**Part 2**

## **Diagnosis and Imaging of Astigmatism**

56 Astigmatism – Optics, Physiology and Management

Yao, K.; Tang, X. & Ye, P. (2006). Corneal astigmatism, high order aberrations, and optical

Vol. 22, No. 9, Suppl. (November 2006), pp. S1079–S1082.

quality after cataract surgery: microincision versus small incision. *J Refract Surg*,

## **Astigmatism – Definition, Etiology, Classification, Diagnosis and Non-Surgical Treatment**

Dieudonne Kaimbo Wa Kaimbo *Department of Ophthalmology, University of Kinshasa, DR Congo* 

## **1. Introduction**

## **1.1 Definition**

Astigmatism (from the Greek "a" meaning absence and "stigma" meaning point) is a refractive error (ametropia) that occurs when parallel rays of light entering the nonaccommoding eye are not focused on the retina [American Academy of Ophthalmology (AAO), 2007]. Astigmatism occurs when incident light rays do not converge at a single focal point. The cornea of the normal eye has a uniform curvature, with resulting equal refracting power over its entire surface. **Most astigmatic corneas are normal also.** In some individuals, however, the cornea is not uniform and the curvature is greater in one meridian (plane) than another, much like a **football as a rugby ball.** Light rays refracted by this cornea are not brought to a single point focus, and retinal images from objects both distant and near are blurred and may appear broadened or elongated. This refractive error is called astigmatism [AAO, 2007]. As concept astigmatism is at least 200 years old; as name, more than 150. Javal ascribes the concept to T. Young in 1800 and the name to W. Whewell. Bannon and Walseh give an early history [Harris, 2000].

Total astigmatism can be divided into corneal (or keratometric) astigmatism, lenticular astigmatism, and retinal astigmatism. Most astigmatism is corneal in origin. Lenticular astigmatism is a result of uneven curvature and differing refractive indices within the crystalline lens [Abrams, 1993].

It is well accepted that there is some relationship between the eye's corneal and internal astigmatism. In 1890, Javal proposed a rule that predicted the total astigmatism of the eye based on the corneal astigmatism [Grosvenor, 1978; Read et al, 2007].

Javal's rule states: At = k + p(Ac)

Where At is the total astigmatism and Ac is the corneal astigmatism. The terms k and p are constants approximated by 0.5 and 1.25, respectively. Grosvenor, Quintero and Perrigin [Grosvenor et al, 1988] suggested a simplification of Javal's rule and proposed a simplified Javal's rule of At = Ac – 0.5, **that was supported by** Keller and colleagues [Keller et al, 1996]. **It should be pointed out to the reader that with modern topographers and aberrometerss it is possible to measure corneal and internal astigmatism and such estimations like Javal's rule are clinically less relevant.**

Kelly, Mihashi and Howland [Kelly et al, 2004] suggested that the horizontal/vertical astigmatism compensation is an active process determined through a fine-tuning, emmetropisation process. Dunne, Elawad and Barnes [Dunne et al, 1994] investigated **internal or non-corneal** astigmatism, by measuring the difference between ocular and total astigmatism (by cylindrical decomposition). The average internal or **non-corneal** astigmatism was found to be -0.46X98.2° for right eyes and -0.50X99.4° for left eyes. Studies have investigated the astigmatism contributed by the posterior corneal surface [Dunne et al, 1991; Oshika et al, 1998a; Prisant et al, 2002; Dubbelman et al, 2006]. These studies have found levels of astigmatism for the posterior cornea ranging from 0.18 -0.31 D. The curvature of the posterior cornea combined with the refractive index difference between the cornea and the aqueous means that the posterior corneal astigmatism is of opposite sign to that of the anterior cornea. Therefore, the compensation of corneal astigmatism by the eye's internal optics can be attributed, in part, to the astigmatism of the posterior cornea. The compensation of corneal astigmatism by the internal optics of the eye has been known for many years [Grosvenor, 1978; Kelly et al, 2004; Dunne et al, 1994]. Some authors [Kelly et al, 2004] have suggested the possibility of an active "feedback driven" process operating to reduce the total astigmatism of the eye (particularly horizontal/vertical astigmatism).

## **1.2 Epidemiology - prevalence**

Astigmatism **(more than 0.5 diopters)** is a commonly encountered refractive error, accounting for about 13 per cent of the refractive errors of the human eye [Porter et al, 2001; Read et al, 2007].

It is commonly encountered clinically, with prevalence rates up to 30% or higher depending on the age or ethnic groups [Saw et al, 2006; Kleinstein et al, 2003]. Human infants exhibit both high prevalence and high degrees of astigmatism, largely corneal in origin [Read et al,2007; Gwiazda et al, 2000; Mandel et al, 2010]. It lessens in prevalence and amplitude over the first few years of childhood, with an axis shift from against-the-rule (ATR) to with-therule (WTR) [Read et al, 2007; Mandel et al, 2010].

Children as young as preschool age may exhibit visual deficits caused by astigmatism [Dobson et al, 2003]. Although, astigmatism has not been fully investigated in preschool children [Dobson et al, 1999; Shankar and Bobier, 2004], its prevalence is reportedly greater in infants [Gwiazda et al, 1984; Dobson et al, 1984; Mayer et al, 2001] than in schoolchildren [Huynh et al, 2006; Huynch et al, 2007] and is also known to vary with ethnicity [Huynh et al, 2006; Kleinstein et al, 2003; Lai et al, 2010].

The reported prevalence of astigmatism in children aged 3 to 6 years varies in different studies and in different ethnicities [Huynh et al, 2006; Kleinstein et al, 2003; Dobson et al, 1999; Shankar & Bobier, 2004; Fann et al, 2004; Giordano et al, 2009]. For example, reported prevalence rates of astigmatism of 1.00 D or more in children were 44% in 3- to 5-year-old children in a native American population [Dobson et al, 1999], 28.4% in children in the United States [Kleinstein et al, 2003], about 22% in children (mean age 51.1 months) in Canada [Shankar et al, 2004], 21.1% in Hong Kong preschool children [Fan et al, 2004], 4.8% in 6-year-old children in Sydney [Huynh et al, 2006], 11.4% in children in Taiwan [Lai et al, 2010], and 11.2% in children in Sydney [Huynch et al, 2006].

In children or young adults, Kleinstein et al [Kleinstein et al, 2003] found that 28% of their US-based study population aged 5 to 17 years had astigmatism of at least 1.0 D. A study of Australian 6-year-olds found a prevalence of astigmatism of nearly 5% [Huynh et al,2006]. A series of studies carried out in children aged 7 to 15 from different countries but using similar methodology found a wide range of prevalence of astigmatism, varying from approximately 3% in Andra Pradesh, India [Dandona et al,2002], to 7% in New Delhi

emmetropisation process. Dunne, Elawad and Barnes [Dunne et al, 1994] investigated **internal or non-corneal** astigmatism, by measuring the difference between ocular and total astigmatism (by cylindrical decomposition). The average internal or **non-corneal** astigmatism was found to be -0.46X98.2° for right eyes and -0.50X99.4° for left eyes. Studies have investigated the astigmatism contributed by the posterior corneal surface [Dunne et al, 1991; Oshika et al, 1998a; Prisant et al, 2002; Dubbelman et al, 2006]. These studies have found levels of astigmatism for the posterior cornea ranging from 0.18 -0.31 D. The curvature of the posterior cornea combined with the refractive index difference between the cornea and the aqueous means that the posterior corneal astigmatism is of opposite sign to that of the anterior cornea. Therefore, the compensation of corneal astigmatism by the eye's internal optics can be attributed, in part, to the astigmatism of the posterior cornea. The compensation of corneal astigmatism by the internal optics of the eye has been known for many years [Grosvenor, 1978; Kelly et al, 2004; Dunne et al, 1994]. Some authors [Kelly et al, 2004] have suggested the possibility of an active "feedback driven" process operating to reduce the total astigmatism of the eye (particularly horizontal/vertical astigmatism).

Astigmatism **(more than 0.5 diopters)** is a commonly encountered refractive error, accounting for about 13 per cent of the refractive errors of the human eye [Porter et al, 2001;

It is commonly encountered clinically, with prevalence rates up to 30% or higher depending on the age or ethnic groups [Saw et al, 2006; Kleinstein et al, 2003]. Human infants exhibit both high prevalence and high degrees of astigmatism, largely corneal in origin [Read et al,2007; Gwiazda et al, 2000; Mandel et al, 2010]. It lessens in prevalence and amplitude over the first few years of childhood, with an axis shift from against-the-rule (ATR) to with-the-

Children as young as preschool age may exhibit visual deficits caused by astigmatism [Dobson et al, 2003]. Although, astigmatism has not been fully investigated in preschool children [Dobson et al, 1999; Shankar and Bobier, 2004], its prevalence is reportedly greater in infants [Gwiazda et al, 1984; Dobson et al, 1984; Mayer et al, 2001] than in schoolchildren [Huynh et al, 2006; Huynch et al, 2007] and is also known to vary with ethnicity [Huynh et

The reported prevalence of astigmatism in children aged 3 to 6 years varies in different studies and in different ethnicities [Huynh et al, 2006; Kleinstein et al, 2003; Dobson et al, 1999; Shankar & Bobier, 2004; Fann et al, 2004; Giordano et al, 2009]. For example, reported prevalence rates of astigmatism of 1.00 D or more in children were 44% in 3- to 5-year-old children in a native American population [Dobson et al, 1999], 28.4% in children in the United States [Kleinstein et al, 2003], about 22% in children (mean age 51.1 months) in Canada [Shankar et al, 2004], 21.1% in Hong Kong preschool children [Fan et al, 2004], 4.8% in 6-year-old children in Sydney [Huynh et al, 2006], 11.4% in children in Taiwan [Lai et al,

In children or young adults, Kleinstein et al [Kleinstein et al, 2003] found that 28% of their US-based study population aged 5 to 17 years had astigmatism of at least 1.0 D. A study of Australian 6-year-olds found a prevalence of astigmatism of nearly 5% [Huynh et al,2006]. A series of studies carried out in children aged 7 to 15 from different countries but using similar methodology found a wide range of prevalence of astigmatism, varying from approximately 3% in Andra Pradesh, India [Dandona et al,2002], to 7% in New Delhi

**1.2 Epidemiology - prevalence** 

rule (WTR) [Read et al, 2007; Mandel et al, 2010].

al, 2006; Kleinstein et al, 2003; Lai et al, 2010].

2010], and 11.2% in children in Sydney [Huynch et al, 2006].

Read et al, 2007].

[Murphy et al,2002], to 6% in Chinese children [Zhao et al, 2002]. Astigmatism of more than 0.5 D is common among older adults, and the prevalence increases with age among Caucasians from 28% among individuals in their 40s to 38% among individuals in their 80s [Katz et al, 1997]. This increase with age was also seen among African Americans, although the prevalence was about 30% lower than among Caucasians at every age [Katz et al, 1997]. In adult Americans, the prevalence of astigmatism has been reported to be 20% higher among men than women but was not associated with number of years of formal education [Katz et al, 1997]. There have been conflicting data about the association of astigmatism with prematurity or low birth weight, and with retinopathy of prematury [Holmstrom et al, 1998; Larsson et al, 2003; Saw and Chew, 1997; Tony et al, 2004]. Additionally, although studies of adult population indicate that height is associated with eyeball length and corneal flatness and that weight is associated with hyperopic refraction [Wong et al, 2001], the associations among height, weight, and astigmatism have not been described in preschool children.

Some but not all studies find higher rates of astigmatism among subjects with ametropia in either the myopic or hyperopic direction, particularly for higher magnitude spherical refractive errors [Farbrether et al,2004; Kronfeld & Devney, 1930; Mandel et al, 2010].

The presence of high astigmatism is associated with the development of amblyopia and progressive myopia [Fulton et al, 1982; Gwiazda et al, 2000]. The presence of astigmatism has also been found to be associated with higher degrees of myopia, with an increased progression of myopia by some studies [Ninn-Pedersen, 1996; Fulton et al, 1982; Gwiazda et al, 2000; Tong et al, 2002; Farbrother et al, 2004; Fan et al, 2004; Heidary et al, 2005] whereas other studies have found little to no association between the presence of astigmatism and the presence and progression of myopic refractive errors. However, there does appear to be an association between astigmatism and the development and progression of myopia [Read et al, 2007].

