Ординатура / Офтальмология / Английские материалы / Ocular Periphery and Disorders_Dartt, Bex, Amore_2011

Astigmatism

M J Cox, University of Bradford, Bradford, UK

ã 2010 Elsevier Ltd. All rights reserved.

Glossary

Against-the-rule – Ocular astigmatism in which the meridian with greater optical power in the eye is horizontal.

Astigmat – An individual with ocular astigmatism. Axis meridian – The meridian of a cylindrical surface that is flat and consequently has no optical power. Emmetropization – The active process of reduction in refractive error toward an ideally focused system that occurs in the human eye during the first 2 years of development.

High-order wave front aberrations – Wave front aberrations that are expressed using cubic, or higher, powers of the light ray’s distance from the pupil center to predict the amount of aberration.

Meridional amblyopia – A lack of contrast sensitivity to high and medium spatial frequency contours oriented along a particular meridian without any refractive error or ocular pathological process affecting the visual function.

Paraxial optics – Image forming through an optical system where only rays traveling close to the optical axis of the system and/or at small angles to this axis are considered.

Penetrating keratoplasty – A surgical procedure to remove corneal material and replace it with material from a donor cornea.

Stokes lens – A lens constructed from two symmetrically counter-rotating cylindrical lenses of equal absolute power but opposite sign. These combine to make a continuously variable power crossed-cylinder lens.

Wave front aberrations – Deviations of a wave front of light propagating through an optical system from a perfect spherical wave front.

With-the-rule – Ocular astigmatism in which the meridian with greater optical power in the eye is vertical.

The Definition and Etymology of

Astigmatism

The earliest forms of correction for visual loss caused by refractive errors in the eye used spherical spectacle lenses.

These are rotationally symmetrical about the optical axis and, considering paraxial optics, produce a point image from a point object on the axis of the lens. This type of image forming is known as stigmatic, from the Greek stigma, meaning a branding mark. Astigmatism describes an optical system where any nonpoint image is formed from a point object. In practice, astigmatism commonly refers to the simplest extension of stigmatic image formation, namely where the optical system forms two perpendicular line images from an axial point object, each at a different distance along the optical axis.

In an astigmatic optical system the power varies as a function of the meridian, with a maximum and minimum power in meridians that are perpendicular. This variation in power approximates very well to a sinusoidal function, as seen in the formula

where Fy is the power in the meridian at y , measuring angles anticlockwise from the horizontal, FSph is the power in the meridian of minimum power, FCyl is the difference in power between the meridians of maximum and minimum power, and a is the angle of the meridian of maximum power.

The double angle ½2ðy aÞ& in eqn [1] demonstrates that the power varies through a complete cycle as we rotate the meridian 180 around the optical axis.

Newton is said to be the first to describe the variation in optical power with meridian and the consequent formation of line foci, but did so in the rather specialized form of oblique astigmatism. It was left to Thomas Young to first describe and measure ocular astigmatism, a finding which was a by-product of his attempts to measure his own refractive error as a starting point for investigating accommodative mechanisms in the human eye. He found his own astigmatism to be around 1.75 D and even had additional evidence to suggest that its source was a tilt in his crystalline lens. Airy was the first individual to measure and correct his ocular astigmatism. Wollaston, Ostwalt, and Tscherning discovered means by which spectacle lenses could be manufactured to minimize lens-induced oblique astigmatism.

The above discussion concerns regular astigmatism, where two perpendicular axes of symmetry exist within the optical system and the relationship between power and the angle of the meridian is known. In irregular astigmatism this symmetry does not exist over the aperture through which light travels to form an image. Locally, over much smaller apertures, such symmetry may be present, but for

the purposes of image formation by the optical system or eye it is absent. This results in objects that do not form line images but rather two elongated spreads of light, even at best focus. Furthermore, these two elongated images are not oriented perpendicularly. All eyes contain some degree of irregular astigmatism but this is rarely visually limiting except in pathological processes where the irregular astigmatism is large. Examples of such pathology include keratoconus; lenticonus; corneal scarring, inflammation, dystrophy, and degeneration; pterygium; mechanical effects on the cornea from neighboring structures such as the lids or sclera or following the use of rigid contact lenses; lens dislocation; localized lens index changes; and polycoria and ectopic pupils. In ocularly healthy individuals with unusually large pupils and statistically higher levels of irregular astigmatism, visual function can be affected in low and medium light levels.

