+ +

Regular and irregular astigmatism

THEastigmatism is a common eye defect. When we talk aboutastigmatism and its correction, we under generally the 'regular' character of astigmatism; regular astigmatism is often defined as the component of astigmatism is it possible to fix by a glass of bezel, in contrast to astigmatism said irregular.


Origin of irregular astigmatism

Irregular astigmatism is observed in some eye conditions, which may involve the cornea or the lens: irregular deformation of the cornea (ex: Keratoconus, corneal SCAR), asymmetry (ex: decentering after) LASIK), generates of irregular astigmatism of corneal origin.

Internal irregular astigmatism can be caused by an ectopy of the lens (Marfan disease), cataracts (inhomogeneity of the cristallinien kernel), a displacement or a toggle of the implant (tilt) after cataract surgery.

Irregular astigmatism brings together the optical aberrations that it was not possible to study in detail before the widespread use of the eye OPD. Thanks to the OPD, irregular astigmatism study corresponds to the collection and analysis of so-called aberrations of "high level". The type and rate of these aberrations are specified by the study of ocular wave-front, that allows to split the aberrations that make it up in terms of different degrees. The coupling of the aberrometric to the corneal topographer (ex: topo aberromere OPD - Nidek, or iTrace - SCAN Tracey) allows to study specifically the aberrations induced by the front of the cornea (from the measurement of topography of the cornea). By subtracting the aberrations of the cornea to the entire eye, we can estimate the rate of aberration of internal origin.


Regular astigmatism

Regular astigmatism is a regular change in the defocus with azimuth. The defocus is quantified through the terms of degree 2 in the classification of Zernike. The decomposition into polynomials of Zernike phase shifts of the Wavefront attributes to regular astigmatism two components: Z(2,-2) and Z (2.2). These components are 'independent' (mathematically, it is said that they are orthogonal: they allow to break down all regular astigmatism in a combination of these two terms).

Zernike terms for regular astigmatism

The terms of degree 2 correspond to 'regular' says astigmatism and defocus (myopia or hyperopia)


The value of the coefficients C(2,-2) and C (2.2) which weigh these terms depends on the direction (in degrees) and the magnitude (in power) of regular astigmatism:

In case of astigmatism direct or inverted (oriented exactly 90 ° vs 0 °), only the C (2,2) component has a value non-zero (negative if direct astigmatism, positive if astigmatism reverses). The value of C (2, -2) = 0

In case of astigmatism oblique (oriented to exactly 45 ° vs 135 °), only the C (2, -2) component has a value not zero, and the component C (2,2) = 0.

The astigmatismes focused on other areas (ex: 25 ° vs 115 °) result in a combination of values non-null for C(2,-2) and C (2, 2).

The magnitude of the regular astigmatism is equal to the square root of the sum of the squares of the components C(2,-2) and C (2, 2).

Regular astigmatism is corrected in glasses, refractive surgery (LASIK, PKR) and cataract (toric implant) surgery.

Astigmatism correction is based on the use of a device that generates an astigmatism of same magnitude but oriented at 90 ° of astigmatism to be corrected.

Zernike astigmatism correction

Regular astigmatism correction is based on the induction of an astigmatism equivalent in magnitude, but oriented at 90 °. Here the phase shift induced by regular astigmatism is represented by a polynomial of Zenike Z(2, +/-2) (bottom). A corrector device induces an equivalent phasing in magnitude, but it must be oriented so that this phase shift is oriented at 90 ° to that of the eye. In this way, the sum of these phase shifts results in a phase shift zero. In the case of a toric implant in cataract surgery, should be to align the implant in an optimal way, depending on the orientation of corneal astigmatism. The toric implant fixes that the regular component from astigmatism.


Irregular astigmatism

It corresponds to the phase shifts caused by aberrations of degree greater than or equal to 3. A moderate rate of irregular astigmatism is measured for human eyes, and this rate increases with the dilation of the pupil. The most frequently recovered aberrations are of type coma: Z (3, -1) and Z (3,1), trefoil: Z (3, -3) and Z (3.3), Z (4.0) and Z (6,0) spherical aberration.

Irregular astigmatism is not correctable by glasses. It can be reduced by wearing rigid contact lenses, a laser photoablation custom, or the treatment of the cause (ex: biased implant).

Keratoconus, corneal () deformationcaused by the eye rubbing According to the author of this site) causes of the type coma aberration because corneal asymmetry causes an asymmetric phase shift. The optical path from the fovea is short in region where the cornea is less arched (in superior) and longer in the region where the cornea is more arched.

keratoconus coma aberration

Keratoconus is usually a significant degree of corneal asymmetry; the lower camber results in a phase delay (lengthening of the optical path), while the portion less arched (in top) trained a phase advance. The phase shift is represented by the type of coma aberration, whose rating in the classification of the Zernike polynomials is Z(3,+/-1).

