism caused by advanced Keratoconus is more often reverse or oblique. Similarly, there is the appearance of a reversed astigmatism in late result of operations of radial keratotomy. Pellucid marginal degeneration comes pathognomonic way of a reverse astigmatism. Congenital astigmatism that accompanies strong myopia is often direct. Nuclear cataract usually induced astigmatism (original cristallinienne) to reverse direction. Finally, if the posterior face of the cornea this a toricite such as astigmatism, it generates (optical effect) is mostly opposite.
Astigmatism: formulas and conversions
There are various formulations to express a refractive error with astigmatism, according to signs assigned to the sphere and the cylinder.
For example, the expression - 2 (-1 x 0 °) understands itself as an excess of optical power of 3D at 90 ° and 2 D at 0 °. We correct this compound myopic astigmatism by placing on a mount to test a concave glass-2D and a concave cylindrical glass-1 D according to the 0 ° axis (this glass reduces the power of a diopter adjustment next to the 90 ° axis, and has no effect against the axis 0 °). An equivalent formulation for the realization of a glass of bezel is:-3 (+ 1 × 90 °).
To express an astigmatism in 'positive cylinder', or negative, or can use the following conversion formulas:
sphere (cylinder in positive x A °) is equivalent to (sphere + positive cylinder) (cylinder negative x A + 90 °)
example:-1 (+ 2 × 30 °) is equivalent to + 1 (-2 × 120 °)
sphere (negative cylinder x A °) is equivalent to (sphere + negative cylinder) (positive cylinder x A + 90 °)
example: + 2 (-3 x 10 °) is equivalent to-1 (+ 3 x 100 °), at least for the realization of an optical eyeglass prescription. For the realization of a surgery refractive photoablative)LASIK(, PRK), the consequences of these formulations in corneal tissue removed could be different (see profiles of ablation).