origen del queratómetro (inglés)

SURVEY OF OPHTHALMOLOGY VOLUME 55 � NUMBER 5 � SEPTEMBER–OCTOBER 2010

HISTORY OF OPHTHALMOLOGYMICHAEL MARMOR, EDITOR

Origins of the Keratometer and its Evolving Rolein OphthalmologyRon Gutmark, MD,1 and David L. Guyton, MD2

1The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA; and 2The Wilmer Eye Institute, The JohnsHopkins Hospital, Baltimore, Maryland, USA

� 2010 byAll rights

Abstract. The keratometer, or ophthalmometer as it was originally known, had its origins in theattempt to discover the seat of accommodation in the eye. Since that early beginning, it has been re-invented a number of times, with improvements and modifications made in the original principles ofits design for new applications that arose as ophthalmology advanced. The cornea is not onlyresponsible for the majority of the refraction in the eye, but is also readily accessible for measurementand modification. The keratometer’s ability to measure the cornea has allowed it to play a central rolein critical advances in ophthalmic history. This review describes the origins and principles of thisinstrument, the novel applications that led to the keratometer’s continued resurgences over its nearly250-year history, and the modern devices that have borrowed its basic principles and are beginning toreplace it in common clinical practice. (Surv Ophthalmol 55:481--497, 2010. � 2010 Elsevier Inc. Allrights reserved.)

Key words. astigmatism � contact lens � cornea � doubling mechanism � history � IOLpower calculation � keratometer � ophthalmic devices � ophthalmometer � refractivesurgery

Keratometer Development and Origins accommodation.68 Eventually, they concluded that

As early as the late 1700s, scientists attempted todevelop techniques of measuring the cornea’scurvature because of their interest in determiningthe mechanism of visual accommodation. JesseRamsden and Everard Home were among thosewho proposed that accommodation occurred pri-marily from changes in the cornea. To prove theirtheory, Ramsden and Home attempted to measureits curvature. In 1779, after trying several designs,they settled on one that consisted of a telescope thatexamined a doubled, reflected image in thecornea.88 This enabled them to measure whetherthe curvature of the cornea changed during

481

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no significant changes occurred, but maintainedthis notion as one of three mechanisms actingconcurrently to allow accommodation of the eye:(1) change in the cornea’s radius, (2) change in thedistance between the crystalline lens and the retina,and (3) change in the shape of the crystalline lens.68

In 1801, Thomas Young described experimentsthat he conducted on himself in an attempt toclarify which of the three mechanisms was actuallyoccurring during accommodation. He wrote:

I shall take the range of my own eye, as beingprobably about the medium, and inquire whatchanges will be necessary in order to produce

0039-6257/$ - see front matterdoi:10.1016/j.survophthal.2010.03.001

482 Surv Ophthalmol 55 (5) September--October 2010 GUTMARK AND GUYTON

it [accommodation]; whether we suppose theradius of the cornea to be diminished, or thedistance of the lens from the retina to beincreased, or these two causes to act conjointly,or the figure of the lens itself to undergo analteration.126

Fig. 1. von Helmholtz’s original ophthalmometer. (a)von Helmholtz’s sketches of his ophthalmometer. (b)Drawings of enclosure for glass plates used to doubleimage (vertical and horizontal cross sections).120 (c)Sketch of the mires of the von Helmholtz ophthalmom-eter, illuminated from behind by candles.118

Basic Principles and Early Designs

Early attempts at measuring the cornea relied onrulers and compasses,122,126 but the accuracy ofthese methods was not sufficient. The first impor-tant step that led to the creation of the modernkeratometer was the realization that reflections ofobjects in the eye could be utilized as an accurateway to measure the corneal curvature. By treatingthe cornea as a spherical convex mirror, one caneasily determine the radius of curvature of this‘‘mirror’’ by employing the laws that govern re-flections and the geometric relations of similartriangles (Details in Appendix A).

The first task in designing the keratometer was tomeasure the size of the reflected image of the objecton the cornea. This issue had already been addressedby astronomers attempting to measure the sizes ofcelestial bodies, such as the sun, and the distancesbetween stars by the use of two threads of a spider webplaced in the image plane of an astronomicaltelescope. These threads were then aligned with twopoints whose distance was being measured. In themid-1800s, Kohlrausch and Senff119 applied thistechnique to the cornea; however, accurate measure-ments were still difficult because of the constantmovements of the eye and head.

The inaccuracies caused by these small movementswere addressed by optically doubling the image. Thisidea was first employed in 1753 by Savary106 indeveloping a heliometer to measure the apparentdiameter of the sun in apogee and perigee. Toaccomplish this, Savary adjusted the magnified,doubled images of the sun in perigee (closest toearth, larger image) so they touched, and latermeasured the distance needed to cause the imagesto touch when the sun was in apogee (farthest fromthe earth, smaller image). Ramsden88 borrowed thisconcept to develop a keratometer in 1779. Seventy-four years later, in 1853, Hermann vonHelmholtz118,119 used the ideas of the astronomerClausen12 to create a keratometer that doubledimages with two glass plates instead of prisms. Invon Helmholtz’s design (Fig. 1), the two images aredisplaced from one another by tilting two movableglass plates (Fig. 2a) in opposite directions until theextremities of the images touch one another. Thisamount of displacement equals the size of the image

(Fig. 2b and 2c). Because the doubled images movetogether, head or eye movements have an equal effecton both and do not affect the measurement.

