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Astigmatism - explanations

Astigmatism is an optical defect from which it is often difficult to provide a simple explanation. The following articles have explanatory aspects: they can be read after reading this page is an attempt to didactic explanation of what is astigmatism in terms of 'bright journey' rays refracted by an optical system with astigmatism

Most aspects of the rating of astigmatism, the Scriptures and conversion formulae are available on this page: astigmatism, definitions and formulations.

End of page, general concepts relating to the correction of astigmatism will be addressed. They are addressed in more detail in the pages dedicated to the implants-rings, and to the profiles of laser ablation for the correction of astigmatism.

 

Astigmatism: general definition

Astigmatism in ophthalmology is an optical common eye defect for a defective vision known as cylindrical, can be associated with the so-called spherical ametropia (myopia or hyperopia), and causes a Visual blurring that is not correctable by a single spherical glass. Astigmatism indeed requires a correction by a "cylindrical" said glass (cylinder), a toric lens, or a toric implant. Astigmatism can be isolated (simple astigmatism) or associated myopia, hyperopia or presbyopia (compound astigmatism). It is a completely operable defect in refractive and cataract surgery.
Astigmatism can be regular or irregular. We discuss here the case of regular astigmatism, or "cylindrical defocus" which corresponds to astigmatism regular that can be corrected in glasses (irregular astigmatism corresponds to all the optical aberrations of high degree that are not correctable by glasses).
Regular astigmatism can be corrected by wearing a glass of bezel, but also by a toric contact lens, or the realization of appropriate refractive surgery (laser often ring implant, corneal incisions relaxing more rarely).

Astigmatism: a three-dimensional optical defect

To apprehend the astigmatism, reason in the three dimensions of space. A representation of the eye Cup can schematically represent the path of light rays in myopic, normalsighted or farsighted eyes.

representation of the rays in a myopic eye farsighted or have astigmatism in two dimensions

In cutting plane (in a bi-dimensional world), the eye restricted to a cutting plan (a Meridian, highlighted in red at the level of the cornea) may be short-sighted, Emmetropic either astigmatic. Whatever the cut plane, the path of rays is the same in one eye has no astigmatism. In an astigmatic eye, the refraction of light rays varies with the cutting plane. Ocular astigmatism can be represented accurately in the three dimensions of space.

In an astigmatic eye, the refraction of light rays varies with the Meridian considered; one eye may be Emmetropic according to a direction (ex: horizontal Meridian) and short-sighted (or farsighted) according to another (ex: vertical Meridian). In an astigmatic eye, there are two special meridians, which are mutually perpendicular: these are meridians of extreme power: one is the strongest (maximum vergence) the other is the least powerful (minimum vergence).

changes in vergence Meridian vertical and horizontal astigmatic eye

The eye has an overall spherical geometry, and the refraction of light rays can vary according to the axis of the considered meridians. In this example, if the vertical (90 °) Meridian has an excess of optical power (the cornea is more cambered along this axis), the eye can be short-sighted next to this direction. Conversely, if the horizontal Meridian (0 °) has a default of optical power (the cornea is less arched along this axis), the eye can be farsighted according to this direction.

The astigmatic eye has an optical defect (ametropia), whose peculiarity is to vary according to the axis of the considered Meridian. All meridians may be too powerful (myopia) but have a variation of power between them. "The eye then presents an astigmatism said" myopic compound.  These concepts will be developed further.

The path of light rays in an astigmatic eye is relatively complex: the refracted rays intersect never all in one point: there is no stigma. In the example (illustration), the eye is nearsighted according to the vertical and farsighted Meridian according to the horizontal Meridian (there is necessarily a pair of oblique meridians - unrepresented here - which are normalsighted).

tri dimensional representation of eye astigmatism

In this example (eye with a live mixed astigmatism - see below -, the refraction of light rays is represented according to the two plans cuts through the eye meridians of extreme power. For the Middle meridians located between these extreme meridians, there is a continuous variation of the optical power (the most powerful 90 ° / 270 ° at least powerful 0 ° / 180 °). The difference of vergence generates a complex journey to light rays.