In general, regular astigmatism is common; irregular astigmatism has been considered an uncommon refractive error. However, with the advent of computerized video keratography, the prevalence of some patterns definable as irregular may be as high as 40%, and significant irregularity may reside in the posterior corneal surface [Alpins, 1998; Bogan et al, 1990; Oshika et al,1998b]. A degree of irregularity seems common among contact lens wearers [Wilson & Klyce, 1994]. Prior to vectorial assessment of the cornea, no generally accepted definition of irregular corneal astigmatism included all these eyes in the spectrum previously regarded as normal. Because best corrected visual acuity may be limited by mild irregularity and given the frequency of these findings in "normal" eyes, it may be asked whether altering these patterns deliberately may improve vision in eyes that see "normally" by current measures [Oshika et al, 1998b]. **The vectorial value of the topographic disparity (TD) can be used to define and to quantify irregularity [Goggin et al, 2000].** There is a "spectrum of normally" in which the TD ranges from zero to one. Values greater than 1.00 D represent significant irregularity, though this may be an arbitrary boundary whose value may be determined by further experience with this standardized measurement gauge [Goggin et al, 2000]

Astigmatism results from uneven or irregular curvature of the cornea or lens.

Corneal and noncorneal factors contribute to **total astigmatism** [Van Alphen, 1961; Tronn, 1940; Sorsby, Leary & Richards, 1962; Curtin, 1985]. Corneal astigmatism is mainly due to an aspheric corneal anterior surface [Sheridan & Douthwaite, 1989] . In 10% of people the effect is neutralized by the back surface [Sheridan & Douthwaite, 1989; Sorsby et al, 1966; Sorsby et al, 1962]. The curvature of the back surface of the cornea is not considered in most studies because it is more difficult to measure. Non-corneal factors can be due to errors in the curvature of the anterior and posterior crystalline lens surfaces, an irregularity in the refractive index of the lens, or an eccentric lens position [Van Alphen, 1961; Tron, 1940; Sorsby, Leary & Richards, 1962; Gordon & Donzis, 1985].

The axis of astigmatism has been studies extensively [Gwiazda et al, 1984; Dobson et al, 1984; Huynh et al, 2006; Fan et al, 2004, Ehrlich et al, 1997]. The prevalence of ATR astigmatism is reportedly high in children younger than 4 years [Gwiazda et al, 1984; Dobson et al, 1984; Mayer et al, 2001].

## **2. Etiology, astigmatism types, classification**

#### **2.1 Etiology**

Despite extensive research, the exact cause of astigmatism is still not known [Read et al, 2007] . One possible explanation of the aetiology of astigmatism is that astigmatic refractive errors are genetically determined. Numerous studies have been undertaken to investigate the influence of genetics on astigmatic development. However, the studies into genetics and astigmatism present some conflicting results. Certain studies indicate some degree of heritability of astigmatism and also tend to favour an autosomal dominant mode of inheritance [Hammond et al, 2001; Clementi et al, 1998]. Other studies favour a stronger environnemental influence [Teikari & O'Donnell, 1989; Teikari et al, 1989; Valluri et al, 1999; Lee et al, 2001]. It would appear that both genetic and environmental factors have roles in the development of astigmatism. The exact nature of these mechanisms is still not fully understood.

Other possible causes include mechanical interactions between the cornea and the eyelids and/or the extraocular muscles or a visual feedback model in which astigmatism develops in response to visual cues [Read et al, 2007].

Astigmatism can be divided into congenital and acquired categories. When acquired, it may be secondary to certain disease states or a result of ocular surgery or trauma. Astigmatism has multifactorial etiologies and can arise from the cornea, the lens, and even the retina [Raviv & Epstein, 2000]. Corneal astigmatism usually accounts for most of the measured cylindrical refraction.

The occurrence of irregular astigmatism varies from natural to surgically induced causes. Examples of natural causes include primary irregular astigmatism and secondary irregular astigmatism caused by various corneal pathologies associated with elevated lesions, such as keratoconus or Sallzmann's nodular degeneration [Rapuano, 1996]. Examples of surgically induced astigmatism include pterygium removal, cataract extraction, lamellar and penetrating keratoplasty, myopic keratomileusis, radial and astigmatic keratectomy, PRK, and laser in situ keratomileusis (LASIK). Other causes of irregular astigmatism include corneal trauma and infection [Tamayo Fernandez & Serrano, 2000].

There are several diseases and syndromes that are associated with an increased prevalence of astigmatism. Some of them are reported in Table 1.

#### **2.2 Astigmatism types - classification of astigmatism**

Ocular astigmatism can occur as a result of unequal curvature along the two principal meridian of the anterior cornea (known as corneal astigmatism) and /or it may be due to the posterior cornea, unequal curvatures of the front and back surfaces of the crystalline lens, decentration or tilting of the lens or unequal refractive indices across the crystalline lens (known as internal or **non-corneal** astigmatism). The combination of the corneal and the

because it is more difficult to measure. Non-corneal factors can be due to errors in the curvature of the anterior and posterior crystalline lens surfaces, an irregularity in the refractive index of the lens, or an eccentric lens position [Van Alphen, 1961; Tron, 1940;

The axis of astigmatism has been studies extensively [Gwiazda et al, 1984; Dobson et al, 1984; Huynh et al, 2006; Fan et al, 2004, Ehrlich et al, 1997]. The prevalence of ATR astigmatism is reportedly high in children younger than 4 years [Gwiazda et al, 1984;

Despite extensive research, the exact cause of astigmatism is still not known [Read et al, 2007] . One possible explanation of the aetiology of astigmatism is that astigmatic refractive errors are genetically determined. Numerous studies have been undertaken to investigate the influence of genetics on astigmatic development. However, the studies into genetics and astigmatism present some conflicting results. Certain studies indicate some degree of heritability of astigmatism and also tend to favour an autosomal dominant mode of inheritance [Hammond et al, 2001; Clementi et al, 1998]. Other studies favour a stronger environnemental influence [Teikari & O'Donnell, 1989; Teikari et al, 1989; Valluri et al, 1999; Lee et al, 2001]. It would appear that both genetic and environmental factors have roles in the development of

Other possible causes include mechanical interactions between the cornea and the eyelids and/or the extraocular muscles or a visual feedback model in which astigmatism develops

Astigmatism can be divided into congenital and acquired categories. When acquired, it may be secondary to certain disease states or a result of ocular surgery or trauma. Astigmatism has multifactorial etiologies and can arise from the cornea, the lens, and even the retina [Raviv & Epstein, 2000]. Corneal astigmatism usually accounts for most of the measured

The occurrence of irregular astigmatism varies from natural to surgically induced causes. Examples of natural causes include primary irregular astigmatism and secondary irregular astigmatism caused by various corneal pathologies associated with elevated lesions, such as keratoconus or Sallzmann's nodular degeneration [Rapuano, 1996]. Examples of surgically induced astigmatism include pterygium removal, cataract extraction, lamellar and penetrating keratoplasty, myopic keratomileusis, radial and astigmatic keratectomy, PRK, and laser in situ keratomileusis (LASIK). Other causes of irregular astigmatism include

There are several diseases and syndromes that are associated with an increased prevalence

Ocular astigmatism can occur as a result of unequal curvature along the two principal meridian of the anterior cornea (known as corneal astigmatism) and /or it may be due to the posterior cornea, unequal curvatures of the front and back surfaces of the crystalline lens, decentration or tilting of the lens or unequal refractive indices across the crystalline lens (known as internal or **non-corneal** astigmatism). The combination of the corneal and the

astigmatism. The exact nature of these mechanisms is still not fully understood.

corneal trauma and infection [Tamayo Fernandez & Serrano, 2000].

of astigmatism. Some of them are reported in Table 1.

**2.2 Astigmatism types - classification of astigmatism** 

Sorsby, Leary & Richards, 1962; Gordon & Donzis, 1985].

**2. Etiology, astigmatism types, classification** 

Dobson et al, 1984; Mayer et al, 2001].

in response to visual cues [Read et al, 2007].

cylindrical refraction.

**2.1 Etiology** 

Aarskog syndrome Albinism Alport syndrome Anterior polar congenital cataract and corneal astigmatism Blepharophimosis Chalazia Charge association Cohen syndrome Congenital fibrosis of the extraocular muscles sundrome Congenital ptosis Congenital sensorineural hearing loss Craniosynostotic syndrome Distal arthrogryposis type IIb Down's syndrome Ehlers-Danlos syndrome (EDS) type 1 Epiblepharon Epibulbar dermoids Essential blepharospasme Eyelid and orbital haemangiomas Facial naevus flammeus Fetal alcohol syndrome Floppy eyelid syndrome Fragile X syndrome General fibrosis syndrome (GFS) Hearing impaired and deaf students Idiopathic nystagmus Infantile nystagmus syndrome Iridocorneal endothelial syndrome Kabuki Make-up (Niikawa-Kuroke) syndrome Keratoconus Laurence-Moon-Biedl syndrome Lenticonus Linear nevus sebaceous syndrome Mental handicap Mobius syndrome Momes syndrome (Mental retardation, obesity, mandibular prognathisme with eye and skin anomalities) Morquio syndrome Nail-patella syndrome New MCA/MR syndrome Pellucid marginal corneal degeneration (PMCD) Peters anomaly Phaces syndrome Pigmentary retinopathy: Autosomal recessive pericentral pigmentary retinopathy Posterior amorphous cornealdysgenesis Prader-Willi syndrome Preterm newborn infants Pterygium Renal-Coloboma syndrome associated with mental development Retinitis pigmentosa Sclerocornea Seckel syndrome


Table 1. Some conditions, diseases and syndromes associated with astigmatism

internal astigmatism gives the eye's total astigmatism (that is, total astigmatism equals corneal astigmatism plus internal astigmatism) [Read et al, 2007]. Corneal astigmatism is often classified according to the axis of astigmatism as being either with-the-rule (WTR), oblique or against-the-rule (ATR). The principal meridians-the meridians of maximum and minimum corneal curvature-are usually at right angles to each other in astigmatism and are usually (but not necessarily) in the vertical and horizontal planes. Astigmatism can be described as regular or irregular.

In regular astigmatism, which is the more common form, the cornea would resemble a **football as a rugby ball** standing on one end or on its side or, less often, tipped to one side. In regular astigmatism, there are two principal meridians separated by 90 degrees; the best spectacle-corrected visual acuity (BSCVA) is at least 20/20 and, in the case of corneal astigmatism, corneal topography displays a symmetrical bow—tie pattern. In regular astigmatism, the refractive power varies successively from one meridian to the next, and each meridian has a uniform curvature at every point across the entrance pupil. The meridian of greatest and least power, the so-called principal meridians, are always located at meridian 90 degrees apart [Abrams, 1993; AAO, 2007; Raviv & Epstein, 2000].

Various types of regular astigmatism have been identified on the basis of the refractive power and position of the principal meridians, as described in Table 2 when accommodation is relaxed in non-astigmatic eyes and in astigmatic eyes with with-the-rule astigmatism (greater curvature in the vertical meridian, plus cylinder axis 90°, minus cylinder axis 180°).