Therefore, the first keratometer was created onthe foundation of two fundamental principles: (1)Assuming the cornea to be a spherical reflectingsurface, the radius of curvature of the cornea can becalculated from measuring the image produced bythe reflection in the cornea of an object of knownsize and distance from the cornea. (2) An accuratemeasurement of the image size, even with somemovement of the eye, can be determined using theimage-doubling concept. Following von Helmholtz,others sought to improve upon it, but the basicprinciples remained the same. Among subsequentdesigners, Louis Emile Javal and Hjalmar AugustSchiøtz deserve special mention. In 1881, theyconverted von Helmholtz’s original design, whichwas primarily useful as a laboratory instrument, intoa device that could be more easily used in clinicalpractice (Fig. 3).56 Their instrument included miresilluminated from the front by candles, rather thantrans-illuminated from behind, to create the

Fig. 2. (a) Diagram of von Helmholtz’s double-platesetup, where a is the near plate, b is the far plate, c is theimage of the of the mire on the cornea, and c1 and c2 arethe doubled images of c, that the observer would see. (b)Explanation of doubling principle: The displacementrequired to move the second images so that it just touchesthe primary image (x), is equal to the size of image (x). (c)Representation of the doubling principle using mires ofthe Bausch & Lomb Keratometer.

Fig. 3. Javal-Schiøtz ophthalmometers. (a) Original Javal-Schiøtz ophthalmometer using two candles to front-illuminate two movable mires.8 (b) Later design of theJaval-Schiøtz ophthalmometer using electric lamps forillumination of a printed protractor mire.16

ORIGINS OF THE KERATOMETER 483

reflections from the cornea. This allowed the deviceto be rotated around its axis to enable measure-ments in multiple meridians.22

The creation of the von Helmholtz ophthalmom-eter (keratometer) and the improvements thereaf-ter allowed ophthalmologists and scientists to usethe device for various applications, particularly thequantitative measurement of corneal astigmatism,which Thomas Young had described half a centuryearlier.

Keratometric Refractive Index

The keratometer provides the information neces-sary to determine the radius of curvature of theexternal surface of the cornea (see equation A.1 inAppendix A). Although this is a useful quantity forthe characterization of the shape of the cornea—andhas its applications, as we will see—ophthalmologistswere more interested in determining the power of thecornea. To this end, it is necessary to convert radius ofcurvature to power. This conversion can be per-formed easily for a single spherical refracting surface,given the radius of curvature of the surface and theindices of refraction on either side of the surface.Performing this conversion for a two-sided refractingelement such as the cornea requires knowledge of the

radius of curvature of both the anterior and posteriorfaces (see Appendix B).

Mathematical methods exist for accurately calcu-lating the refractive dioptric power of an opticalsystem such as the cornea with two refractivesurfaces.30 However, the keratometer measures onlythe radius of curvature of anterior surface of thecornea. Thus, calculations based only on the re-fractive index of the cornea and that of air will leadto over-estimation of the corneal power, as they willnot consider the negative refractive power of theposterior corneal surface. Direct measurements ofthe corneal posterior surface are difficult, so inorder to correct for this error, it is necessary toestimate the posterior corneal curvature based onthe curvature of the anterior surface. This is done byassuming that the anterior and posterior surfaces ofthe cornea relate to each other by a constantfactor.23,24,78,79 This assumption has been shown to


be accurate in the majority of eyes.30 Once theconstant factor is determined, the value ofthe radius of curvature of the posterior surface ofthe cornea can be easily computed. The mathemat-ical relationships for an optical system with tworefractive surfaces can be used to calculate thecorrect power, or alternatively, a ‘‘compensated’’index of refraction for the cornea can be used,which takes into account the constant relationshipbetween the two surfaces. This ‘‘compensated’’index of refraction is known as the keratometricindex of refraction.

The true index of refraction of the corneal stromais approximately 1.376.78,79 In order to account forthe --5.00 to --7.00 diopter refractive power of theposterior surface of the cornea,21,65 there havehistorically been a number of different values ofthe keratometric index used. Based on the reducedschematic eye of Listing,67 von Helmholtz consid-ered ‘‘the whole corneal system . . . as a lens likea watch-crystal surrounded by aqueous humor onboth sides,’’ and ‘‘consequently, we may just as wellconsider the aqueous humor as extending clear outto the anterior surface of the cornea.’’118,119 Hewent on to say that, ‘‘this assumption is . . . almostnecessary for the reason that, while the measure-ments of the outer surface of the cornea areaccurate enough, the data with respect to the innersurface are not sufficiently reliable.’’118,119 vonHelmholtz used the value of 1.3365118,119 as thekeratometric index. Later, Javal and Schiøtz used1.337, which they ascribe to a value determined byLudwig Mauthner.52 Subsequently, Javal used a valueof 1.3375 because, according to Marius Tscherning(who worked in the same laboratory as Javal), itallowed for an expedient calculation of 45 D, givena radius of curvature of 7.5 mm (see equation B.1 inAppendix B).116,117