Ocular Astigmatism: Prevalence and

Age-Related Changes

Ocular astigmatism is important for two main reasons. First, it prevents optimal retinal image formation and leads to a loss of contrast in the retinal image. It can be argued that it is more debilitating than either myopia or hypermetropia as, unlike myopia, there is no object distance at which a clear retinal image can be formed and unlike hypermetropia, it is not possible to overcome the refractive defect by using one’s accommodation. Second, if the high levels of astigmatism that are naturally present during early infancy do not reduce during the process of emmetropization, then permanent meridional amblyopia can occur leading to lack of visual sensitivity to small oriented details in later years, even when the astigmatism has been refractively corrected. In addition, some suggest that visual blur during early life may help to drive the development of myopia in later years. Uncorrected ocular astigmatism may be one such cause of visual blur, and an association between ocular astigmatism and myopia development has been found.

Almost all neonates have significant amounts of astigmatism caused by an unusually steep cornea in one meridian, although the angle of this meridian with higher power is not consistent across the population. Early development reduces this cornea-generated astigmatism such that by 4–6 years of age only around one-twentieth of the population has ocular astigmatism in excess of 1 D and in the great majority of young astigmats, the meridian with the greatest power is vertical (or within 15 of vertical, the so called with-the-rule astigmatism). In later childhood (5–17 years of age) the proportion of individuals with at least 1 D of astigmatism increases up to around a quarter, with a higher risk for Asians and Hispanics (around a third), and a lower risk for African-Americans (around a fifth).

In adults, about two-thirds of the population have measureable astigmatism (> 0.25 D), but the majority of this is at low levels (<1 D). Estimates suggest that the prevalence of higher amounts of ocular astigmatism (>1 D) in adults ranges from about 10–20%, dropping to only 0.5% for astigmatism in excess of 4 D. A general trend can also be found in the adult population concerning the angle of the meridian of greatest power. In younger adults (<40 years of age) this is predominantly with-the-rule. In older adults it is predominantly against-the-rule. This change is believed to be due to the changes in the effects of the upper and lower lids on the cornea as the lids age and the tension generated by the lids on the cornea reduces. The lids squeeze on the upper and lower cornea in youth, flattening the cornea directly underneath them but steepening the corneal cap in the vertical meridian. The mechanical effects of the collagen structure within the cornea cause a consequent flattening of the cornea in the horizontal meridian. With aging, the cornea steepens overall, but the steepening in the vertical meridian is offset by the reduction in lid tension, leaving a steeper corneal curvature in the horizontal meridian and a consequent change from with-the-rule to against-the-rule ocular astigmatism.

The Origin of Ocular Astigmatism

The cornea is the major refracting surface in the eye and the ocular astigmatism is best correlated with the astigmatism generated by the cornea. Both the anterior and posterior surfaces of the cornea generate astigmatism and show similar changes in curvature as a function of meridian. Due to the aqueous humor immediately behind the cornea, the refractive power of the posterior surface is only about one-tenth of the anterior surface power and of opposite sign. Keratometers, when used to predict the refractive power of the cornea from anterior corneal curvature measurements in a meridian, account for this by adjusting the value used for the refractive index of the cornea. The physiological value of the corneal refractive index is believed to be close to 1.38, but the majority of keratometers (and their keratographic successors) utilize a value of 1.3375.

With the exception of corneal astigmatism associated with syndromic conditions, there is a complex pattern of heredity associated with corneal astigmatism in the general population, with some evidence of autosomal dominant inheritance patterns, but it seems likely that polygenic inheritance with variable penetrance exists. Unidentified environmental factors are also believed to influence the corneal astigmatism.

There is good evidence to suggest that the corneal shape, and hence the corneally generated ocular astigmatism, is influenced by lid position, tension, and shape.