In irregular astigmatism, which is less common, the corneal "**rugby ball**" would appear out of its customary shape and/or bumpy. The condition of irregular astigmatism is variously defined. A comprehensive definition is given by Duke-Elder [Duke-Elder, 1970], who describes it as a refractive state in which "refraction in different meridians conforms to no geometrical plan and the refracted rays have no planes of symmetry". It may be defined as an astigmatic state not correctable by a sphero-cylindrical lens [Azar and Strauss, 1994]. Irregular astigmatism can be regularly irregular or irregularly irregular. In regularly irregular astigmatism, two principal meridians exist but are either asymmetrical or not 90 degrees apart and is typified by either unequal slopes of the hemimeridians along a single


#### Table 2. Classes of regular astigmatism

64 Astigmatism – Optics, Physiology and Management

Table 1. Some conditions, diseases and syndromes associated with astigmatism

at meridian 90 degrees apart [Abrams, 1993; AAO, 2007; Raviv & Epstein, 2000].

curvature in the vertical meridian, plus cylinder axis 90°, minus cylinder axis 180°).

internal astigmatism gives the eye's total astigmatism (that is, total astigmatism equals corneal astigmatism plus internal astigmatism) [Read et al, 2007]. Corneal astigmatism is often classified according to the axis of astigmatism as being either with-the-rule (WTR), oblique or against-the-rule (ATR). The principal meridians-the meridians of maximum and minimum corneal curvature-are usually at right angles to each other in astigmatism and are usually (but not necessarily) in the vertical and horizontal planes. Astigmatism can be

In regular astigmatism, which is the more common form, the cornea would resemble a **football as a rugby ball** standing on one end or on its side or, less often, tipped to one side. In regular astigmatism, there are two principal meridians separated by 90 degrees; the best spectacle-corrected visual acuity (BSCVA) is at least 20/20 and, in the case of corneal astigmatism, corneal topography displays a symmetrical bow—tie pattern. In regular astigmatism, the refractive power varies successively from one meridian to the next, and each meridian has a uniform curvature at every point across the entrance pupil. The meridian of greatest and least power, the so-called principal meridians, are always located

Various types of regular astigmatism have been identified on the basis of the refractive power and position of the principal meridians, as described in Table 2 when accommodation is relaxed in non-astigmatic eyes and in astigmatic eyes with with-the-rule astigmatism (greater

In irregular astigmatism, which is less common, the corneal "**rugby ball**" would appear out of its customary shape and/or bumpy. The condition of irregular astigmatism is variously defined. A comprehensive definition is given by Duke-Elder [Duke-Elder, 1970], who describes it as a refractive state in which "refraction in different meridians conforms to no geometrical plan and the refracted rays have no planes of symmetry". It may be defined as an astigmatic state not correctable by a sphero-cylindrical lens [Azar and Strauss, 1994]. Irregular astigmatism can be regularly irregular or irregularly irregular. In regularly irregular astigmatism, two principal meridians exist but are either asymmetrical or not 90 degrees apart and is typified by either unequal slopes of the hemimeridians along a single

Short syndrome Sjögren syndrome Sjögren-Larsson syndrome

Spherophakia Spina bifida Sticker syndrome Titled disc syndrome Treacher Collins syndrome Trisomy 8 mosaic syndrome Usher Syndrome type III Velo cardiofacial syndrome Weill-Marchesabni syndrome

Cataract surgery Penetrating keratoplasty Refractive surgery

described as regular or irregular.

Trauma Infection

> meridian (the "asymmetric bow-tie") or hemimeridians of equal slope but not aligned with each other (the "angled bow-tie" or nonorthogonal astigmatism). A combination of both patterns usually occurs [Goggin et al, 2000]. Irregularly irregular astigmatism does not have identifiable prime meridians. In irregular astigmatism, which can be clinically significant in conditions such as keratoconus and other corneal ectasias; corneal basement membrane and stromal dystrophies; corneal scarring; and post-surgical corneas (e.g., following penetrating keratoplasty, radial keratotomy, and complicated refractive surgery), the magnitude and the axis of astigmatism vary from point to point across the entrance pupil [AAO, 2007]. An irregularly irregular state is seen when even computerized topography cannot demonstrate a recognizable pattern, and the corneal surface can only be described as rough or uneven [Goggin et al, 2000]. It is associated with decreased BSCA, which is correctable only with a rigid contact lens. Current refractive surgical technologies, including incisional and excimer laser surgery, are designed for the treatment of regular astigmatism. **Excimer lasers are now in clinical use that can address irregular corneal astigmatism.**

> Typically, irregular astigmatism is used to describe a variety of asymmetric aberrations such as coma, trefold and quadrafoil. The widely adopted use of Zernike polynomials to describe the detailed components of the eye's optics has made the use of the term 'irregular' astigmatism largely redundant [Read et al, 2007].

> A recent study investigating corneal topography has classified astigmatism according to the changes occurring in the astigmatism of the peripheral cornea [Read et al, 2006]. Corneal astigmatism was classified as being stable, reducing or increasing in the peripheral cornea.

## **3. Symptoms**

Distortion or blurring of images at all distances is one of the most common astigmatism symptoms. This may happen vertically, horizontally, or diagonally. There can be indistinctness of objects, circles become elongated into ovals and a point of light begins to tail off. Symptoms of eye strain such as headaches [Kaimbo Wa Kaimbo & Missotten, 2003], photophobia, and fatigue are also among the most common astigmatism symptoms. Reading small print is difficult with astigmatism. Other symptoms may include: squinting, eye discomfort, irritation, sore or tired eyes, distortion in the visual field, monocular diplopia, glare, difficulty driving at night…

## **4. Diagnosis**

The evaluation of astigmatism requires an assessment of both patient's history and examination [AAO, 2005]. The history should incorporate the elements of the comprehensive medical eye evaluation in order to consider the patient's visual needs and any ocular pathology.

Evaluations of astigmatism include visual acuity, potential visual acuity, refraction, ultrasonic pachymetry, keratometry, and videokeratography. The depth of the corneal lesion can be measured using an optical pachymeter [Campos et al, 1993]. The combination of manifest refraction, slit-lamp examination, and keratometry is generally sufficient for detecting most anterior abnormalities.

## **4.1 Retinoscopic**

The refractive state of the whole optical pathway is estimated by retinoscopy. Retinoscopy is the initial step in refractometry. It is used to determine the approximate nature and extent of a refractive error and to estimate the type and power of the lens needed to correct the error. Retinoscopy is sometimes referred to as objective refractometry because it requires no participation or response from the patient. The typical patterns of irregular astigmatism are known to the experienced retinoscopist and include "scissoring" of the reflex and jumbled or uninterpretable reflexes.

## **4.2 Wavefront analysis**

This emerging method measures the refractive status of the whole internal ocular light path at selected corneal intercepts of incident light pencils [Harris, 1996]. By comparing the wavefront of a pattern of several small beams of coherent light projected through to the retina with the emerginging reflected light wave front, it is possible to measure the refractive path taken by each beam and to infer the specific spatial correction required on each path.

## **4.3 Keratometric**

Performed with a device called keratometer or ophthalmometer, keratometry is the measurement of a patient's corneal curvature. As such, it provides an objective, quantitative measurement of corneal astigmatism, measuring the curvature in each meridian as well as the axis. Keratometry is also helpful in determining the appropriate fit of contact lenses. The appearance of irregular mires on attempted keratometry is characteristic, sometimes precluding measurement to an aligned endpoint. This is a measure exclusively of the anterior corneal surface irregularity, but it may be affected by the tear film.

The major limitation to keratometry is the assumption that the cornea is a spherocylindrical surface with a single radius of curvature in each meridian, and with a major and minor axis separated by 90 degrees. Additionally, keratometry measures only four points approximately 3 mm apart and provides no information about the cornea central or peripheral to the points measured. Finally, mild corneal surface irregularities can cause mire distortion that precludes meaningful measurement [Wilson & Klyce, 1991]. In most cases, the curvature over the visual axis is fairly uniform, and this simple measurement is sufficiently descriptive. However, keratometry is not useful for measuring corneas that are likely to depart from spherocylindrical optics, as commonly occurs in refractive surgery [Arffa, Klyce & Busin, 1986], keratoconus, and many other corneal abnormalities.

## **4.4 Topographic**

66 Astigmatism – Optics, Physiology and Management

The evaluation of astigmatism requires an assessment of both patient's history and examination [AAO, 2005]. The history should incorporate the elements of the comprehensive medical eye evaluation in order to consider the patient's visual needs and any ocular

Evaluations of astigmatism include visual acuity, potential visual acuity, refraction, ultrasonic pachymetry, keratometry, and videokeratography. The depth of the corneal lesion can be measured using an optical pachymeter [Campos et al, 1993]. The combination of manifest refraction, slit-lamp examination, and keratometry is generally sufficient for

The refractive state of the whole optical pathway is estimated by retinoscopy. Retinoscopy is the initial step in refractometry. It is used to determine the approximate nature and extent of a refractive error and to estimate the type and power of the lens needed to correct the error. Retinoscopy is sometimes referred to as objective refractometry because it requires no participation or response from the patient. The typical patterns of irregular astigmatism are known to the experienced retinoscopist and include "scissoring" of the reflex and jumbled

This emerging method measures the refractive status of the whole internal ocular light path at selected corneal intercepts of incident light pencils [Harris, 1996]. By comparing the wavefront of a pattern of several small beams of coherent light projected through to the retina with the emerginging reflected light wave front, it is possible to measure the refractive path taken by each beam and to infer the specific spatial correction required on

Performed with a device called keratometer or ophthalmometer, keratometry is the measurement of a patient's corneal curvature. As such, it provides an objective, quantitative measurement of corneal astigmatism, measuring the curvature in each meridian as well as the axis. Keratometry is also helpful in determining the appropriate fit of contact lenses. The appearance of irregular mires on attempted keratometry is characteristic, sometimes precluding measurement to an aligned endpoint. This is a measure exclusively of the

The major limitation to keratometry is the assumption that the cornea is a spherocylindrical surface with a single radius of curvature in each meridian, and with a major and minor axis separated by 90 degrees. Additionally, keratometry measures only four points approximately 3 mm apart and provides no information about the cornea central or peripheral to the points measured. Finally, mild corneal surface irregularities can cause mire distortion that precludes meaningful measurement [Wilson & Klyce, 1991]. In most cases, the curvature over the visual axis is fairly uniform, and this simple measurement is sufficiently descriptive. However, keratometry is not useful for measuring corneas that are likely to depart from spherocylindrical optics, as commonly occurs in refractive surgery

anterior corneal surface irregularity, but it may be affected by the tear film.

[Arffa, Klyce & Busin, 1986], keratoconus, and many other corneal abnormalities.

**4. Diagnosis** 

pathology.

**4.1 Retinoscopic** 

or uninterpretable reflexes.

**4.2 Wavefront analysis** 

each path.

**4.3 Keratometric** 

detecting most anterior abnormalities.

The appearance of some patterns of videokeratoscopic irregularity has been described above. They, of course, extend the diagnosis of irregularity using the Placido disc alone.

Corneal topography is frequently used to evaluate irregular astigmatism associated with keratoconus or corneal warpage, to assess the corneal surface after penetrating keratoplasty, and to investigate causes of visual loss of unknown etiology [AAO, 1999]. It is also useful for fitting contact lenses. It has been known for over a century that the cornea is the major refractive element of the eye, and numerous efforts have been made to provide qualitative and quantitative information about the corneal surface. This has not been a simple task given that the cornea possesses an irregular, aspherical surface that is not radially symmetric. These efforts have led to the gradual development of instruments, such as the keratometer, that can analyze the corneal surface. In 1984 Klyse reported combining the videokertaoscope, digital imaging, and a modern high-speed computer, and since then computerized topography has continued to be an evolving technology [Carrol, 1994; Klyce, 1984; Maguire, 1997; Rapuano, 1995; Wilson & Klyce, 1991; Binder, 1995]. Three types of systems are currently used to measure corneal topography, and they are categorized as Placido based, elevation based, and interferometric.

Corneal topography is useful in helping to evaluate patients with unexplained visual loss and in determining and documenting the visual complications from corneal dystrophies, scars, pterygia, recurrent erosions, and chalazia.

Videokeratography is more sensitive than retinoscopy, and it requires less clinical technical expertise and interpretation. Retinoscopy might also be useful to detect irregular astigmatism, but it is difficult to classify the origin of irregular astigmatism from the retinoscopic images.

## **4.5 Clinical**

A common test to confirm the presence of corneal irregularity is its successful correction with a hard contact lens and the improvement of best corrected visual acuity.

## **5. Non-surgical treatment of astigmatism**

The various modes of non surgical treatment of astigmatism include: eyeglasses (spectacles), contact lenses and treatment of the cause.

## **5.1 Eyeglasses**

Eyeglasses are the simplest and safest means of correcting a refractive error (astigmatism), therefore eyeglasses should be considered before contact lenses or refractive surgery [AAO, 2002; AAO, 2007]. A patient's eyeglasses and refraction should be evaluated whenever visual symptoms develop [AAO, 2005]. Patients with low refractive errors (low astigmatism) may not require correction; small changes in astigmatism corrections in asymptomatic patients are generally not recommended [AAO, 2007]. Full correction may not be needed for individuals with regular astigmatism. Adults with astigmatism may not accept full cylindrical correction in their first pair of eyeglasses or in subsequent eyeglasses if their astigmatism has been only partially corrected. In general, substantial changes in axis or power are not well tolerated.

#### **5.1.1 Types and uses of corrective lenses**

Pure cylindrical lenses, or cylinders, differ from spheres in that they have curvature, and thus refractive power, in only one meridian. They may be convex or concave and of any dioptric power. The meridian perpendicular to (90° from) the meridian with curvature is called the axis of the cylinder. By convention, the orientation (position in space) of the cylinder is indicated by the axis, which ranges from 0° (horizontal) through 90° (vertical), and back to 180° (the same as 0°). In contrast to a spherical lens, a cylinder focuses light rays to a focal line rather than to a point. The power meridian is always 90 degrees away from the axis. Therefore, if the axis is 45 degrees, the power meridian is at 135 degrees. A cylinder is specified by its axis. The power of a cylinder in its axis meridian is zero. Maximum power is 90 degrees away from the axis. This is known as the power meridian. The image formed by the power meridian is a focal line parallel to the axis. There is no line focus image formed by the axis meridian, because the axis meridian has no power.