 

Understand eye astigmatism

The true complexity of astigmatism is the effect that it prints to the light path. The documents that give a clear description of the astigmatism are quite rare.
For example, most of the supposed patterns explain the optical aberration caused by astigmatism are summarily a path of rays through a toric lens (which is so purveyor of astigmatism) and who converge focal called perpendicular lines. As noted above, the schematic representation of astigmatism requires a schema comprising the three dimensions of space.
 Most of the students in ophthalmology believe to know and understand the consequences of ocular astigmatism. There is often, in fact, they are having some difficulty not even present a satisfactory definition, victims of rough or too simplistic teaching.
Thus, even if it is part of the daily life of the ophthalmologist, understanding of the real optical phenomena caused by astigmatism is often imperfect, or is based on misconceptions (which does not make an accurate diagnosis and a prescription for effective correction).
I wanted this educational challenge and expose a method teaching and illustrated here to explain without simplifications too abusive nature and means of correction of astigmatism in the eye.
The specificities of the surgical correction of astigmatism (ex:) LASIK and astigmatism) stem from the peculiarities of this optical defect. This page mainly focus on describing the characteristics of the blur induced astigmatism, and the journeys of rays in an astigmatic eye.

Astigmatism: basics

Astigmatism: lack of stigma

The eye is a complex optical system for the formation of the image of the scene observed on the retina. This image is then sampled by the mosaic of retinal photoreceptors. If the image formed on the retina is faithful, the vision is clear. The perceived images of the surrounding worlds are complex, consisting of various colors, patterns, etc. However, we can simplify things and consider that an image is constituted of a set of basic points.
One equating the object looked at a point; If the image of this point is itself a point (all rays intersect at a point) and that it is formed on the retina, so the vision of this point is true: the point is a point. The image formed on the retina being equated to a set of basic points: if each point is imaged as a point, then the image will be restored accurately. The property of an optical system being of an object point a point image is called the stigma. We guess that astigmatism (a private) corresponds to the absence of stigma; This loss of the stigma reduces the quality of the image and explain Visual blurring caused by astigmatism.
In the absence of optical defect, only diffraction occurs to reduce the optical quality of the eye. In optimal conditions (no aberration, and pupil dilated to minimize diffraction), the dimensions of the image formed from a point light source is slightly extended, but its diameter is of the same order as that of a cone of the fovea (approximately two microns). The fovea is the region of the retina that is useful for precise vision and where the density of cones is maximum. This density allows a resolution)Visual acuity) of the order of 20/10.
The uncorrected astigmatism eye presents a lower acuity, as it forms a not true (IE larger that required only diffraction) of a point source, and this explains the blur caused by astigmatism: rays intersect in a point, there is no stigma.
The astigmatic see blur, but contrary to widespread belief, does not perceive the surrounding world "twisted" without its lens correction. This "belief" is probably born of the realization of the distortion that induce the lenses for the correction of astigmatism, especially through the edges. Thus, the characteristics of the works of the painter El Greco, known for his propensity to represent characters tapered and "vertically disproportionate" cannot be explained by the existence of an astigmatism in this artist. Wearing corrective glasses lenses for astigmatism can certainly lead to some distortion, but the optical understanding of astigmatism and the development of corrective lenses is widely after the Renaissance and so the existence of the painter the Greco.

 

Effect of astigmatism on the optical path

Astigmatism is a complex optical defect. This complexity is related to the difficulty to tri-dimensionelle represent the effect caused by this aberration. In other words, it is difficult to make a fair representation of the wrong path of light rays refracted by a flawed system of astigmatism.
To understand the nature of regular astigmatism, just remember that the optical power of a lens depends on its curvature. The higher, more the focal length will be short. We can thus closer curvature and power of a lens; for a lens purveyor of astigmatism, curvature (and thus the optical power) varies between the meridians.
focal length lens

The lens shown here "in cut" focuses a beam of incident Ray in a home (only the emerging rays of the lens are represented). Beyond the home, the rays diverge. If a retina is located in terms of the focus of the lens, the image can be punctual. In below or beyond, it will be non-point.