Performing a task that alters the usual lid position, for instance prolonged reading, produces measureable but temporary changes in the corneal shape and astigmatism. Extra-ocular muscles may also influence the corneal shape, certainly showing effects following changes as dramatic as those induced by strabismus surgery where the extraocular muscles are recessed or resected.

Corneal astigmatism is also associated with some welldescribed syndromes, such as Down’s syndrome and Treacher Collins syndrome (also known as Treacher Collins–Franceschetti syndrome or mandibulofacial dysostosis). Changes in the orientation of the palpebral aperture correlate with the axis of the astigmatism, the most powerful corneal meridian lying perpendicular to the axis connecting the inner and outer canthus.

In addition to ocular astigmatism being generated by the cornea, it is also influenced by the shape and position of the anterior and posterior surfaces of the crystalline lens, as well as the refractive index distribution of the crystalline lens. Accurate in vivo measurements of the shape of the anterior and posterior surfaces of the crystalline lens are difficult to make. Consequently, it is not known how great a contribution crystalline lens surface shape makes to ocular astigmatism, as opposed to the effect of surface position and refractive index changes. What is known is that the internal astigmatism, that is, that generated by the crystalline lens, partially compensates for the corneal astigmatism and it is believed that some active feedback process is responsible for this compensation. Decentration and tilt of the optical axis of the crystalline lens with respect to that of the cornea will also induce astigmatism. The average internal astigmatism is 0.5 D against-the-rule and this does not appear to alter significantly with age. This is too great to be explained by crystalline lens tilt alone, as the required tilt is 4–5 times the average tilt found for the crystalline lens.

Refractive index changes in the cortex of the crystalline lens, commonly associated with age-related cortical cataract, are also able to induce internal astigmatism, with the axis of the astigmatism believed to be associated with the long axis of the cortical opacity. Other pathological conditions that lead to abnormally large displacement of the crystalline lens also induce astigmatism, including sectoral weakness in the zonular supports of the crystalline lens in conditions such as Marfan’s syndrome and homocystinuria, following blunt trauma, and associated with hypermature cataract. Lenticonus is a condition that results in conically shaped lens surfaces inducing large amounts of both regular and irregular astigmatism.

Image Formation and Refractive

Specification in Astigmatism

The basic image-forming process that occurs in astigmatic imaging can be seen in Figure 1.

Standard Notation for Specifying Astigmatic Refraction

Here, the front surface of the lens is a cylindrical surface. Note the straight line section of the lens front surface in the XX0 meridian compared to the curved section in the YY0 meridian. This cylindrical surface is created by rotating a line about an axis. The orientation of this axis defines the axis meridian of the cylindrical surface. The distance of the line from the axis defines the radius of curvature, and hence power of the surface. The back surface of the lens is a spherical surface, and the lens is described as a spherocylindrical lens. Although used at one time in the production of spectacle lenses, such lens designs are now very uncommon and nearly all spectacle lenses used to correct

astigmatism use a toric back surface, which is defined using two perpendicular radii of curvature.

The front surface power in the axis meridian is 0, while in the perpendicular meridian (the power meridian) it is FCyl. The angle of the axis meridian is measured from the perspective of looking at a person with astigmatism. An angle of 0 is represented by 180 but the degree sign is omitted. If the power of the spherical back surface in this lens was FSph, then we would denote the lens power as

FSphDS=FCylDC 180

where DS is dioptres of spherical power. DC is dioptres of cylindrical power. FCyl is the difference in power between the meridians of maximum (Fmax) and mini-

mum (Fmin) absolute power and is a signed value. Conversion between positive cylinder and negative cylinder

notation is a straightforward process of

A third much less commonly used notation is crossedcylinder notation where the Fmax and Fmin meridians are considered as two separate cylindrical lenses. If Fmax is

þ2.00 DC 180 and Fmin is þ1.00 DC 90 then the crossed-cylinder specification for the lens is