With the rule astigmatism is corrected with a plus cylinder lens between 60 and 120 degrees. Against the rule astigmatism is corrected with a plus cylinder between 150 and 30 degrees. Therefore, oblique astigmatism is from 30 to 59 and 121 to 149 degrees.

Pure cylindrical lenses are used in ophthalmology only for testing purposes. Theoretically, a pure cylindrical lens-one that possesses power in only one meridian-might be used to correct astigmatism. However, most astigmatic individuals are hyperopic or myopic as well and require correction in more than one meridian. To provide the correction they need, a lens formed from the combination of cylinder and sphere is generally required.

#### **5.1.2 Spherocylinders**

A spherocylinder, as its name suggests, is a combination of a sphere and a cylinder. It is sometimes also called a toric lens, but in practice is often referred to as a cylinder for the sake of simplicity. If a spherical lens may be imagined as cut from an object shaped like a basketball, a spherocylindrical lens can be thought of as cut from an object shaped like a **football as rugby ball**. Unlike the spherical "basketball", which has the same curvature over its entire surface, the spherocylindral "**rugby ball**" has different curvatures in each of two perpendicular meridians. The meridian along the length of the **rugby ball** is termed the "flat" meridian, and the one at the **rugby ball's** fat center is termed the "steep" meridian. Because the perpendicular radii of its curvature are not equal, a spherocylinder does not focus light to a single focal point, as does a sphere. Rather, it refracts light along each of its two meridians to two different focal lines.The clearest image is formed at a point between these two focal lines, which is given the geometric term circle of least confusion. The ability of a spherocylindrical lens to refract light along each of two meridians makes it ideal to correct myopia or hyperopia that is combined with astigmatism. The spherocylinder can supply varying amounts of plus and/or minus correction to each of the two principal meridians of the astigmatic eye.

#### **5.2 Contact lenses**

Before contact lens fitting, an ocular history including past contact lens experience should be obtained and a comprehensive medical eye evaluation should be performed [AAO, 2005; AAO, 2007]. Patients should be made aware that using contact lenses can be associated with the development of ocular problems, including microbial corneal ulcers that may be vision threatening, and that overnight wear contact lenses is associated with an increased risk of ulcerative keratitis [Stehr-Green et al, 1987].

Irregular astigmatism occurs when by retinoscopy or keratometry, the principal meridians of the cornea, as a whole, are not perpendicular to one another. Although all eyes have at least a small amount of irregular astigmatism, this term is clinically used only for grossly irregular corneas such as those occurring with keratoconus or corneal scars. Cylindrical spectacle lenses can do little to improve vision in these cases, and so for best optical correction, rigid contact lenses are needed.

High astigmatic errors can be corrected effectively with rigid gas-permeable and hybrid contact lenses. In cases of greater amounts of corneal astigmatism, it may be preferable to use a bitoric or back surface toric contact lens design in order to minimize corneal bearing and improve centration. Aspheric designs may also be useful for this application. Customdesigned soft toric contact lenses provide another means to correct high astigmatic refractive errors. These contact lenses offer good centration when properly fitted, a flexible wear schedule, and improved comfort in some patients. Regardless of the design chosen, adequate contact lens movement is essential for comfortable wear and maintenance of corneal integrity.

#### **5.3 Treatment of the cause**

Treatment of astigmatism may include the management of the associated condition.

### **6. References**

68 Astigmatism – Optics, Physiology and Management

dioptric power. The meridian perpendicular to (90° from) the meridian with curvature is called the axis of the cylinder. By convention, the orientation (position in space) of the cylinder is indicated by the axis, which ranges from 0° (horizontal) through 90° (vertical), and back to 180° (the same as 0°). In contrast to a spherical lens, a cylinder focuses light rays to a focal line rather than to a point. The power meridian is always 90 degrees away from the axis. Therefore, if the axis is 45 degrees, the power meridian is at 135 degrees. A cylinder is specified by its axis. The power of a cylinder in its axis meridian is zero. Maximum power is 90 degrees away from the axis. This is known as the power meridian. The image formed by the power meridian is a focal line parallel to the axis. There is no line focus image formed

With the rule astigmatism is corrected with a plus cylinder lens between 60 and 120 degrees. Against the rule astigmatism is corrected with a plus cylinder between 150 and 30 degrees.

Pure cylindrical lenses are used in ophthalmology only for testing purposes. Theoretically, a pure cylindrical lens-one that possesses power in only one meridian-might be used to correct astigmatism. However, most astigmatic individuals are hyperopic or myopic as well and require correction in more than one meridian. To provide the correction they need, a

A spherocylinder, as its name suggests, is a combination of a sphere and a cylinder. It is sometimes also called a toric lens, but in practice is often referred to as a cylinder for the sake of simplicity. If a spherical lens may be imagined as cut from an object shaped like a basketball, a spherocylindrical lens can be thought of as cut from an object shaped like a **football as rugby ball**. Unlike the spherical "basketball", which has the same curvature over its entire surface, the spherocylindral "**rugby ball**" has different curvatures in each of two perpendicular meridians. The meridian along the length of the **rugby ball** is termed the "flat" meridian, and the one at the **rugby ball's** fat center is termed the "steep" meridian. Because the perpendicular radii of its curvature are not equal, a spherocylinder does not focus light to a single focal point, as does a sphere. Rather, it refracts light along each of its two meridians to two different focal lines.The clearest image is formed at a point between these two focal lines, which is given the geometric term circle of least confusion. The ability of a spherocylindrical lens to refract light along each of two meridians makes it ideal to correct myopia or hyperopia that is combined with astigmatism. The spherocylinder can supply varying amounts of plus and/or minus correction to each of the two principal

Before contact lens fitting, an ocular history including past contact lens experience should be obtained and a comprehensive medical eye evaluation should be performed [AAO, 2005; AAO, 2007]. Patients should be made aware that using contact lenses can be associated with the development of ocular problems, including microbial corneal ulcers that may be vision threatening, and that overnight wear contact lenses is associated with an increased risk of

Irregular astigmatism occurs when by retinoscopy or keratometry, the principal meridians of the cornea, as a whole, are not perpendicular to one another. Although all eyes have at

by the axis meridian, because the axis meridian has no power.

**5.1.2 Spherocylinders** 

meridians of the astigmatic eye.

ulcerative keratitis [Stehr-Green et al, 1987].

**5.2 Contact lenses** 

Therefore, oblique astigmatism is from 30 to 59 and 121 to 149 degrees.

lens formed from the combination of cylinder and sphere is generally required.


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## **Diagnosis and Imaging of Corneal Astigmatism**

Jaime Tejedor1,2 and Antonio Guirao3

*1Hospital Ramón y Cajal, 2Universidad Autónoma de Madrid, 3Universidad de Murcia, Spain* 

### **1. Introduction**

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Accurate diagnosis and measurement of corneal astigmatism is of vital importance for treatment. Refractive and corneal astigmatic power and axis values are correlated but not coincidental. Corneal power and astigmatism amount measurements have a considerable degree of variability, which may be due to systematic error of the devices employed. Test to test variations may be falsely estimated as surgically induced refractive or astigmatic changes. Manual and automated keratometry instruments sometimes yield non-coincidental corneal power and axis readings, with differing reproducibility or repeatability. Even among modern automated keratometry, Placido-disk based videokeratoscopy and advanced slit-scanning or Scheimpflug technology scanning, diverging corneal measurements have been reported, which are attributable to different underlying methodology, reliability and repeatability.

In this chapter, we will summarize the basic functioning principles of the main devices used for the evaluation of corneal power and astigmatism. We will also review published studies about variations in corneal power measurements using different equipment, in astigmatic power and axis calculated values, and correlation obtained among measurements taken with different instruments. Results reported by different authors will be compared with our own data where available.

#### **2. Keratometry**

## **2.1 Principles of keratometry**

A keratometer measures the radius of curvature of a small portion of the central cornea assuming it to be spherical, with constant radius of curvature, and radially symmetrical. Radius is calculated using geometric optics considering the cornea as a spherical reflecting surface (Horner et al, 1998), based on the fact that the front surface of the cornea acts as a convex mirror. The cornea is a high-powered mirror. With a constant distance between the eye and keratometer, the corneal radius is directly proportional to the size of the reflected image it produces (Purkinje I) and indirectly proportional to the size of the object (see Figure 1). To measure the size of the image relative to the object, the tiny image has to be magnified (American Academy of Ophthalmology [AAO], 2005). Because the eye is constantly moving, with 2 base to base prisms positioned so that the baseline splits the pupil, the observer sees two images separated by a fixed amount (Rabbetts, 1998). Any oscillation of the cornea will affect both images, and separation between them will not change (doubling principle). Therefore, the observer may arrive to the desired measurement position more easily.

Fig. 1. Schematic diagram presented to illustrate the principles of keratometry. The cornea is a spherical reflecting surface or mirror. An illuminated object of known size or height (h) is placed at a known distance from the cornea. By similar triangles, the ratio of object height to distance (x, distance from mires to convex mirror focal plane, approximated by d, distance from the mires to the image) equals the ratio of image size (h') to focal distance (-f). The radius of curvature, which is twice the focal distance, is then calculated. u: distance from object to cornea; v: distance from cornea to image; c: center of curvature of the cornea.

Keratometers do not measure refractive power of the cornea. Measurements of radius of curvature, r (meters) can be converted to power, P (diopters) using the formula P= (n2-n1)/r, where n1 is the refractive index of the first medium, and n2, refractive index of the second medium. It applies to the anterior (air-cornea) and posterior (cornea-aqueous) corneal surface, but the curvature of the posterior corneal surface is not actually measured, estimating the total corneal power by a reduced refractive index, standard keratometric index (usually n= 1.3375), that takes into account the negative power of about -6.00 diopters of the corneal back surface (Corbett et al, 1999). Because the refractive index of air is n1= 1, P= 0.3375/r. Helmholtz and other early designers of keratometers were interested in measuring the contribution of the cornea to the refractive power of the eye, as if the cornea was a lens with a single refracting surface. Theoretically, if one wishes to know the refractive power of only the anterior corneal surface, one must multiply the dioptric reading on the keratometer by a factor of 1.114 to correct for Helmholtz's fudge factor (Krachmer & Mannis, 2005). Javal and Schiötz chose 1.3375 as calibration index probably influenced by the fact that 7.5 mm corresponds exactly to 45 D (Haag-Streit), and that in normal corneas the posterior radius of curvature averages 1.2 mm less than that of the anterior surface. Several studies showed that this power overestimates the total power of the cornea by approximately 0.56 D. Other manufacturers adopted 1.332 or 1.336 as calibration index, which many authors consider the best choice because it is the accepted value for the refractive index of tears and the aqueous humor. The anterior radius of the cornea and a net index of refraction of 4/3 (1.333) is commonly used today to calculate the net power of the cornea. Using this lower value, the total power of a cornea with an anterior radius of 7.5 mm

Fig. 1. Schematic diagram presented to illustrate the principles of keratometry. The cornea is a spherical reflecting surface or mirror. An illuminated object of known size or height (h) is placed at a known distance from the cornea. By similar triangles, the ratio of object height to distance (x, distance from mires to convex mirror focal plane, approximated by d, distance from the mires to the image) equals the ratio of image size (h') to focal distance (-f). The radius of curvature, which is twice the focal distance, is then calculated. u: distance from object to cornea; v: distance from cornea to image; c: center of curvature of the cornea.

