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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.

The formulation of a cylindrical glass can be "misleading": + 1 × 90 ° corresponds to add a diopter power to... 0 ° (less and less on the meridians obliques until 90 °).

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.

-Astigmatism: formulation

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 °

Compound astigmatism

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).




31 responses to "Astigmatism: definitions and formulations"

  1. Aline Modassie says:

    Hello I want to know if the astigmatism can be permanently treated otherwise than by the correction of the glasses. If yes how and only cost.
    Thank you

  2. Dr. Damien Gatinel says:

    Astigmatism can be corrected surgically by laser (PKR, or LASIK). The cost of refractive surgery generally ranges between 1000 and 2000 euros per eye, depending on the techniques, surgeons, etc.

  3. Peillon says:

    Hello, can the axis of astigmatism vary over time? In 2012 I was comfortable with glasses: OD - 1.25 (+ 0.75) 90 ° and OG - 1.75 (+ 0.50) 80 °, today I'm wearing: OD - 1.00 (+ 0.50) (5) and OG - 1.75 (+ 0.50) 90 ° and I find them very uncomfortable. Thank you.

  4. Dr. Damien Gatinel says:

    Astigmatism has actually varied significantly, "direct" it became indirect (reverse). If this is not an error of prescription, this kind of variation is, in my experience, patients who are often rubbing the eyes. These friction induce this kind of astigmatism by distorting the cornea gradually.

  5. Jogues says:

    Hello, I'm 22 years old and I'm astigmatism. I do not know if it is very serious, my prescription is: od – 0.50 (-0.50) 180 ° and og Pl (-0.50) 180 °. My concern is to know first if the heartburn has an impact on the eyes because every time it burns, the left eye hurts simultaneously. Second, I would like to have a little technical explanation on my frequent headaches. Thank you!

  6. Dr. Damien Gatinel says:

    Your astigmatism is very low in magnitude, and should not be causing pronounced headaches. There are no links between astigmatism and stomach aches. However, stress can quite be causing headaches, and stomach pain. I advise you to consult your attending physician.

  7. Bartkowiak says:

    On a medical visit in the near future, it is required to be able to have lenses of which my correction power does not exceed 3 diopters.
    My correction is as follows:
    OD:-2.50 (+ 4.00) to 90 °
    OG:-1.00 (+ 4.00) to 90 °
    Does it fit not to exceed 3 diopters?
    Thanks in advance.

  8. Dr. Damien Gatinel says:

    It all depends on what is meant by "not exceeding 3 diopters". If it is 3 diopters of "spherical equivalent", then you are in the standard (spherical equivalent-0.50 d OD and + 1.00 d og). It should be noted that the magnitude of your astigmatism (the difference between the most flat and the most arched meridian) exceeds this value. But it is most likely the spherical equivalent that is discussed for the medical visit.

  9. Bartkowiak says:

    Thank you bcp for your clear and accurate answer!

  10. Jaillet Lucas says:

    Hello, some points are not very clear to me in my ophthalmology classes;

    In general, when a refractive formula is given, it is not the intrinsic refractive formula of the eye but already an optical correction envisaged; A myopic eye with an excess of 2 diopters does not mark up + 2 but directly-2; The reverse for a hyperopic eye with a deficit of 2 diopters so noted + 2 and non-2 (which is its intrinsic deficit); And a myopic eye with excess of 2 diopters and astigmatism with an excess of 2 diopters on the axis 90 is rated-2 (-2 x 0 °) in negative cylinder and-4 (+ 2 x 90 °) in positive cylinder; Is this good?

    The logical Web Consultation – > Optical prescription therefore imposes a writing directly in optical prescription that must read the reverse to find the true refractive formula of the eye?

    Thanks in advance!

  11. Dr. Damien Gatinel says:

    Your observations are all fair. It should be admitted that the formulations used are derived from "arbitrary" conventions. The important thing is to use the same "logic" for all case encountered.

  12. Sara Algeria says:

    Hello I have a two and a half year old girl who was diagnosed with astigmatism of More1, 5 for both eyes (I do not have the order MTN but I vai send you the exact figures) my qustions are:
    Is this serious as an ocular problem?
    Is wearing glasses mandatory?
    What will be the consequences if his astigmatism is not correct (I don't want her to wear glasses)
    Thank you Dr

  13. Dr. Damien Gatinel says:

    It is very important that your daughter astigmatism can wear glasses to correct her astigmatism. This one is not serious in itself, but could be causing a visual development delay for your daughter if, due to a blurred vision constantly, she could not have a good visual acuity for the rest of her life (everything is played before 6 O U 7 years). Trust your ophthalmologist and optician for the realization of suitable optical equipment.

  14. Robin says:

    Hello the optician Ma made glasses in OD:-3 (+ 0.75) at 15 °. But the Optalmo to marked OD:-2.25 (-0.75) 105 °. Optician made tests and told me that it was equivalent to what had found the Optalmo but apparently not? Thank you for your clarification.