þ1:00 DC 90=þ 2:00 DC 180

Ocular Image Formation in Astigmatism

The eye that suffers from astigmatism can usually be successfully studied by considering it to have a single toric corneal refracting surface with perpendicular meridians of maximum and minimum power. The image forming is very similar to that shown in Figure 1, where the more powerful meridian is vertical, denoting an eye having with-the-rule astigmatism. This astigmatic image pencil is known as the conoid of Stu¨rm. Rays from a distant axial point that fan out in the vertical meridian (shown in green) are brought to a focus closer to the lens than the rays that fan out in the horizontal meridian (shown in blue). Hence, in the focal plane of the vertical meridian there is horizontal defocus and a horizontal line image is formed. In the focal plane of the horizontal meridian there is a vertical line image. Dioptrically (but not geometrically) equidistant between these two line images, the defocus in the horizontal and vertical (and all other) meridians is equal and the defocused image has its smallest spread, the circle of least confusion (CLC).

At other image planes in the light pencil, the image is a horizontal ellipse if measured anterior to the CLC and a vertical ellipse if measured posterior to the CLC.

Paraxial optics can be used to determine the size and position of these astigmatic focal images. For a distant object (vergence of 0 D) and a pupil diameter d, the length of the anterior focal line is

The length of the posterior focal line is

The diameter of the CLC is

Given that FCyl found in human eyes is <1 D in around

80% of the cases, and the average value for Fmax is around 60 D it is evident that eqns [5] and [6] will produce very

similar results that are about twice the value of the result from eqn [7]. Thus, the focal lines give around twice as large an extent of blur as the CLC. This is helpful in explaining some of the effects of ocular astigmatism on human visual performance.

Classification of Ocular Astigmatism

Ocular astigmatism is divided into five categories depending upon where the retina lies with respect to the conoid of Stu¨rm:

. The anterior focal line lies behind the retina – compound hypermetropic astigmatism;

. The anterior focal line lies on the retina – simple hypermetropic astigmatism;

. The anterior and posterior focal lines lie on either side of the retina – mixed astigmatism;

. The posterior focal line lies on the retina – simple myopic astigmatism;

. The posterior focal line lies in front of the retina – compound myopic astigmatism.

Most individuals with astigmatism have one or other form of compound astigmatism.

Astigmatic Blurring and Visual Perception

Unless the CLC is coincident with the retina, as is only possible in mixed astigmatism or hypermetropic astigmatism when accommodation is used, the retinal blur patches in an uncorrected astigmat will be oriented. In myopic astigmatism the long axis of the blur patch will typically be oriented along the more powerful corneal

meridian, and in hypermetropic astigmatism along the less powerful corneal meridian. Contours and edges in a scene that are parallel to the long axis of the blur patch will appear relatively clear, while those perpendicular to this axis will appear to be most blurred. As most scenes contain more contrast energy for horizontal and vertical orientations than for oblique orientations, there is often useful nonblurred information available to the viewer who has with-the-rule or against-the-rule astigmatism compared to a viewer with obliquely oriented astigmatism. This can be measured with visual acuity results, where with-the-rule and against-the-rule astigmatism produce a smaller loss of visual acuity than astigmatism along an oblique axis. In addition, as the line spacing in printed text is larger than the letter spacing, horizontal blurring is worse for reading than vertical blurring. An astigmat will benefit when reading printed text if

he/she accommodates to a position where the vertical focal line is on the retina. For a with-the-rule astigmat, this would typically mean more accommodation is required to bring the vertical focal line (which is more posterior) onto the retina, compared with the accommodation required by an against-the-rule astigmat, for whom the vertical focal line is more anterior. If moderate to large amounts on myopia are present in addition, then the text would be best held at a distance that places the vertical focal line on the retina.