Keratometers do not measure refractive power of the cornea. Measurements of radius of curvature, r (meters) can be converted to power, P (diopters) using the formula P= (n2-n1)/r, where n1 is the refractive index of the first medium, and n2, refractive index of the second medium. It applies to the anterior (air-cornea) and posterior (cornea-aqueous) corneal surface, but the curvature of the posterior corneal surface is not actually measured, estimating the total corneal power by a reduced refractive index, standard keratometric index (usually n= 1.3375), that takes into account the negative power of about -6.00 diopters of the corneal back surface (Corbett et al, 1999). Because the refractive index of air is n1= 1, P= 0.3375/r. Helmholtz and other early designers of keratometers were interested in measuring the contribution of the cornea to the refractive power of the eye, as if the cornea was a lens with a single refracting surface. Theoretically, if one wishes to know the refractive power of only the anterior corneal surface, one must multiply the dioptric reading on the keratometer by a factor of 1.114 to correct for Helmholtz's fudge factor (Krachmer & Mannis, 2005). Javal and Schiötz chose 1.3375 as calibration index probably influenced by the fact that 7.5 mm corresponds exactly to 45 D (Haag-Streit), and that in normal corneas the posterior radius of curvature averages 1.2 mm less than that of the anterior surface. Several studies showed that this power overestimates the total power of the cornea by approximately 0.56 D. Other manufacturers adopted 1.332 or 1.336 as calibration index, which many authors consider the best choice because it is the accepted value for the refractive index of tears and the aqueous humor. The anterior radius of the cornea and a net index of refraction of 4/3 (1.333) is commonly used today to calculate the net power of the cornea. Using this lower value, the total power of a cornea with an anterior radius of 7.5 mm would be 44.44 D. A useful rule of thumb is that a radius of difference of 0.2 mm indicates approximately 1 D of corneal astigmatism, for average radii and small amounts of astigmatism (Howes, 2009). For an estimation of only the front surface power of the cornea, a refractive index of 1.376 should be used, which is the true corneal index.

Calculations are based on the geometry of a spherical reflecting surface (Horner et al), although the cornea is described as prolate, flattening from center to periphery, and ellipsoid (i.e., true apical radius is steeper than measured, and steeper than the peripheral cornea). Quantitative data are based on only four points in the central 3 millimeters ring mire of the cornea in the standard keratometer, but different types of keratometer use differently sized mires at differing separations. Therefore, it provides gross qualitative indication of corneal regularity between them. Keratometry assumes paraxial optics, and is not valid when higher accuracy is required or peripheral areas have to be measured. When the cornea differs from a spherocylindrical surface lens, the keratometer does not measure it accurately.

Other limitations of keratometry are: (1) the assumption that the corneal apex, line of sight, and axis of the instrument coincide, which is not usually true, (2) the formula approximates the distance to focal point by the distance to image, (3) the power in diopters depends on an assumed index of refraction, and (4) the "One-position" instruments, in which it is possible to measure two orthogonal meridians without rotating the instrument, assume regular astigmatism (Horner et al, 1998).

Keratometers measure corneal astigmatism as the difference between the powers of the two principal meridians, and they have been the classical devices used to determine astigmatism of the cornea.

## **2.2 Types of keratometer**

There are two main types of keratometer, manual and automated keratometers.

## **2.2.1 Representative models of manual keratometer**

In the Javal-Schiötz keratometer (1880), the doubling is fixed and the separation of the mires is varied by moving them symmetrically round a circular path approximately concentric with the cornea under test (Rabbetts, 1998). In the traditional pattern, one the mires is red and the other green, and they have to be set in apposition to measure the flatter and steeper meridian (two-position keratometer), any overlap producing yellow. In off-axis position with respect to the cornea, the black central line of one mire image becomes out of alignment with its fellow on the other mire. Scissors distortion may also be apparent.

Another commonly used keratometer is the Bausch and Lomb keratometer (1932). Mire separation (object size) is fixed and doubling variable (image size measured). It is the typical one-position instrument in current use (Rabbetts, 1998). A lamp bulb illuminates the circular mire, and three images of the mire are seen in the eyepiece, a central one and two others doubled in mutually perpendicular directions. The central image appears slightly doubled unless in correct focus. Plus and minus signs surrounding the circular mires are used as measurement marks. When correct meridional alignment has been established, the two radius settings can be made in sequence by adjusting the doubling, when the adjacent plus and minus signs are brought into exact coincidence. There is a fixation point for the patient who sees a reflection of his own eye.

The range of measurement of the keratometer is frequently from 36.00 to 52.00 D, but in some cases it is very wide, from 28.00 to 60.00 D (Topcon OM-4).

## **2.2.2 Automated keratometers**

The Humphrey autokeratometer measures corneal curvature by projecting three beams of near infrared light on to the cornea in a triangular pattern within an area about 3 mm in diameter. After reflection, they are received by directional photo-sensors which effectively isolate rays making a predetermined angle with the instrument's optical axis. This recalls a variable doubling keratometer in which the mires subtend a constant angle at the cornea. The source is a light-emitting diode (LED) and the ray paths are reversed. The precise location of the reflection point on the cornea is determined by the position of a rotating chopper which sweeps across all three beams and is imaged in the plane of the cornea by a projector lens. From the information provided by the three beams, the principal radii and meridians of the cornea can be calculated. At the start, the patient fixates a central red LED while the instrument is aligned by the operator and monitoring systems (Rabbetts, 1998).

Canon, Nidek, and Topcon have their respective auto-keratometers, usually combined with an auto-refractor. In Canon models an annular lens projects collimated light from a ring mire on to the cornea. The mire reflection is projected on to a detector system consisting of five sectors. From the light distribution on each of these sectors the computer is able to calculate the corneal radii. The diameter of the measuring zone is slightly larger than that of the Bausch and Lomb instrument. In the Topcon instrument, the observation system is telecentric, and a pinhole aperture restricts the rays reflected from the cornea to paths parallel to the instrument's axis (Rabbetts, 1998). Diameter of corneal zone measured varies among automated keratometers. For example, Nidek ARK510A uses 3.3 mm, whereas Humphrey ARK599 uses 3.0 mm. However the IOLMaster incorporated keratometer utilizes a 2.3 mm measurement diameter (Goggin et al, 2010).

The Scheiner principle is the basis of many automated refractors, which also give keratometry (MacInnis, 1994). Using a double aperture system, when the object of regard is placed conjugate to the retina a single clear image is formed. Under a condition of ametropia, the image is double, and can be converted to a single image with an optometer. This can be done by focusing visible or infrared light on the retina, and different meridians could be measured to determine astigmatism.

## **3. Computerized corneal topography**

Corneal power and astigmatism may be measured also using computerized devices. Methods for measuring corneal topography fall into two broad categories: reflection-based and projection-based methods.

### **3.1 Reflection-based methods**

Videokeratoscopy arose from the desire of investigators to quantitate the corneal shape information available in keratoscope images. Keratoscopes were designed more than 100 years ago, when investigators realized that the diseased cornea could have a curvature that differed significantly from a spherocylindrical lens. The keratoscopes project an illuminated target, more complex than that of keratometers, to generate an image reflected by the corneal surface. Reflection-based methods commonly take the form of Placido-disk type concentric rings. The images of multiple reflected luminous concentric circles projected on the corneal surface are digitally analyzed. Therefore, curvature of the posterior cornea is not actually measured. The position of each point to be measured on the many circle mires from the center to the periphery of the cornea should be determined first. Most systems measure

The Humphrey autokeratometer measures corneal curvature by projecting three beams of near infrared light on to the cornea in a triangular pattern within an area about 3 mm in diameter. After reflection, they are received by directional photo-sensors which effectively isolate rays making a predetermined angle with the instrument's optical axis. This recalls a variable doubling keratometer in which the mires subtend a constant angle at the cornea. The source is a light-emitting diode (LED) and the ray paths are reversed. The precise location of the reflection point on the cornea is determined by the position of a rotating chopper which sweeps across all three beams and is imaged in the plane of the cornea by a projector lens. From the information provided by the three beams, the principal radii and meridians of the cornea can be calculated. At the start, the patient fixates a central red LED while the instrument is aligned by the operator and monitoring systems (Rabbetts, 1998). Canon, Nidek, and Topcon have their respective auto-keratometers, usually combined with an auto-refractor. In Canon models an annular lens projects collimated light from a ring mire on to the cornea. The mire reflection is projected on to a detector system consisting of five sectors. From the light distribution on each of these sectors the computer is able to calculate the corneal radii. The diameter of the measuring zone is slightly larger than that of the Bausch and Lomb instrument. In the Topcon instrument, the observation system is telecentric, and a pinhole aperture restricts the rays reflected from the cornea to paths parallel to the instrument's axis (Rabbetts, 1998). Diameter of corneal zone measured varies among automated keratometers. For example, Nidek ARK510A uses 3.3 mm, whereas Humphrey ARK599 uses 3.0 mm. However the IOLMaster incorporated keratometer utilizes

The Scheiner principle is the basis of many automated refractors, which also give keratometry (MacInnis, 1994). Using a double aperture system, when the object of regard is placed conjugate to the retina a single clear image is formed. Under a condition of ametropia, the image is double, and can be converted to a single image with an optometer. This can be done by focusing visible or infrared light on the retina, and different meridians

Corneal power and astigmatism may be measured also using computerized devices. Methods for measuring corneal topography fall into two broad categories: reflection-based

Videokeratoscopy arose from the desire of investigators to quantitate the corneal shape information available in keratoscope images. Keratoscopes were designed more than 100 years ago, when investigators realized that the diseased cornea could have a curvature that differed significantly from a spherocylindrical lens. The keratoscopes project an illuminated target, more complex than that of keratometers, to generate an image reflected by the corneal surface. Reflection-based methods commonly take the form of Placido-disk type concentric rings. The images of multiple reflected luminous concentric circles projected on the corneal surface are digitally analyzed. Therefore, curvature of the posterior cornea is not actually measured. The position of each point to be measured on the many circle mires from the center to the periphery of the cornea should be determined first. Most systems measure

**2.2.2 Automated keratometers** 

a 2.3 mm measurement diameter (Goggin et al, 2010).

could be measured to determine astigmatism.

**3. Computerized corneal topography** 

and projection-based methods.

**3.1 Reflection-based methods** 

between 256 and 360 points around the circumference of each mire, but leave unmeasured the areas between the mires (Krachmer & Mannis, 2005). Videokeratoscopes commonly use a polar coordinate system to identify a specific corneal position relative to the center of the image, at a distance from the center and at a defined angular position. The image is twodimensional, and doesn't provide information on changes in corneal elevation.

When axial measurements are taken (Corbett et al, 1999), these units assume the angle of incidence to be nearly perpendicular, and the radius of curvature to be the distance from the corneal surface to the intersection with the visual axis or line of sight of the patient (axial distance). The slope of a curved surface is the gradient of the tangent at a particular point (first differential of a curve). Slope could be referred to as the angle (θ) between the tangent vector of the curve at that point and the x unit vector or center corneal axis. It is converted to radius of curvature by the equation r= d/cos θ, where d is the distance from the point on the corneal surface to the axis. Curvature is given by к= dθ/ds, where s is the arclength parameter, and amounts to к= |y''|/ [1 + (y')2]3/2. Axial maps curvature values approximate the power of the central 2-4 mm of the cornea, where sphericity may be assumed. From these values, an iterative process algorithm is used, making a series of assumptions, to describe the shape and power of the peripheral cornea with less accuracy, because elevation of a point in the z-axis cannot be determined directly by reflection-based methods. Variable degrees of surface smoothing are incorporated in the algorithms. The only position on the surface at which axial measurements are an accurate reflection of local refractive power is in the paraxial portion of the cornea. Normal corneas show decreasing power toward the periphery as displayed by the Placido-disk based topographers, which intuitively indicates the normal flattening of the cornea, but does not represent the true refractive powers. Based on Snell's law, the corneal power must increase in the periphery, due to the increasing angle of incidence, in order to refract the light into the pupil (spherical aberration).

In tangential maps, the instantaneous radius of curvature is calculated at a certain point (Horner et al, 1998; Corbett et al, 1999). The radius corresponds to the sphere with the same curvature at that point, determined by taking a perpendicular path through the point in question, in a plane that intersects the point and the visual axis, but not based on distance to the axis. Stated another way, local radius of curvature is calculated at each point with respect to its neighbouring points by estimation of the best-fit sphere, without reference to the visual axis or the overall shape of the cornea. There is greater accuracy in the periphery of the cornea and in representing local changes. Tangential maps show less smoothing of the curvature than axial maps.

The maps described attempt to depict the underlying shape of the cornea by scaling curvature through the familiar dioptric notation instead of radius millimeters, and powers are then mapped using standard colors to represent diopter changes. Diopters are relative units of curvature but not the equivalent of diopters of corneal power (Figure 2).

To represent shape directly, maps may display a z height from an arbitrary plane (iris, limbus, best-fit or reference sphere), plotted to show differences but not directly clinically important data, although the z values are frequently used to derive radius of curvature at that point.