The image of a point will be formed in a timely manner in a plan (plan called focal since it corresponds to the focus of the lens). This plan is more close to the lens that it has a significant curvature. Beyond this focal plane, the light continues are journey, being more convergent beam but diverge.

The following figure shows three sections of lenses of different power. They don't focus the rays parallel to the same distance because they have a different curvature.
focal length compared

The focal plane of the represented lens at the top is in front of the lens of the environment (less curved) and still further from the lens to the bottom (still less curved). The color used for the representation of the rays has no importance (the light is here monochromatic - same color or wavelength)

Lentils represented in the previous illustrations were represented in the Cup: only a meridian of the lens (section plane through the center of the lens) is represented.

Imagine a 'solid' lens in a 3 dimensional space, whose curvature varies regularly according to the meridians, between two meridians of extreme power (less powerful and more powerful) and perpendicular between them; such a lens is said to ring. It can be seen as a continuous sections of variable power lens Assembly.
It cannot make a point source a one-time image, because the rays refracted by the lens will go to focus at a different distance according to the Meridian they will through. Thus, there is no ideal plan to collect the image of a point (although as we shall see, some plans are better than others).
Most of the representations of the optical path formed by a provider of astigmatism system are limited to the description of the path of the rays refracted by some meridians.  We will do the same, but by adding color and perspective.
In this example, only the meridians called "extreme" (the more curved and less curved) of the lens are represented. The more curved Meridian vertical and light refracted by the vertical Meridian converges logically in front of the refracted through the horizontal Meridian.
toric lens

Toric lens: representation of the path of light refracted by the two meridians of extreme curvature. Red rays are refracted through the Meridian vertical, more curved, and blue rays are refracted through the horizontal Meridian (less curved). The home of blue rays is located at the back of the shelves shown in red (the color is used for educational purposes and does not match a chromaticism any)

 

The result is a relatively complex figure, which looks a bit like a tail of plane (let us remember that we have represented the path of light rays according to the two extreme meridians).
Now imagine moving a screen along the train of the refracted rays. There are the 'remarkable' positions where there is a particular spread of light...
plan toric lens
We realize the source of the famous images of focal lengths in the form of 'line', characteristic of patterns representative of eyes with astigmatism.
toric lens focal

The main so-called focal lengths correspond to a linear stretch of the refracted light, in respective directions parallel to those of the main meridians. Between these extreme focal plan, is located the said plan of the smaller circle.

 

Let's not forget that this simplified representation fails voluntarily to represent the rays refracted by the other meridians (not extreme, intermediate meridians) of the lens.
You can however add the path of the rays refracted by two of these intermediate meridians (whose focal length is obviously located between that of extreme meridians) on our schema. At this stage, it is important to design the route of part of the light refracted by these intermediate meridians is a 'oblique' trajectory, IE that part of the incident energy does not remain in the plane perpendicular to the direction of propagation. This corresponds to the complex notion of astigmatism of the oblique beams ("skew rays") in English.
lens ring lens extra

Schematic representation of the path of the rays refracted by the meridians of extreme power, and two intermediate meridians (rays represented in green). The effect of the 'deviation' of these oblique beams is not represented.

 

If we continue this method by adding the rays refracted by any other intermediate meridians, one begins to understand the complicated nature of the path of the light beam caused by the refraction of a lens or a diopter which presents a toricite (effect of regular astigmatism).
The envelope of all the rays refracted by an astigmatic system is called conoid Sturm (Sturm conoid).
conoide sturm

Representation approached and schematic of rays focused by a toric lens, forming a conoide of Sturm.