Figures 2 and 3 demonstrate the effects of astigmatic blur, compared to spherical blur, for Snellen letters and oriented contours (Figure 2) and an interior scene (Figure 3) when there is simple myopic astigmatism (or equivalent spherical error) present in with-the-rule (axis 180 ), against-the-rule (axis 90 ) and oblique (axis 135 ) meridians. The images are taken from the viewer’s

Figure 3 The effects of astigmatic blur, compared to spherical blur, for an interior scene. Simple myopic astigmatism (or equivalent spherical error) is present in the following meridians: with-the-rule (axis 180 ), upper left panel; against-the-rule (axis 90 ), upper right panel; and oblique (axis 135 ), lower left panel. The level of blur is that of a narrow failure to pass the European vision standard for driving.

perspective and the level of blur chosen is that of a narrow failure to pass the European vision standard for driving. The induced spherical error is half that of the induced cylindrical error such that the diameters of the blur circle for the spherical lens and the CLC for the cylindrical lens would be matched.

Oblique Astigmatism

Even in an optical system that is rotationally symmetrical, the formation of images from off-axis object points will result in astigmatism, known as oblique astigmatism. This should not be confused with conventional astigmatism along an oblique axis meridian, which is due to different radii of curvature of the refracting surface in different meridians. In the eye, oblique astigmatism is important because the fovea is offset from the best approximation to an optical axis that the eye has, so that the objects that form an image on the fovea are nearly always slightly offset from this optical axis. It is also the dominant form of aberration in image formation for the peripheral retina.

Figure 4 shows the image-forming properties in oblique astigmatism. Rays in the tangential plane, the one containing the optical axis and the chief ray, form a line image oriented in the sagittal plane. Rays in the sagittal plane (the

plane containing the chief ray that is perpendicular to the tangential plane) form a line image oriented in the tangential plane. In this biconvex lens, the tangential images form nearer the lens than the sagittal images, but for any given lens power the relative locations of the tangential and sagittal images depend upon the relative powers of the two surfaces of the lens, assuming that there is an aperture stop behind the refracting surface as is the case in the eye or when a spectacle lens is used in front of an eye. The distance from the tangential image to the image position found in a system free from oblique astigmatism is always three times the equivalent distance for the sagittal image. Circumferential image contours are formed clearly in the tangential image plane. In the sagittal image plane, radial image contours are formed clearly.

Any ocular astigmatism caused by oblique astigmatism at the fovea can be corrected with the usual refractive techniques and the oblique astigmatism that is present in the periphery of the visual field is unimportant in normal visual function as the retinal ganglion cell mosaic limits the visual resolving power of the eye to a greater extent than the optics. It is argued that ocular oblique astigmatism acts as a useful high spatial frequency filter to prevent aliasing and the consequent perception of reverse motion in the peripheral visual field.

Oblique astigmatism in refractive correction using spectacles is important. As the eye rotates to view different objects in the field of interest it will make different angles with the optical axis of any spectacle lens, and this will then cause different amounts of oblique astigmatism to be generated by the lens.

Ocular Astigmatism During Near Work

In addition to the nature of the visual task typically being different for near work compared to distance viewing, occasionally the ocular astigmatism itself, or its correction, can change. The power and/or axis of the ocular astigmatism at near compared to distance viewing may be affected by the following factors:

. when the eyes converge and depress for near work they tend to excyclotort;

. the suspensory ligaments of the crystalline lens may not be uniform, causing induced astigmatic changes in the lens during accommodation;

. the ciliary muscle fibers themselves may not exert uniform force on the crystalline lens;

. the crystalline lens may not be homogenously plastic, inducing irregular shape changes during accommodation;

. the pupil or lens may displace with respect to the corneal axis during accommodation inducing some change in the oblique astigmatism.

The power of the astigmatic correction using spectacles can change due to near vision effectivity when the astigmatic or spherical refractive error is large.

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Tangential focus

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Sagittal focus

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statistics for refractive errors, assessing change in refractive error, or when trying to determine the effects of a refractive error when used in conjunction with other optical equipment or other induced refractive errors. Two main alternative forms of notation have been suggested: power vector notation and matrix notation.

Power vector notation resolves the optical power of any sphero-cylindrical lens into three components, a spherical component M, and two crossed-cylinder components, J0 and J45, with their axes at either 90 /180 or 45 /135 , respectively. Equal values of the components in this notation will lead to equal retinal blur circle sizes. Equations for computing the M, J0, J45 values from the conventional FSph/FCyl y are given below:

While this notation is useful for adding, subtracting, and multiplying by a scalar when dealing with thin sphero-cylindrical lenses, it is much less convenient to use when multiplying lens powers (as required when computing the powers of multiple lens systems or dealing with thick lens systems) or computing the prismatic effects of lens systems.