#### **3.2 Projection-based methods**

In projection-based methods, an image is formed on the cornea, frequently using a slit beam scan, but sometimes by a grid pattern, Moiré interference fringes, or laser interferometry. Height or elevation data measurements above a reference plane are immediately available

Fig. 2. Reflection-based system videokeratography. Using Alcon Eye Map EH-290, 1.4 D of corneal astigmatism, with an ellipsoid-bow tie intermediate pattern color map, is depicted.

from these systems (Corbett et al, 1999). Slope and curvature data can be calculated directly. Axial and tangential maps can also be obtained using these devices. These systems provide a more sensitive measure of variation in contour across the corneal surface, particularly in terms of slope and curvature. Refractive power measures derived are less accurate, due to the assumptions and approximations made during its calculation.

In slit-scanning systems, the machines project a series of slit beams at closely spaced intervals across the cornea. The computer software identifies the location of the anterior and posterior corneal margins of each individual slit section, and by smoothing digitized information, infers the shape and corneal thickness (Krachmer & Mannis, 2005). The resultant smoothed data in the Orbscan, a commercially available instrument that performs these functions, include anterior corneal curvature, posterior corneal curvature, and regional differences in corneal thickness between them. A color coding scheme is used for anterior corneal curvature, posterior corneal curvature and regional pachymetry maps. Output artifact under certain situations like opacities of the stroma, or inaccurate digitizing of the posterior corneal surface, anterior to the real posterior cornea, when measuring post-LASIK corneas, may occur.

Fig. 2. Reflection-based system videokeratography. Using Alcon Eye Map EH-290, 1.4 D of corneal astigmatism, with an ellipsoid-bow tie intermediate pattern color map, is depicted. from these systems (Corbett et al, 1999). Slope and curvature data can be calculated directly. Axial and tangential maps can also be obtained using these devices. These systems provide a more sensitive measure of variation in contour across the corneal surface, particularly in terms of slope and curvature. Refractive power measures derived are less accurate, due to

In slit-scanning systems, the machines project a series of slit beams at closely spaced intervals across the cornea. The computer software identifies the location of the anterior and posterior corneal margins of each individual slit section, and by smoothing digitized information, infers the shape and corneal thickness (Krachmer & Mannis, 2005). The resultant smoothed data in the Orbscan, a commercially available instrument that performs these functions, include anterior corneal curvature, posterior corneal curvature, and regional differences in corneal thickness between them. A color coding scheme is used for anterior corneal curvature, posterior corneal curvature and regional pachymetry maps. Output artifact under certain situations like opacities of the stroma, or inaccurate digitizing of the posterior corneal surface, anterior to the real posterior cornea, when measuring post-LASIK

the assumptions and approximations made during its calculation.

corneas, may occur.

A rotating Scheimpflug camera generates Scheimpflug images in three dimensions in Pentacam and Galilei systems. In no more than 2 seconds a complete image of the anterior segment is generated. Any eye movement may be detected by a second camera and corrected for in the process. Scheimpflug images are digitalized and transferred, and a 3D virtual model of the anterior eye segment is calculated. Anterior and posterior cornea elevation and curvature data are thus obtained. Corneal thickness is consequently derived.

High-frequency ultrasound and optical coherence tomography are techniques for corneal imaging, at an early stage of development for three-dimensional reconstruction of the cornea.

## **4. Definitions for the evaluation of corneal measurement devices**

Accuracy refers to the degree of closeness of measurements of a quantity to its actual (true) value (validity). In accurate measurements the systematic error is small.

Precision of a measurement system, including repeatability and reproducibility, is the degree to which repeated measurements under unchanged conditions show the same results (reliability). Measurements are precise when the random error is small. Repeatability is usually considered as the variability of the measurements obtained by one same person (intraobserver) while measuring the same item repeatedly, under the same conditions and over a short period of time. When two measurements are taken using the same device, coefficient of repeatability may be calculated as COR= 1.96 x Standard Deviation (of difference between the two measurements). Reproducibility is the variability of the measurement system caused by differences in operator behavior, or variability of the average values obtained by several operators (interobserver) while measuring the same item.

## **5. Evaluation of the cornea using keratometry**

Keratometry may be used not only to estimate the dioptric curvature of the anterior ("total") cornea and infer astigmatism but also to evaluate the quality of the corneal surface. In the presence of pathology in the central visual axis, keratometric mires would be irregular. Every time readings are taken, the quality of the mires should be described as regular, when they overlap perfectly, or mildly to markedly irregular, when they do not overlap perfectly (Krachmer & Mannis, 2005). These patterns may help to predict best-corrected visual acuity, because the examiner can judge with some certainty the visual potential from the anterior corneal surface abnormalities. In patients with keratoconus, inferior corneal steepening is easily observed by taking readings with the patient looking straight ahead and subsequently looking up slowly. Inferior steepening is present when the vertical mires slowly spread apart and get smaller. For most normal corneas, keratometry is sufficiently accurate for contact lens fitting and intraocular lens power calculation.

An important limitation of keratometry is the measurement of the cornea following LASIK or PRK procedures. The measurements are not accurate because the assumed net index of refraction is no longer appropriate for the new relationship of the front and back radius of the cornea. Following keratorefractive surgery, the assumptions that the central cornea may be approximated by a sphere and that the radius of curvature of the posterior cornea is 1.2 mm less than that of the anterior cornea, are no longer true (Howes, 2009). Automated keratometers which sample a smaller central area of the cornea (about 2.6 mm) relative to manual keratometers, provide more accurate values of the front radius of the cornea, because the transition areas are far outside the zone that is measured. However, measures of the cornea are still not accurate. Automated and manual keratometers overestimate the power of the cornea proportionately to the amount of LASIK or PRK performed (by approximately 14%).

The accuracy and precision of keratometry depends largely on the care with which the instrument to cornea distance is adjusted, which requires accurate focusing of the eyepiece upon its graticule, especially in manual keratometers, and alignment of the instrument with the patient's eye. The latter is not always easy due to the small field of view, and isolated areas of the objective aperture, in instruments with doubling systems, with an exit pupil of possibly 3 mm overall diameter. The instrument utilizes small reflected areas no less than 1 mm and up to 1.7 mm from the center (Rabbetts, 1998). Because of the peripheral flattening, keratometer readings are slightly longer than the vertex radius. The error would probably not exceed 0.05 mm on a normal eye. A local distortion of the cornea in the region of the reflection areas will cause a corresponding distortion of the mires and uncertain focusing. Since the image is formed by reflection from the tear layer, variations in it may affect the quality and size of the image. The limits set by diffraction on the accuracy of keratometers indicate that the limit on repeatability could be no lower than 0.2 D, corresponding to a spread of about 0.04 mm on average radii. Reported accuracy of the Bausch and Lomb keratometer measurements vary from ± 0.25 D to ± 0.93 D (Rabbetts, 1998).

Repeatability of corneal power measurements with keratometer is good, but with different levels of precision depending on the study. Mean difference between the measured and actual surface power using Bausch and Lomb keratometer (Karabatsas et al, 1998) in four steel balls (2.7 mm to 3.4 mm radius of curvature) was -0.11 D (SD 0.09). Karabatsas et al found a coefficient of repeatability for intraobserver measurements of 0.22 D for steep meridian power and 0.18 D for flat meridian power, using 10 SL/O Zeiss keratometer. For steep and flat meridian axis, COR was 5° to 8°, and for astigmatism COR was between 0.20 D and 0.26 D, with the same device. Interobserver COR for steep axis power was 0.24 D, and for flat axis power was 0.20 D. For steep and flat meridian axis COR was 8°, and for astigmatism, COR was 0.28 D. In postkeratoplasty corneas, COR was greater than in normal corneas, but better than using topographic maps.

Elliott et al reported (Elliott et al, 1998) that Bausch and Lomb manual keratometer showed poorer repeatability than automated keratometry devices (Nikon NRK-8000 and Nidek KM-800). Coefficient of repeatability values for the vertical, torsional, and horizontal meridians were 0.55 D, 0.42 D and 0.70 D, respectively, for the B&L keratometer. However, the Nikon coefficients of repeatability for the same meridians were, respectively, 0.34 D, 0.23 D, and 0.27 D, whereas the Nidek values were, respectively, 0.34 D, 0.18 D, and 0.32 D. The same conclusion is reached by Shirayama et al, who measured repeatability as coefficient of variation (ratio of the SD of the repeated measurements to the mean in %), to study B&L manual keratometer and IOL Master, in addition to different topographer devices (Shirayama et al, 2009). IOL Master showed a CV of 0.09 (±0.07) and B&L manual keratometer showed a CV of 0.18 (±0.12). However, Intraclass correlation (ICC) was high with the two devices (0.99 in both keratometers). In this study, automated keratometry had also higher repeatability than Galilei Dual Scheimpflug analyzer and Humphrey Atlas Corneal Topographer. These devices had CV of 0.12 (±0.07) and 0.22 (±0.12), respectively, with B&L manual keratometry in an intermediate position between the two. ICC of the

manual keratometers, provide more accurate values of the front radius of the cornea, because the transition areas are far outside the zone that is measured. However, measures of the cornea are still not accurate. Automated and manual keratometers overestimate the power of the cornea proportionately to the amount of LASIK or PRK performed (by

The accuracy and precision of keratometry depends largely on the care with which the instrument to cornea distance is adjusted, which requires accurate focusing of the eyepiece upon its graticule, especially in manual keratometers, and alignment of the instrument with the patient's eye. The latter is not always easy due to the small field of view, and isolated areas of the objective aperture, in instruments with doubling systems, with an exit pupil of possibly 3 mm overall diameter. The instrument utilizes small reflected areas no less than 1 mm and up to 1.7 mm from the center (Rabbetts, 1998). Because of the peripheral flattening, keratometer readings are slightly longer than the vertex radius. The error would probably not exceed 0.05 mm on a normal eye. A local distortion of the cornea in the region of the reflection areas will cause a corresponding distortion of the mires and uncertain focusing. Since the image is formed by reflection from the tear layer, variations in it may affect the quality and size of the image. The limits set by diffraction on the accuracy of keratometers indicate that the limit on repeatability could be no lower than 0.2 D, corresponding to a spread of about 0.04 mm on average radii. Reported accuracy of the Bausch and Lomb

Repeatability of corneal power measurements with keratometer is good, but with different levels of precision depending on the study. Mean difference between the measured and actual surface power using Bausch and Lomb keratometer (Karabatsas et al, 1998) in four steel balls (2.7 mm to 3.4 mm radius of curvature) was -0.11 D (SD 0.09). Karabatsas et al found a coefficient of repeatability for intraobserver measurements of 0.22 D for steep meridian power and 0.18 D for flat meridian power, using 10 SL/O Zeiss keratometer. For steep and flat meridian axis, COR was 5° to 8°, and for astigmatism COR was between 0.20 D and 0.26 D, with the same device. Interobserver COR for steep axis power was 0.24 D, and for flat axis power was 0.20 D. For steep and flat meridian axis COR was 8°, and for astigmatism, COR was 0.28 D. In postkeratoplasty corneas, COR was greater than in normal

Elliott et al reported (Elliott et al, 1998) that Bausch and Lomb manual keratometer showed poorer repeatability than automated keratometry devices (Nikon NRK-8000 and Nidek KM-800). Coefficient of repeatability values for the vertical, torsional, and horizontal meridians were 0.55 D, 0.42 D and 0.70 D, respectively, for the B&L keratometer. However, the Nikon coefficients of repeatability for the same meridians were, respectively, 0.34 D, 0.23 D, and 0.27 D, whereas the Nidek values were, respectively, 0.34 D, 0.18 D, and 0.32 D. The same conclusion is reached by Shirayama et al, who measured repeatability as coefficient of variation (ratio of the SD of the repeated measurements to the mean in %), to study B&L manual keratometer and IOL Master, in addition to different topographer devices (Shirayama et al, 2009). IOL Master showed a CV of 0.09 (±0.07) and B&L manual keratometer showed a CV of 0.18 (±0.12). However, Intraclass correlation (ICC) was high with the two devices (0.99 in both keratometers). In this study, automated keratometry had also higher repeatability than Galilei Dual Scheimpflug analyzer and Humphrey Atlas Corneal Topographer. These devices had CV of 0.12 (±0.07) and 0.22 (±0.12), respectively, with B&L manual keratometry in an intermediate position between the two. ICC of the

keratometer measurements vary from ± 0.25 D to ± 0.93 D (Rabbetts, 1998).

corneas, but better than using topographic maps.

approximately 14%).

corneal topographer devices was similar to that showed by keratometers (0.99). When results of power measurements were compared between the four devices, all devices were significantly correlated with each other (Pearson correlation coefficient= 0.99 in all pairs).