  15. Dr. Damien Gatinel says:

    These formulas are the same. Ophthalmologists commonly use the so-called "negative cylinder" formulas, which opticians often convert into a "positive cylinder" for the production of glasses.

  16. Godwin says:

    Hello. Here is what is written on my prescription:
    OD: 0.50 CYL 180 °
    OG 0.50 CYL 180 °
    I don't understand much. Can you explain to me please?
    I constantly have headaches..
    Is this a case of low, very low, or medium astigmatism?

  17. Dr. Damien Gatinel says:

    This is a low astigmatism, but that could still explain a bit of visual fatigue if not corrected.

  18. SALOUA says:

    Hello the optician made my little glasses in OD:-0.25 (-1.00 a 5 °). OG:-0.50 (-0.25 to 180 °)
    But the Optalmo to marked OD:-0125 (+ 100) 0 °. OG:-0075 (+ 025) 0 °
    Is this equivalent?
    Is wearing glasses mandatory?

  19. Dr. Damien Gatinel says:

    It seems to be an equivalent formula (transposition into a positive cylinder formula), and this correction should be worn if it improves your vision and comfort.

  20. Made says:

    What is the increase in inverse astigmatism with age?
    Is this corneal astigmatism that becomes – direct because of the eyelid pressure that is – strong or the internal astigmatism that becomes + reverse and why?
    Thank you

  21. Dr. Damien Gatinel says:

    This is an interesting question: the two mechanisms you suggest are possible. The eye rubbing Chronicles can induce a corneal deformation characterized by a lower camber, with slight upper and central flattening. Because of the constraint of "curvature retention", if the central and upper vertical corridor of flattent, the lateral areas of the corneal surface must be bent ("torque effect" because the overall curvature of the cornea must remain unchanged-in case of isometric distortion which is a priori the case here)... and this then causes the appearance or accentuation of reverse astigmatism (the appearance of the keratoconus arises from the same mechanism, but in this case Frictions are particularly frequent, supported, and have major thinning and irregularities. In addition, the so-called "nuclear" cataracts are usually the cause of internally reverse astigmatism. This particular direction corresponds may be to a orientatino of the internal "sutures" of the Crystalline lens Which densifieraient preferentially according to certain axes, with as a result an astigmatism called "inverts" (on "non-compliant").

  22. ROLLAND says:

    If a person has to wear 0.00 (-1.00) 90 °, does it mean that it converges too much 1dioptrie on the horizontal axis?
    Kind regards

  23. Dr. Damien Gatinel says:

    Yes, that's exactly it! It is true that the wording of the correction does not allow to apprehend this characteristic in a very intuitive way...

  24. Elizabeth says:

    my prescription says: OD: + 0.50 (-0.50 to 116 °) and OG:-1.25 (-. 25 to 60 °)
    Gold on the optician's quotation it is indicated OD: 0.00 (+ 0.50) 26 ° and OG:-1.50 (+ 0.25) 150 °

    I understood that I had a different astigmatism with each eye but I do not understand why the quotation does not conform to the Ordinance. I would like to know your point of view before confirming my glasses order. Thank you

  25. Sarah IGREJA says:

    Is an axis at 0 ° equal to an axis at 180 °. My lenses have an axis at 180 ° while on the prescription is 0 °. Thank you bcp

  26. Dr. Damien Gatinel says:

    The 0 ° axis is effectively equal to the 180 ° axis for astigmatism correction.

  27. Dr. Damien Gatinel says:

    These formulas are actually identical; It is a transposition of a prescription in cylinder called "negative" by the ophthalmologist in a "positive" cylinder requirement for the realization of glasses by the optician.

  28. Cardi says:

    My 3-year-old daughter was diagnosed with farsightedness and astigmatism at the end of June. She wears glasses that will have to be changed in 4-6 months with her final correction (+8/9)
    Here is his current correction:
    OD: (110-1.50)+5.50
    Is there a possible evolution?
    How's the surgery going?
    Thanks for your reply.

  29. Dr. Damien Gatinel says:

    Only monitoring will make it possible to judge the evolution, in principle the future growth of the eye should not allow to catch up this degree of hyperopia. Eyeglass correction is indicated, and surgery is only possible in adulthood in this context.

  30. Alia Ben says:

    I am in a career in graphic design, so very often in front of the computer.
    I sometimes have a headache at the end of the day so I went to see an ophthalmologist. I can see very well on both eyes, no myopia or hyperopia. I have no correction in the lens of the left eye, but for the right eye:
    I have astigmatism and my prescription says -0.50 to 10°.
    Is this correction really useful for something -0.50 to 10° it doesn't seem like much?
    With nothing in the other eye, it wouldn't be an unnecessary correction, would it?
    Are you advising me to wear the glasses anyway?
    Thank you very much

  31. Dr. Damien Gatinel says:

    It is indeed unlikely that this very slight and unilateral correction will be useful in this context!

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