 

The colors here are used to allow a better visualization of the figure, (and have nothing to do with the effect of "chromaticism" on polychromatiques aberrations).
For as complicated as it is, this figure can be understood concretely by our experience of the screen interposed in the path of the rays of the conoid Sturm.
This approach also provides a more accurate representation of the optical distortion induced astigmatism that the simple representation of focal lengths in the form of scattered feature:
focal sturm

The representation of the paths of the rays of the astigmatic system is limited here to the intersection between the rays and the plans where it would collect the image so formed.

 

Several points are worth noting:
-the shape of the focal spot varies between the more or less elongated ellipse in space located outside the main 'lenses'.
-the shape of the focal spot is looking overall circular in the space between the lenses.
The optical quality (extension of the focal spot) reduction is lower if we collect the image of the source point in a plan that is located between the main focal lengths (so-called zone of the smaller circle).

Classification of astigmatism

This simplified figure provides a key to represent the different types of astigmatism encountered in clinical practice, which are classified according to the position of main focal lengths with respect to the retina plans eye concerned.
Astigmatism classification

Schematic classification of different types of astigmatism (simple, mixed, compound, complex), myopiques and hypermetropiques.

 

Mixed astigmatism, when it is moderate, is compatible with good eyesight not corrected, as the degradation of the stigma is less than case of compound myopic astigmatism. The retina is located in the region of the smaller circle.  It however often induces symptoms of 'visual fatigue.

Direct and indirect astigmatism

By convention, a direct astigmatism (or in - line with the rule) induces a focusing of rays so that the focal length 'vertical' is located in a furthest plan of the pupil entrance as the "horizontal" focal length A direct astigmatism is caused by a more pronounced curvature vertical meridians of the cornea (or lens).
An indirect astigmatism (or non-conformity-against the rule) induces a focusing of rays so that the 'horizontal' focal length is located in a more distant plan of the pupil of entry than the focal length 'vertical '. An indirect astigmatism is caused by a less pronounced curvature of the vertical meridians of the cornea (or the lens).
Astigmatism with the rule against

Schematic representation of indirect astigmatism (opposite) and direct. Horizontal and vertical focal lengths is logically backwards. Upstairs: corneal topographies corresponding to a source of astigmatism toricite reverse (left) and direct (right)

The direction of astigmatism has functional consequences: simple indirect myopic astigmatism (reverse) corresponds to a situation where the retinal image of a point is a 'line in' vertical for objects close together; This orientation promotes sharper print perception that if the image of a point was a horizontal line. A slight reverse myopic astigmatism is able to facilitate reading without correction of a presbyter, without too penalizing the vision from afar.

Principles of optical correction of astigmatism

There is some confusion in the literature about the action of the lenses used for the correction of astigmatism in the eye.
To be effective, this correction:
(1) use a "cylindrical" said glass (or o-ring, which is the same) in order to restore the stigma in a focal plane, that is to say bring to a single home the rays focused by the set formed by the cornea, the lens and the corrector glass
(2) use a spherical glass to move this unique home plan of the retina.
Note that step 1) just in the case of a simple astigmatism.
The following diagram shows the effect of a positive cylindrical glass on the refraction of an o-ring cornea, which the arched axis is vertical.
Refraction is: plan (+ 1 × 90 °). It is a simple astigmatism.  The cornea is a toricite such that the power of the horizontal Meridian is insufficient ("missing' a diopter of vergence to the 0 ° axis).
cylindrical glass positive

Schematic representation of the effect of a cylindrical glass (+ 1 × 90 °) for a corneal astigmatism correction (the cornea is schematized by the representation of the two major meridians in the Cup). Corneal astigmatism is related to the lack of power of the horizontal Meridian (1 diopter). This glass adds a (vergence) power of 1 diopter next to the horizontal meridian of the cornea. It is 'neutral' next to the vertical Meridian. "" Must not interpret the correction of astigmatism as the "Advanced" the vertical focal (the glass has no action plan), but as his disappearance with the correction of astigmatism of the cornea, which comes down to focus in the same plane all meridians of the couple 'cornea + corrector glass'.