## **6. Use of topographic maps in the evaluation of the cornea**

The videokeratoscopy image may be examined in a specific fashion to detect alterations of normal concentric pattern, checking for artifacts (Maguire, 2005) when total and astigmatic corneal power is obtained. Focal tear film abnormalities appear as localized mire distortions, which may be caused by epithelial irregularity, mucus in the tear film, or exaggerated tear meniscus in the upper or lower lid. Central mires may be inspected to detect evidence of irregular astigmatism. Irregular astigmatism causes the mire to have an egg shape, or some other shape that differs from the circular or the elliptical shape corresponding to a cornea that approximates a spherocylindrical lens. When the space between adjacent mires reduces from the central to the peripheral cornea, the cornea is steepening, whereas wider spacing indicates relative flattening.

Placido disc or reflection-based topography units do not have the ability to measure the central 1.8 to 2.0 mm of cornea, and this information is currently extrapolated from the smallest reflected ring. This information from the central cornea is most important, since this is the crucial pathway for light through the pupil. Photoreceptor alignment weighs this central light more importantly, thus accounting for the Stiles-Crawford effect. Increasingly important is the ability to precisely measure the posterior cornea as opposed to their merely relying on the assumed relationship that exists between the anterior and posterior surfaces, as occurs in reflection-based systems, when only effective measures of the anterior cornea are obtained. This relationship does not hold constant when a corneal injury or keratorefractive surgery alters the anterior corneal curvature only. As a result, our estimation of overall or true corneal power includes potential error in these eyes, as previously described for keratometry. This is considered the predominant source of error when trying to calculate IOL power in patients who have undergone previous corneal refractive surgery.

A problem reported soon in the development of Placido-based systems was the susceptibility to errors in alignment and focusing. A small error of alignment or focusing in a test sphere (0.2 mm) can cause a fairly significant change in the measurement (Horner et al, 1998). Vertical misalignment can cause asymmetry that might be mistaken as early keratoconus. Where the videokeratoscope axis intersects the cornea with respect to the references of the eye remains a challenge. The geometric center of the cornea (anatomic center equidistant from opposite limbuses) or corneal apex (point of greatest sagittal height, z) may be a useful reference for contact lens design, but from an optical point of view, the pupillary axis (line from the center of the entrance pupil perpendicular to the corneal surface), line of sight (straight line from the fixation point to the center of the entrance pupil), or visual axis (ray from the fixation point that passes undeviated, through the nodal points, to the fovea), could be used as reference for these instruments. Mandell suggested the point where the line of sight intersects the cornea as a useful reference, whereas the visual axis, and its corneal intercept, is difficult to locate objectively (Mandell & Horner, 1993). However, when alignment of the instrument is implemented by manual or automated means, the axis of the videokeratograph becomes normal to the cornea, and passes through the center of curvature of the cornea and the coaxially sighted reflex centre, i.e., the site of the corneal light reflex when the cornea is viewed coaxially with the light source. This point is nasally displaced, but considered to be closer to the corneal intercept of the visual axis than to the corneal intercept of the line of sight. Mandell examined this issue in detail (Mandell, 1994). In no case was the corneal intercept of the line of sight on the instrument axis, and infrequently the apex position was on the videokeratograph axis.

Another cause of spurious topography is irregularities in the tear film, particularly in reflection-based systems, because videokeratoscopes image the air-tear interface, and not exactly the corneal epithelium (Corbett et al, 1999). Pooling of tears in the lower meniscus produces a focal steepening, and thinning of the tear film by drying shows a localized flattening of the surface. Poor tear quality can interfere with the accuracy of the measurements in different ways, but some of these artifacts can be overcome by asking the patient to blink immediately before the image is captured.

Color-coded maps were initially developed for videokeratoscopy (Corbett et al, 1999). The warmer colors (red, orange, yellow) represented the steeper areas, whereas the cooler colors (green, blue) marked the flatter zones. A similar color-coded scale was applied to height maps with the introduction of projection-based systems, in which the high areas were depicted by warm colors, and the low areas by cool colors.

It is important to check the type of scale on the map under study. The label on the scale gives the type of measurement being displayed: height (mm or µm), slope (adimensional or mm/mm), curvature (mm), or power (diopters). The first step before studying the map is to check the number of steps, interval between the steps, and the range covered by the scale. Many systems enable the user to choose between a standardized absolute scale, in which there is a fixed color-coding, that is, the same colors always represent the same curvatures or powers, and the same for all subjects, and a normalized relative scale, in which the number of colors are automatically adjusted to the range of diopter values in that single map. In an adjustable scale map, the operator may select the step interval and diopter range of the contour (Corbett et al, 1999).

Height, curvature or power data can be presented as a plot of difference from a flat reference plane, a sphere of known size or an idealized corneal shape. Different commercial systems give indices of different names, which summarize a particular feature of the cornea. These include simulated keratometry (equivalent but not similar to measurements of keratometer), asphericity, surface asymmetry index (difference in corneal power between points 180° apart in the same ring), inferior-superior value (difference between superior and inferior points 3 mm from the center), surface regularity index (local regularity of the corneal surface in the central 4.5 mm diameter), index of surface variance (deviation of individual corneal radii from the mean value), index of vertical asymmetry (degree of symmetry of corneal radii with respect to the horizontal meridian). Some of these indices correlate with visual function or potential visual acuity. A keratoconus index is also presented by different systems. Using information from this and other indices, and additional clinical data, an index of suspicion of keratoconus or keratoconus level classification may be obtained. Anterior and posterior surface elevation data shown by slitscanning or Scheimpflug photography systems also help diagnose keratoconus (typically, differences greater than +15 µm for anterior elevation indicate keratoconus).

Some authors have classified the topography of normal corneas according to the shape of the contour corresponding to the middle of the scale, in five patterns: round, oval, symmetric bow tie, asymmetric bow tie, and irregular (Bogan et al, 1990). The videokeratoscopic representation of corneal regular astigmatism (toric surface) has the

the corneal light reflex when the cornea is viewed coaxially with the light source. This point is nasally displaced, but considered to be closer to the corneal intercept of the visual axis than to the corneal intercept of the line of sight. Mandell examined this issue in detail (Mandell, 1994). In no case was the corneal intercept of the line of sight on the instrument

Another cause of spurious topography is irregularities in the tear film, particularly in reflection-based systems, because videokeratoscopes image the air-tear interface, and not exactly the corneal epithelium (Corbett et al, 1999). Pooling of tears in the lower meniscus produces a focal steepening, and thinning of the tear film by drying shows a localized flattening of the surface. Poor tear quality can interfere with the accuracy of the measurements in different ways, but some of these artifacts can be overcome by asking the

Color-coded maps were initially developed for videokeratoscopy (Corbett et al, 1999). The warmer colors (red, orange, yellow) represented the steeper areas, whereas the cooler colors (green, blue) marked the flatter zones. A similar color-coded scale was applied to height maps with the introduction of projection-based systems, in which the high areas were

It is important to check the type of scale on the map under study. The label on the scale gives the type of measurement being displayed: height (mm or µm), slope (adimensional or mm/mm), curvature (mm), or power (diopters). The first step before studying the map is to check the number of steps, interval between the steps, and the range covered by the scale. Many systems enable the user to choose between a standardized absolute scale, in which there is a fixed color-coding, that is, the same colors always represent the same curvatures or powers, and the same for all subjects, and a normalized relative scale, in which the number of colors are automatically adjusted to the range of diopter values in that single map. In an adjustable scale map, the operator may select the step interval and diopter range of the

Height, curvature or power data can be presented as a plot of difference from a flat reference plane, a sphere of known size or an idealized corneal shape. Different commercial systems give indices of different names, which summarize a particular feature of the cornea. These include simulated keratometry (equivalent but not similar to measurements of keratometer), asphericity, surface asymmetry index (difference in corneal power between points 180° apart in the same ring), inferior-superior value (difference between superior and inferior points 3 mm from the center), surface regularity index (local regularity of the corneal surface in the central 4.5 mm diameter), index of surface variance (deviation of individual corneal radii from the mean value), index of vertical asymmetry (degree of symmetry of corneal radii with respect to the horizontal meridian). Some of these indices correlate with visual function or potential visual acuity. A keratoconus index is also presented by different systems. Using information from this and other indices, and additional clinical data, an index of suspicion of keratoconus or keratoconus level classification may be obtained. Anterior and posterior surface elevation data shown by slitscanning or Scheimpflug photography systems also help diagnose keratoconus (typically,

differences greater than +15 µm for anterior elevation indicate keratoconus).

Some authors have classified the topography of normal corneas according to the shape of the contour corresponding to the middle of the scale, in five patterns: round, oval, symmetric bow tie, asymmetric bow tie, and irregular (Bogan et al, 1990). The videokeratoscopic representation of corneal regular astigmatism (toric surface) has the

axis, and infrequently the apex position was on the videokeratograph axis.

patient to blink immediately before the image is captured.

depicted by warm colors, and the low areas by cool colors.

contour (Corbett et al, 1999).

appearance of a bow tie, with the bows of the tie aligned along the steeper meridian. This pattern may occur in projection based systems (Figure 3) but, because they measure corneal height, commonly depict a toric surface as a series of concentric ellipses with their long axis in the flatter meridian (Corbett et al, 1999). When a best fit sphere is subtracted from the corneal height data, astigmatism shows as a ridge.

Bogan found a bow pattern in 49% of "normal" patients studied, and they had astigmatism much more frequently, particularly those with symmetric bow ties. In patients with bow patterns but no astigmatism, either the central portion of the cornea is spherical or corneal toricity is compensated by inverse lenticular astigmatism. An asymmetric bow tie represents asymmetry in the rate of change of the radius of curvature from center to periphery. This pattern is obtained sometimes in normal eyes with astigmatism, or in cases of contact lens warpage, early keratoconus, or artifact by poor fixation or decentration. An irregular pattern may also be the result of bad fixation, improper focusing or tear film abnormalities.

Fig. 3. Scheimpflug eye scanner analysis system image of the cornea. This figure illustrates 1.9 D of anterior corneal astigmatism with a bow-tie pattern.

In contact-lens induced corneal warpage, contact lens wear alters the shape of the cornea as a result of mechanical pressure or metabolic factors. Some patients are asymptomatic, others lose several lines of spectacle corrected visual acuity while maintaining good contact lens acuity, or develop contact lens intolerance. Many topographic patterns may result, including irregular astigmatism, change in the axis of astigmatism, asymmetry, but most commonly flattening in the areas of lens bearing and relative adjacent steepening. Frequently, these changes can only be detected by computer-assisted videokeratography.

In reports of early topographers, CMS (Corneal Modeling System) was compared with Bausch and Lomb keratometer while measuring spherical surfaces (Hannush et al, 1989). No significant difference was found between the keratometer and the CMS in either accuracy or precision. Most of the rings in the videokeratograph were within ± 0.25 D of the known curvatures. Using a CMS with 31 rings (Computed Anatomy), mean difference of measured and actual surface power in four steel test balls (2.7 mm to 3.4 mm radius of curvature) was 0.10 D (SD 0.07D). Rings 2 through 26 were read accurately and precisely within ± 0.25 D on three of the four balls. On the steepest ball, values were within ± 0.37 D. In projection (Placido-disk) based videokeratography, repeatability of corneal measurements was frequently inferior to that of keratometry. Intraobserver COR for TMS was 0.3 D for steep meridian power and 0.44 for flat meridian power (Karabatsas et al, 1998). For astigmatism, it was 0.40 D, 22°-26° for steep meridian location, and 13°-30° for flat meridian location. Repeatability of the TMS was found to be observer related and astigmatism related. Interobserver COR was 0.92 D for the steep meridian power, 1.82 for the flat meridian power, and 1.26 D for astigmatism. Regarding axis meridian, interobserver COR was 40° for the steep axis, and 42° for the flat axis. A novice observer was found to have greater COR when compared with an experienced examiner. Higher deviation scores were also observed for corneas with higher astigmatism. In postkeratoplasty corneas, TMS achieved inferior repeatability and reproducibility than keratometry.

Heath et al (1991) concluded that the accuracy of CMS depended on the shape of the surface. For spheres, torics, and aspheric surfaces, 96.9%, 87.5%, and 60.4%, of measurements, respectively, were within ± 0.375 D. The measurements were highly repeatable, with a standard error of 0.02 D for 16 repeated measures.