The alternative matrix representation of lens power is more general and can be used in the above-mentioned instances. A 2 2 matrix,

is defined in thin lenses such that

It is interesting to note the simple transformations between these two systems in thin lenses and their relationship to the Zernike basis function representation of wave front aberrations now commonly used when considering irregular astigmatic refractive error. The Zernike astigma-

value of J45 and Jy, respectively, given a pupil radius r, and using normalized variance terms. This has implications when measuring and correcting ocular astigmatism.

The Measurement of Ocular Astigmatism

Various techniques are employed to measure the extent of ocular astigmatism. The majority are based upon locating the meridians of maximum and minimum power and then minimizing the size of the retinal blur ellipses along those meridians. This may be done objectively or subjectively. Alternatively, different components of the astigmatic power may be measured and the final astigmatic refraction inferred from them.

Subjective methods include the Stenopaeic slit, Jackson’s crossed-cylinder, fan and block, and Stokes lens techniques. Objective methods include retinoscopy, automated refraction, keratometry, and wave front analysis. It is the latter two that have benefited from the greatest development effort in the last few years.

Keratometry

In this method, the image magnification produced by using the anterior corneal surface as a convex mirror is measured along the meridians of maximum and minimum curvature. The sagittal radius of curvature is inferred from this magnification and the corneal astigmatism is inferred from the sagittal curvature the corneal refractive index and the presumed corneal back surface curvature. The ocular astigmatism is then inferred by assuming a fixed value for the internal astigmatism.

An extension to the principle of the keratometer is the corneal topographer that uses either reflected light from the cornea to measure the local curvature, or light (or even sound) scattered from the cornea – tear-film or cornea – aqueous interfaces to measure the local surface heights. It is possible to computer the local curvature from the local surface heights and vice versa. Unlike keratometers, such instruments clearly demonstrate the conicoidal nature of the cornea over most of its surface excluding the limbal region. Estimates of ocular astigmatism can be made by finding the best fitting overall match to the power map provided by the instrument. They also detect and measure irregular astigmatism much more accurately than keratometers. Figure 5 shows a corneal keratometric power map and surface height map from the right eye of an individual with approximately 4.50 D of regular with-the-rule ocular astigmatism. The symmetric bow tie pattern in the curvature map is a typical finding in these types of representations of corneal power in astigmatism and the corneal axis of astigmatism can be clearly identified from both maps.

Wave Front Analysis

Most of the methods of refractive measurement estimate the refractive power of the eye along one meridian at a

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time. In these cases the refractive power in that meridian is a best fit to the combination of low-order refractive errors, high-order wave front aberration, and light scatter in the eye to produce the best perceived retinal image by viewing or varying light rays in only that meridian. If scatter or high-order aberrations are large (as in irregular astigmatism) then maximum and minimum power meridians may not be perpendicular giving a problem (albeit soluble) when attempting to arrive at a sphero-cylindrical refractive error. In addition, because change is restricted to one meridian at a time, and the imaging effects from the two meridians tested may interact, it is far from guaranteed that an optimum solution will be found. Furthermore,

intermediate meridians will also influence image quality and these are not assessed.

The Stokes lens subjective method circumvents these problems to some extent by estimating along two perpendicular meridians at the same time. Corneal topography assessments can theoretically reduce the problem significantly by estimating ocular astigmatism from combining many individual samples of corneal power across the whole pupil area. Wave front analysis, where the refractive power of the eye is also sampled across multiple small apertures across the pupil, also estimates ocular astigmatism from this array of samples and is typically represented using Zernike polynomials. The Zernike terms are

orthogonal to each other and therefore theoretically do not influence one another over a circular pupil. By considering the measurement or expression of ocular astigmatism using this basis, as opposed to along meridians of maximum and minimum power, it is possible to arrive at an astigmatic correction that is optimized for reducing the wave front aberration given a limitation of being able to use only sphero-cylindrical refractive correction such as can be worked onto spectacle lenses, contact lenses, and intraocular lenses. The spherical element of the correction is not well predicted using an equivalent method, however, due to the extra importance of central versus peripheral pupil rays in the wave front. Techniques that can use asymmetrical surfaces, such as laser refractive corneal ablation, directly make use of the additional higherorder terms of the Zernike expression of the optical defect to provide further optimization of the refractive correction. However, neither corneal topography nor wave front analysis can account for the effects of ocular scatter.