 

The "long" of the cylinder (the vertical axis in this example) is optical-neutral. The horizontal "short" (in this example) corresponds to the axis where the lens correction is maximum. This axis is logically placed in the same direction as the thinnest axis (the one where there's a diopter, the horizontal axis), to which he brings the gain of optical power required for the correction of astigmatism.
Strategies for treatment of astigmatism by excimer laser refractive surgery were investigated in various debates. We were able to contribute by using computer modeling.
The following illustration shows the volume which must be photoablaté by the excimer laser to correct a pure hypermetropique astigmatism (+ 1 × 90 °). The effect of photoablatif treatment is to selectively arch the horizontal Meridian.
cylindrical positive treatment

General constraints treatment of astigmatism laser photoablation variable treatment for all of the meridians of the cornea, is needed to reduce the toricite of the cornea.

volumes cylinders ablates

The diagram above against clock the morphologies of the lenses photoablatés for negative cylindrical treatment (up:-3 × 0 °) and a cylindrical treatment positive (down: + 3 × 0 °). Right, graphs represent the change in the refractive apical power next to the axis of the meridians before treatment. The thickness of the edge of the lenticule (dotted lines) varies and marries the power of meridians to correct variations.

The relationship between negative and positive cylinder treatment are shown on the following diagram:

report positive negative cylinder

Peculiarities of treatment of simple myopic astigmatism (cylinder negative processing)

The main feature is related to the need to maintain unchanged the curvature of the initially less arched Meridian, flattening gradually all other meridians, until the more arched Meridian.
The amount of the largest photoablation is thus issued next to the Meridian which the curvature must remain unchanged! This is the origin of the possible 'hypermetropique shift' with some corrections (simple myopic astigmatism we important compound). It involves the realization of a broader transition next to the less arched Meridian area (see the pages dedicated to the) profiles of ablation).

Simple schematic representation of the profile of ablation of myopic astigmatism. The less arched Meridian (here at 0 °) is the one that receives the most laser energy. It is important to level the abrupt fitting on the outskirts of the optical box (extension of the transition zone).

 

Learn more about astigmatism:

Download the article "rediscovering the astigmatism.

Download the article "astigmatism is an aberration of high degree!

Download the article "conduct in front of an evolving astigmatism."

 

14 responses to "astigmatism – explanations"

  1. Ahmed says:

    Hello on my prescribed glasses OD glasses:-1.5 (-5) 180 ° and the same for eye left, so I would like to know the meaning and also if it does not matter?

  2. Dr. Damien Gatinel says:

    You present a myopia associated with a strong astigmatism. -1.50 d corresponds to the degree of your myopia, and-5 D to the power of astigmatism. 180 ° is here the direction of the meridian of the least potent cornea (it is myopic of-1.50 D), while the opposite meridian (according to the Axis 90 °/270 °) presents a myopia of (-1.50) + (-5) =-6.50 D.
    This notation thus masks the "average" degree of your myopia, which is given by the calculation of the spherical equivalent: (-1.50 + (-5/2)) =-4 D
    It is possible to correct you in glasses, or in rigid lenses, refractive surgery is also possible if the balance does not reveal contraindications.

  3. Ahmed says:

    Ok thanks well but is it possible for me in the future to leave the correctors and to have a normal view thank you cordially

  4. Charles says:

    Hello, I have raised a contradiction between I quote:
    The image of a point will be formed on an ad hoc basis in a plane (called the focal plane since it corresponds to the focus of the lens). This plane is all the closer to the lens that this one has an important curvature.. So far all is well and then comes; Direct and indirect astigmatism
    By CONVENTION § § §, direct astigmatism induces a focus of the rays so that the "vertical" focal length is located in a plane farther from the pupil than the "horizontal" focal length. Direct astigmatism is caused by a more pronounced curvature of the vertical meridians of the cornea (or Crystalline lens).
    Indirect astigmatism induces a focus of the rays so that the "horizontal" focal length is located in a plane farther from the pupil than the "vertical" focal length. Indirect astigmatism is caused by a less pronounced curvature of the vertical meridians of the cornea (or Crystalline lens).
    I admit you that this Convention on which is based interpretation of test results in hospital practice, and the theoretical reasoning above quoted (plus the curvature is important plus the focal plane will be close to the lens/pupil) and That besides I have easily understood me seems contradictory even by making the effort to read and reread.
    If you could enlighten me on this point, it would be of great use to me.
    Thank you.