The schema below below represents schematically the emerging wave front of an affected eye of Keratoconus, which is a variation of optical path from the fovea:

Keratoconus generates a phase shift of type coma

Phase shift induced by Keratoconus: the optical path is more "long" in the direction of the top of Keratoconus in the upper part of the cornea. The created dephasing is an aberration of type vertical coma, with a delay to phase in lower, and an advance in superior. Deformation induced by Keratoconus also generates regular, often directed to an oblique way astigmatism.

Keratoconus: regular and irregular astigmatism

Some clinical examples illustrating these differences.


It is a patient with Keratoconus stable, cataract surgery and received a toric implant insertion to correct the regular component from astigmatism. In post operative, Visual acuity is 10/10 without correction by far, and Parinaud 3 without correction closely. The aberrometrique study allows to split the consequences of regular astigmatism corneal (and its compensation by the implant), as well as the persistence of the effects associated with irregular astigmatism (see also:) example review aberrometrique and Keratoconus)

keratoconus OPD SCAN III Nidek topography

Rendering of the anterior corneal curvature. This map is from the "Cornea summary" mode and reveals a toricite and a significant corneal asymmetry with sharper lower camber (curvature instant). Interpreting automated this cornea is "clinical keratoconus" (i.e. "Keratoconus clinical").


The topo-aberrometrique with OPDSCAN III study to explore the relative contributions of the cornea with implant (internal):

Overview Keratoconus and toric implant

Representation in mode (overview) overview of the measure topo aberrometrique in this patient with Keratoconus and surgery of cataract with o-ring implant. Left, map OPD (variations of the refraction in the pupillary area), Center map, axial curvature, and right map OPD internal (variations of the refraction in the pupillary area related to the internal diopters: posterior face of the cornea interface / acqeuse, and o-ring implant mood). We note that the corneal astigmatism is low, while internal and corneal astigmatism are high (close to 7 d) but oriented at 90 °. This mutual neutralization explains the low residual total astigmatism.


This almost total regular astigmatism correction is borne out by the study of the position of the implant (toricite) astigmatism corneal.


Toric IOL display Nidek OPD SCAN III

The image collected in "Toric IOL display" mode has a photo taken in retro illumination, with visualization of the implant. The marks on the implant can identify the orientation of it towards the orientation of corneal astigmatism (right). Here, the implant is perfectly aligned: his astigmatism compensates so that of the cornea.

The map of corneal phase shift induced by the toricite corneal (regular component) is represented here, in microns.

dephasing corneal astigmatism OPD

Representation of the phase shift related to the regular component of corneal astigmatism. (representation of the corneal Wavefront restricted to aberrations Z(2,-2) and Z (2.2))

The representation of the regular component of the toric implant-induced astigmatism reveals a similar magnitude, and direction at 90 °.

dephasing implant o-ring corneal Wavefront

Representation of the regular component of the toric implant-induced astigmatism. Note the orientation at 90 ° from it to the regular component of corneal astigmatism.

The orientation of the implant (its the most powerful Meridian is aligned with the corneal Meridian the least powerful) can be quantified by the study of the components of astigmatism (Zernike polynomials: Z(2,-2) and Z (2,2).)

zernike astigmatism compensation ring implant component

The representation of the ocular Wavefront is restricted to the only aberrations of degree 2 (regular astigmatism). Total regular astigmatism is very fable: corneal and internal components cancel out. The absolute values of the coefficients corresponding to the corneal astigmatism and internal (C2,-2) and C (2,2) are identical, but their sign is opposite, which explains their mutual "neutralization".

map OPD, which shows the refractive fluctuations within the pupillary area, reveals however the presence of an increase in the negative power in lower. This refractive asymmetry is the consequence of the corneal asymmetry (Keratoconus).

OPD toric implant irregular astigmatism

map OPD shows variations in local diopter power (vergence), expressed in diopters, for the entire eye. These variations are related to regular astigmatism and aberrations of high degree. If the eye was affected to an optical defect of type "defocus" (pure myopia: negative defocus in diopters, pure hymermetropie: defocus positive diopters) then the map would be monochrome. In other words, there is no local fluctuations of Dioptric power. The OPD map includes the effect of all aberrations (defocus, but also regular and irregular - astigmatism aberrations of high degree). On this example, there is a gradient of power overall vertical: refraction is rather slightly hypermetropique in the half top of the pupil, and myopic in half less of the pupil. A variation of this type is usually induced by the type coma aberration. She brings a potentially useful for near, vision multifocalite explaining the unusual achievements in near vision not corrected for a patient pseudophake (o-ring monofocal impant)

The OPD map restricted to only optical aberrations of high level confirms the responsibility of the aberrations of high degree in the genesis of the lower power increase.

map OPD HO o-ring implant irregular astigmatism

It is possible to represent the only effect of the aberrations of high degree: map OPD HO or HO means "High Order" (high level). We note the persistence of the curvature gradient vertical: this one is so induced by the "irregular," said asgtigmatisme, who is represented by the aberration type coma (see below), whose origin is essentially corneal (Keratoconus with lower bulge, that increases local refractive power).