The TMS-1 and EyeSys (Placido-disk based systems) were compared by Wilson et al (1992) using spherical surfaces and normal human corneas, and by Antalis et al (1993) using abnormal corneas. The two systems gave similar results, except for a small advantage using the TMS-1 with abnormal corneas. The TMS-1 was slightly more repeatable in the central 0.6 mm than the EyeSys was, according to Maguire et al (1993).

Applegate & Howland (1995) examined the accuracy of the TMS-1 in measuring "true surface topography", using elevation data from the instrument referenced to a plane perpendicular to the videokeratoscope axis, or calculating the elevation by integrating the slope of each sample point. Both methods yielded similar results on spheres, ellipses, and bicurves, with root mean square errors under 5 µm. The elevation found directly from the TMS-1 data files had larger errors, particularly on ellipses. For bicurves, the TMS-1 elevation files had lower errors, on the order of those found on ellipses, whereas calculated elevation had greater error. Surfaces with sharp transitions are not measured accurately, whereas in smooth elliptical surfaces calculating axial curvature yields better results than the elevation files. The error in the elevation files increases toward the periphery (Cohen et al, 1995; Mandell and Horner, 1993). Tomey TMS-2N system provides more reliable elevation files.

Davis and Dresner (1991) compared the accuracy of the EH-270 Alcon system with that of conventional keratometry and found the keratometer to be more accurate on four test spheres. The error increased as the test spheres became steeper. Younes et al (1995) examined the repeatability and reproducibility of Alcon EH-270 taking three measures of both eyes in 39 subjects. Initial repeated measures yielded standard deviations of 0.5 D on

irregular astigmatism, change in the axis of astigmatism, asymmetry, but most commonly flattening in the areas of lens bearing and relative adjacent steepening. Frequently, these

In reports of early topographers, CMS (Corneal Modeling System) was compared with Bausch and Lomb keratometer while measuring spherical surfaces (Hannush et al, 1989). No significant difference was found between the keratometer and the CMS in either accuracy or precision. Most of the rings in the videokeratograph were within ± 0.25 D of the known curvatures. Using a CMS with 31 rings (Computed Anatomy), mean difference of measured and actual surface power in four steel test balls (2.7 mm to 3.4 mm radius of curvature) was 0.10 D (SD 0.07D). Rings 2 through 26 were read accurately and precisely within ± 0.25 D on three of the four balls. On the steepest ball, values were within ± 0.37 D. In projection (Placido-disk) based videokeratography, repeatability of corneal measurements was frequently inferior to that of keratometry. Intraobserver COR for TMS was 0.3 D for steep meridian power and 0.44 for flat meridian power (Karabatsas et al, 1998). For astigmatism, it was 0.40 D, 22°-26° for steep meridian location, and 13°-30° for flat meridian location. Repeatability of the TMS was found to be observer related and astigmatism related. Interobserver COR was 0.92 D for the steep meridian power, 1.82 for the flat meridian power, and 1.26 D for astigmatism. Regarding axis meridian, interobserver COR was 40° for the steep axis, and 42° for the flat axis. A novice observer was found to have greater COR when compared with an experienced examiner. Higher deviation scores were also observed for corneas with higher astigmatism. In postkeratoplasty corneas, TMS achieved inferior

Heath et al (1991) concluded that the accuracy of CMS depended on the shape of the surface. For spheres, torics, and aspheric surfaces, 96.9%, 87.5%, and 60.4%, of measurements, respectively, were within ± 0.375 D. The measurements were highly repeatable, with a

The TMS-1 and EyeSys (Placido-disk based systems) were compared by Wilson et al (1992) using spherical surfaces and normal human corneas, and by Antalis et al (1993) using abnormal corneas. The two systems gave similar results, except for a small advantage using the TMS-1 with abnormal corneas. The TMS-1 was slightly more repeatable in the central 0.6

Applegate & Howland (1995) examined the accuracy of the TMS-1 in measuring "true surface topography", using elevation data from the instrument referenced to a plane perpendicular to the videokeratoscope axis, or calculating the elevation by integrating the slope of each sample point. Both methods yielded similar results on spheres, ellipses, and bicurves, with root mean square errors under 5 µm. The elevation found directly from the TMS-1 data files had larger errors, particularly on ellipses. For bicurves, the TMS-1 elevation files had lower errors, on the order of those found on ellipses, whereas calculated elevation had greater error. Surfaces with sharp transitions are not measured accurately, whereas in smooth elliptical surfaces calculating axial curvature yields better results than the elevation files. The error in the elevation files increases toward the periphery (Cohen et al, 1995; Mandell and Horner, 1993). Tomey TMS-2N system provides more reliable elevation files. Davis and Dresner (1991) compared the accuracy of the EH-270 Alcon system with that of conventional keratometry and found the keratometer to be more accurate on four test spheres. The error increased as the test spheres became steeper. Younes et al (1995) examined the repeatability and reproducibility of Alcon EH-270 taking three measures of both eyes in 39 subjects. Initial repeated measures yielded standard deviations of 0.5 D on

changes can only be detected by computer-assisted videokeratography.

repeatability and reproducibility than keratometry.

standard error of 0.02 D for 16 repeated measures.

mm than the EyeSys was, according to Maguire et al (1993).

the central 3 mm region and increased toward the periphery. Six months later, the differences did not exceed 0.375 D, and the corneal curvatures were found to be slightly steeper toward the center and slightly flatter toward the mid-periphery.

Roberts (1996) compared the accuracy of instantaneous curve algorithms for the Alcon EyeMap, TMS-1, EyeSys Corneal Analysis System, and Keratron on smooth aspheric surfaces. The results showed each of the systems to have approximately the same level of error.

More recently introduced topographers that use scanning slit of the cornea (Orbscan II), Scheimpflug photography images to derive keratometry data of the surface (Pentacam), or double Scheimpflug system combined with a Placido disk (Galilei analyzer) have also been evaluated. A study of curvature readings of the Galilei analyzer and Orbscan II systems demonstrated high intraclass correlation for flat and steep axes keratometry readings in Galilei (0.97 and 0.84, respectively) and Orbscan II (0.96 and 0.95, respectively), which indicates that variation in measurements reported was mainly due to subject-to-subject variation rather than error (Shirayama et al, 2009). The Galilei system provided somewhat flatter K values than the Orbscan II system. However, coefficient of repeatability for the measurements was not reported. Repeated keratometry measurements by the same or a different examiner showed virtually no intraobserver or interobserver variation error (0 to 0.3 D for both devices).The regression coefficient between Orbscan II and Galilei measurements was 0.79, and astigmatism values did not differ significantly between the two.

In a study using the 4-mm zone in Pentacam Scheimpflug technology, reproducibility of two different measures of the cornea taken 1 month apart had an average difference of 0.37 D, with a maximum difference of 0.50 D (Shankar et al, 2008). Pentacam measures the true corneal power in postoperative LASIK and PRK patients to an accuracy of ±0.50D. According to Shankar et al., Pentacam corneal curvature measurements show excellent repeatability. We tested repeatability of Pentacam eye scanner in nine patients, with two measurements in each patient, 5 minutes apart. Intraclass correlation was 0.98, with a standard deviation of difference between mean K measurements of 0.14 D (0.09–0.36).

Because test to test variations occur in corneal measurements, a value could be derived from one test to the next, which has been termed astigmatism measurement variability. It would be similar to calculation of surgical change in astigmatic values, termed surgically induced astigmatism, but without surgical intervention. In a recent study, 4 keratometric devices were used to examine astigmatism measurement variability, and to determine which was most reliable, and which produced the least bias, including Nidek ARK510A, Humphrey ARK599, IOLMaster V3.02, and Pentacam HR7900 (Goggin et al, 2010). Intraclass correlation for flat and steep K keratometric measurements, and for the meridian of the steep K for each eye, were all greater or equal to 0.93, except for Pentacam steep meridian, which was 0.85. Nidek had particularly high ICC for the 3 measurements, as was IOLMaster, except for steep K meridian which was somewhat lower in IOLMaster. Nidek was the most precise of the 3 devices, as indicated by lower CV values than the other instruments.

Nidek, Humphrey, and IOLMaster produced similar astigmatism measurement variability values (0.24 ± 0.2 D, 0.22 ± 0.13 D, and 0.28 ± 0.25 D, respectively), but Pentacam produced a significantly larger value (0.46 ± 0.46 D, p= 0.01). The vector means for the astigmatism measurement variability were small, but larger for and IOLMaster and Pentacam (Nidek, 0.03 D x 41°; Humphrey, 0.08 D x 12°; Pentacam, 0.14 D x 115°; IOLMaster, 0.10 D x 142°), whereas Nidek had the lowest value. Nidek ARK510A is more reliable than the other 3 devices. All studied devices demonstrated a clinically significant astigmatism measurement variation (0.22 to 0.46 D), which means that a significant proportion of keratometric surgically induced astigmatism reported in the literature may be due to variation in keratometric measurement.

According to our data, obtained in 32 patients measured twice (5 minutes apart measurements) using three devices similar to the previous study (Pentacam, IOLMaster, Nidek ARK510) and a manual keratometer (Topcon OM-4 ophthalmometer), the coefficient of repeatability was better for the steep K measurement than for the flat K measurement in all devices except IOLMaster. IOLMaster and Nidek had the best repeatability for K values, but IOLMaster had the lowest COR values (0.1 D for flat and 0.3 D for steep keratometry values). Shankar et al obtained a COR of 0.28 D for mean keratometry in Pentacam anterior corneal measurements, similar to our findings, whereas our COR obtained for steep K was 0.6 D using this instrument for anterior corneal surface. The lowest COR for the flat axis measurement was that of Nidek (24°). Regarding astigmatic cylinder, the lowest COR was again for IOLMaster (0.33 D), followed by Nidek (0.62 D). Figure 4 depicts Bland-Altman 95% confidence interval limits of agreement for flat K values obtained with the IOLMaster.

Fig. 4**.** Repeatability of IOLMaster automated keratometry readings. Bland-Altman analysis showing 95% confidence interval limits of agreement of difference between two measurements of the flat K readings (KfdIOL) versus mean flat K measurements (MfIOL), using IOLMaster technology.

Intraclass correlation was high for K values, flat axis, and astigmatism. ICC for steep and flat K values was 0.99 and 0.97 in Nidek, 0.99 and 0.99 for IOLMaster, 0.98 and 0.82 in OM-4, and 0.96 and 0.88 for Pentacam, respectively. ICC for the flat axis was 0.98 for Nidek, 0.91 for IOLMaster, 0.72 for OM-4, and 0.92 for Pentacam. ICC for astigmatic cylinder was 0.86 for Nidek, 0.98 for IOLMaster, 0.90 for OM-4, and 0.3 for Pentacam anterior corneal surface.

## **7. Conclusions**

88 Astigmatism – Optics, Physiology and Management

devices. All studied devices demonstrated a clinically significant astigmatism measurement variation (0.22 to 0.46 D), which means that a significant proportion of keratometric surgically induced astigmatism reported in the literature may be due to variation in

According to our data, obtained in 32 patients measured twice (5 minutes apart measurements) using three devices similar to the previous study (Pentacam, IOLMaster, Nidek ARK510) and a manual keratometer (Topcon OM-4 ophthalmometer), the coefficient of repeatability was better for the steep K measurement than for the flat K measurement in all devices except IOLMaster. IOLMaster and Nidek had the best repeatability for K values, but IOLMaster had the lowest COR values (0.1 D for flat and 0.3 D for steep keratometry values). Shankar et al obtained a COR of 0.28 D for mean keratometry in Pentacam anterior corneal measurements, similar to our findings, whereas our COR obtained for steep K was 0.6 D using this instrument for anterior corneal surface. The lowest COR for the flat axis measurement was that of Nidek (24°). Regarding astigmatic cylinder, the lowest COR was again for IOLMaster (0.33 D), followed by Nidek (0.62 D). Figure 4 depicts Bland-Altman 95% confidence interval limits of agreement for flat K values obtained with the IOLMaster.

Fig. 4**.** Repeatability of IOLMaster automated keratometry readings. Bland-Altman analysis

measurements of the flat K readings (KfdIOL) versus mean flat K measurements (MfIOL),

showing 95% confidence interval limits of agreement of difference between two

keratometric measurement.

using IOLMaster technology.

Focusing and alignment are very important issues in the use of keratometers and corneal topographers to determine K diopter values and astigmatism. Automated keratometers have higher repeatability than manual keratometers and topographers. Corneal topographers can provide direct measurements of height and corneal periphery, but their main limitation for the moment is repeatability.

## **8. References**