The Correction of Ocular Astigmatism

Spectacles

Spectacles are the most common form of correction for ocular astigmatism. Except in unusual circumstances these lenses are successful in providing optimal visual function. In a limited number of individuals with unusually high irregular astigmatism and/or under conditions where the eye’s pupil is very large, the other nonrotationally symmetric optical aberrations such as coma, trefoil, tetrafoil, and secondary astigmatism can reduce the visual performance significantly despite the correction of regular astigmatism.

Spectacle correction of high levels of regular astigmatism also produces spatial distortions due to the different levels of relative spectacle magnification in the different meridians. These make it difficult to binocularly fuse objects that are viewed through the more peripheral parts of the lenses. Patients corrected in this way will often learn to limit this effect by substituting head movement for eye movements when viewing outside a limited area from the optical center of the lens. Misperceived orientations of features and contours in the field of view also occur in high levels of regular astigmatism. Perceptual adaptation takes place over about a 2-week period to ameliorate this effect. Changing the power of the lenses significantly can, however, lead to a return of the perceptual problems.

Tscherning offered a solution to the problem of spectacle lens-induced oblique astigmatism by deriving the necessary lens forms (distribution of lens power between the front and back surfaces) to eliminate oblique astigmatism from spectacle lenses with a given refractive index and for use viewing objects at a given distance. These lens forms are known as punctal (or point focal) lenses. It is more

common today to use minimum tangential error, where the tangential image plane is designed to be of a specified power that is independent of the angle of viewing. While this leaves a small residual astigmatic error, it reduces the spherical power error found in punctal lens designs where power changes as a function of viewing angle.

Spectacle lenses with an aspheric surface can also be used to reduce or eliminate oblique astigmatism with the additional benefit of a flatter front surface that makes the lens look less bulbous and also allows the lens to be thinner and hence lighter. The disadvantage is that aspheric lenses must be centered on the visual axis correctly or they induce, rather than reduce oblique astigmatism and other nonrotationally symmetric aberrations. Progressive addition lenses (PALs, also known as varifocals), with their aspheric surface induce astigmatism in a similar way as they can be centered for only two zones in the lens.

Contact Lenses

Contact lens correction of astigmatism can be with rigid or soft lenses. Spherical rigid contact lenses can eliminate the majority of regular or irregular corneal astigmatism. Ensuring the correct fitting of the rigid contact lens limits the amount of correction that can be provided with this method and bitoric lenses, with front and back toric surfaces, are needed for high degrees of astigmatism. Toric front surface rigid contact lenses can be used in cases of internal astigmatism that require correction. Most soft contact lenses flex sufficiently to align to the shape of the anterior corneal surface and so do not correct corneal astigmatism through a tear lens in the same way that rigid lenses do. Front surface toric soft contact lenses are required for the proper correction of ocular astigmatism.

In either rigid or soft contact lens correction of ocular astigmatism, many of the optical problems associated with spectacle correction are relieved. Meridional image magnification, near vision effectivity, and differential prismatic effects are all greatly reduced in contact lens correction. One of the principal difficulties in using contact lenses to correct astigmatism is in maintaining a stable rotational alignment between the contact lens and the cornea.

Surgery

Surgical control or correction of ocular astigmatism usually relies upon altering the shape of the cornea. This is most commonly done by making circumferential incisions in the corneal periphery. This reduces the tensile forces across the corneal stroma in that location, steepening the cornea locally, but flattening it across the pupil in the meridian which intersects with the incision. It is common because cataract surgery is common and most cataract surgery uses a corneal incision, the incision usually being