  5. Dr. Damien Gatinel says:

    Thank you for your message. There is no contradiction, because it should not be conceived that the vertical focal lengths correspond only to light refracted by the vertical and horizontal meridians. In case of direct astigmatism, the vertical meridian is the most arched, and the rays from a distant source converge and intersect in a plane in front of this vertical focal length (it actually intersect in the plane of the horizontal focal length). Figures 6, 7 and 8 on the page explain this point.

  6. Cathy says:

    I am a student in dentistry I would like to know during the correction with cylindrical letilles, their powers dependent on the focal or well of the meridian?!
    For example the following ex:
    either + 2 (+ 1.5) 90 ° or + 3.5 (-1.5) 0 °
    The 1st value 3.5 corresponds to the vertical meridian or to the vertical focal?!

  7. Dr. Damien Gatinel says:

    The first value corresponds to the horizontal meridian (the eye is Hyperopic + 3.50 D "horizontally", and 1.50 is + 3.50-1.50 "vertically", the intermediate meridians take precisely intermediate values between these two values). This is not intuitive according to the notations, which are only conventions, originally intended for the realization of glasses of glasses by an optician. Opticians generally use an expression of the so-called positive-cylinder astigmatism (the first here + 2 (+ 1.50 × 90 °)). The "focal length" is another concept, which refers to the focus of light by the astigmatism system. Focal lengths are formed by all the meridians that refract the light, it is not possible to say that a meridian forms a particular focal length (many diagrams illustrating the supposed path of the light rays are tainted with errors on this subject).

  8. Dylan says:

    Hello J Ai + 2 to the right eye (-4.25) 10 ° and + 1, 5 to the left eye (-3.75) 175 °. What do you think? Thank you

  9. Dr. Damien Gatinel says:

    You present an astigmatism called "mixed" because your eye can be considered both myopic, and hyperopic, depending on the direction according to which it is considered! Astigmatism is also direct. It is certainly a congenital form of astigmatism. This type of vision defect is eligible for refractive LASIK surgery. A correction in glasses or lenses is of course indicated to correct the vision.

  10. Karim says:

    Hi, I'm a medical student.

    Thank you very much for these schematics, I finally understood these histories of meridians and classification of astigmatism:)

  11. Bear says:

    Hello
    My 15 year old daughter is very hyperopic and astigmatism:
    D + 4.75 (-1.25 0 °)
    G + 4.75 (-1.00 0 °)
    She's had glasses since she was 1 years old and would like to switch to Lenses.
    – Are there any contraindications?
    – is a term surgical intervention feasible?
    Thank you

  12. Dr. Damien Gatinel says:

    The wearing of lenses is possible, and does not compromise the subsequent realization, in a small ten years for example, of refractive surgery in LASIK.

  13. Veronique says:

    Hello doctor,

    I am astigmate, my ophthalmologist used to prescribe me the following correction at the level of the astimagtism:

    OD plan (-0.75 100 °) add 1.75
    OG + 0.25 (-0.75 80 °) add 1.75

    By going to renew my glasses, the optician prescribed me:
    Od plan (-075 95 °) add 1.75
    OG + 0.25 (-0.50 90 °) add 1.75

    At the level of the left eye, I wish to have your opinion before committing myself.

    Thank you and good luck.

  14. Dr. Damien Gatinel says:

    The difference in correction is quite minor and should not destabilize you beyond measure!

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