The aberrations of high degree study confirms the presence of a high rate of type coma aberration: this aberration represents the essence of responsible "irregular" astigmatism aberrations


aberrations high degree astigmatism irregular HOA

Topo aberrometrique review allows to separate the phase shifts induced by the cornea (to downtown) earlier on the Wavefront eye total (left). By subtraction, we obtain the cumulative effect of the posterior side of the cornea and the toric implant. We note that type coma aberrations dominate the total and corneal wave front. There is a significant rate of coma "internal." This is due in part to the posterior corneal asymmetry, and the refractive index gradient opposed between posterior and aqueous which is opposite in sign (and less) than that which separates air from the front of the cornea. The posterior face of the cornea, which deformation is often more pronounced than that of the anterior face of the cornea, neutralizes a significant proportion of previous coma. Another explanation for this internal compensation is "mechanical." the phase shift of type coma translated first asymmetric refraction, which generates an asymmetric route rays refracted towards the toric implant; This asymmetry causes a second refraction that compensates for this first asymmetry (Artal and al.) The human eye us year example of robust optical desing. J live, 2006; 10 (6): 1-7

The effect of ocular components and their contributions to the regular and irregular astigmatism can be studied using the maps "Optical quality" (optical quality):

PSF MTF convolution

Wave-front measurement to calculate PSF (distribution of the light intensity of a point source on the retina), the MTF (contrast of the retinal image) and a simulation of the projection of a retinal image of an optotype plance. Upstairs, the effect of the regular component from astigmatism is represented: note spread large and diffuse the light intensity: overall circular and not elliptical appearance corresponds to the circle of lesser (mixed astigmatism of spherical equivalent almost zero). The addition of the irregular compoisante induced an asyemtrie in this light distribution. Lander, the simulated effect of the irregular component of single astigmatism (aberrations of high degree) shows a higher vertical light distribution: effect of the type coma aberration). The PSF has a characteristic orientation, with light streaming in the form of 'Comet', whose Summit is less (orientation of the coma aberration).

Ultimately the toric implant helped neutralize the regular component of corneal astigmatism. After implantation and orientation of it, the optical quality of the eye remains tainted by the component "irregular" astigmatism, represented mainly by the coma aberration, consequence of the corneal asymmetry (Keratoconus).

PSF MTF convolution entire eye

The total ocular Wavefront measurement to calculate PSF (distribution of the light intensity of a point source on the retina), the MTF (contrast of the retinal image) and a simulation of the projection of a retinal image of a Board of optotypes. Regular corneal astigmatism is offset by the astigmatism of the implant, which however does not compensate for the irregular component of corneal astigmatism (coma). Note the appearance of the PSF in Comet with a peak of maximum light intensity down.

 Internal irregular astigmatism: ectopy of the lens

The topo - aberrometrique (OPD SCAN) map obtained at a patient presenting a total eye astigmatism at the same time of corneal and internal origin;

corneal astigmatism and internal conjgues

Box highlights the magnitude and orientation of three components of the astigmatism. The map representing the internal vergence (Internal OPD) reveals a vertical the vergence, greater emphasis at the level of the lower Meridian hemi. The axial topographic map (in the Center) shows a regular corneal toricite (regular corneal astigmatism). The irregularity (RMS) is maximum internal (0.742 microns for a pupil of 5.72 mm)

After dilation slit lamp examination reveals the origin of internal regular and irregular astigmatism: there is a sub luxation of the lens induced by rupture of the zonule in lower - in a context of Marfan syndrome. The zonule is an elastic ligament, which keeps the lens in a State of tension at rest. The partial breakdown of the (elastic tissue affected by Marfan disease) zonular fibers causes local relaxation of the lens with localized bulge. This bulge causes an overall increase in the vergence in the vertical axis, more marked next to the disinsertion rupture.

ectopy of the lens with the vergence increase lower release disinsertion

Left, the map 'Internal OPD' which represents the distribution of optical power (vergence) within the pupil who is not induced by the cornea. The right cliché biomicroscopique of the anterior segment of the eye after expansion, which allows to diagnose the subluxation of the lens.

The following image shows the overlap between the map OPD and the photographic image of the review to the slit lamp:

subluxation of the lens and vergence map

The inferior dislocation of the lens causes an increase in localized internal vergence. Right, schematic representation of the geometric change induced by the disinsertion relaxation: the crystalline bomb asymmetrically (arrows)


See also: rotation of toric implant in a patient suffering from Keratoconus and cataract surgery

 Astigmatism - explanations

Corneal astigmatism

2 Responses to "Regular and irregular astigmatism"

  1. Jessie says:

    I have an irregular astigmatism diagnosed by Dr. Saad. I will have rigid lenses but in the meantime it only gets worse. How to slow his progression? For three days, I see the ground distorted and it seems to me far. It's even worse without glasses. Can the irregular astigmastisme be the cause?
    Thank you
    Kind regards

Leave a comment

You can ask questions or comment on this content: for this, use the "comments" form located below. The questions and comments of a general interest will be processed and published, and the information provided on the relevant pages should be clarified or supplemented.

Your e-mail address will not be published. Required fields are indicated with *