Although this was the original proposed kerato-metric index, other values were proposed later byvarious clinicians and scientists and by the manu-facturers of different keratometers. For example,whereas the Haag-Streit and Bausch & Lomb

TABLE

Estimations of the Keratome

SourceEstimated

Keratometric Index

Ho et al45 1.3281 Rotating ScheiDunne et al23 1.3283 Purkinje image

(80 subjects)Dubbelman et al21 1.329 Scheimpflug imEdmund24 1.3300 PhotokeratoscoOlsen et al79 1.3315 Gullstrand’s exFam et al30 1.33273 Orbscan II (Ba

curvature (2

keratometers use the original 1.3375, AmericanOptical chose 1.336, and Zeiss chose 1.332.78,79

Others attempted to offer more accurate estima-tions of the keratometric index based on variousmethods of calculation. Some of these values, andthe methods of calculation, are summarized inTable 1.

Improvements in the Design of theKeratometer

Over the years numerous additions and modifi-cations have been made to the keratometer. Thedifferences among most early keratometers were inthe method of doubling and the method by whichthe images of the mire(s) were aligned with oneanother.114

There are two basic ways of adjusting thealignment of the mire images:

1. Doubling apparatus remains fixed and mirelocation is varied.

2. Doubling apparatus is variable and mire loca-tion is fixed.

Since the introduction of the first keratometers,basic keratometer designs have employed variationson one of these two principles. The original vonHelmholtz model employed variable doublingwhere the position of the two mire images isadjusted by changing the position of the doublingdevice, while the mires remain stationary.

When it was introduced, the Javal-Schiøtz oph-thalmometer incorporated a fixed doubling device,in which the doubling device is stationary, while themire separation is adjusted. In order to adjust thealignment of the images in a fixed doubling device,the size of the object must be changed. This can bedone in a number of ways such as by moving thekeratometer mires laterally (Javal-Schiøtz ophthal-mometer)55 or by employing an iris diaphragm inthe plane of the object to reduce the object size(Reid portable ophthalmometer).90,114

1

tric Index of Refraction

Source of Calculation

mpflug camera (Pentacam, Oculus) (221 subjects)reflection from anterior and posterior corneal surfaces

aging of anterior and posterior curvature (114 subjects)py and pachymetryact schematic eyeusch & Lomb) measurements of anterior and posterior429 subjects)


The manner in which doubling is accomplishedwas also an important distinction between earlyophthalmometers. The Javal-Schiøtz ophthalmome-ter, for instance, was the first to incorporatea Wollaston prism for doubling. This prism’sbirefringence properties create two equally intensediverging light paths, differing only in theirpolarization.56,87

Among the first to produce a Javal-Schiøtz styleophthalmometer were Pfister and Streit (later tobecome Haag-Streit, who have since produceda number of Javal-Schiøtz style ophthalmometers)(Fig. 4a,c,e). At approximately the same time(1888), Leroy and Dubois devised an ophthalmom-eter that was a hybrid of the Helmholtz and Javal-Schiøtz instruments (Fig. 4b). This ophthalmometerused two glass plates to create the doubling effect asin von Helmholtz’s device, but was a fixed doublinginstrument with movable mires like the Javal-Schiøtzdevice. This device was said to be more accuratethan the original Javal-Schiøtz device and was also‘‘considerably cheaper.’’4 Subsequent models of theJaval-Schiøtz style ophthalmometer maintained thefixed doubling principle and have remained largelyunchanged, even retaining the same mire design(Fig. 4c--e).

Fig. 4. Javal-Schiøtz--style ophthalmometers. (a) Pfister-Streiland). (b) Leroy-Dubois (1888).66 (c) Haag-Streit (1950). (HaagOMTE-1. (www.rimc.net). (e) Haag-Streit OM-900 (1997). (Haa

The other method of adjusting the alignment ofthe mire images in a fixed-doubling ophthalmom-eter is to employ an adjustable iris diaphragm as theobject. Thomas Reid devised a portable ophthal-mometer based on this principle (Fig. 5). Thisportable ophthalmometer was positioned so that theiris diaphragm (D) was directed toward an externallight source. This light passing through the irisdiaphragm was directed toward the patient’s eye bya beam splitter prism (P), and would be seen asa disk reflected from the patient’s cornea, whoseimage was doubled with a Wollaston prism (BP).90

Ophthalmometers employing variable doublingwere developed in parallel to the fixed doublinginstruments described earlier. In 1899, theChambers-Inskeep ophthalmometer was introdu-ced.E It was based on the von Helmholtz modeldesign with stationary mires and varied doubling bymoving the doubling apparatus (prisms) longitudi-nally (Fig. 6). Doubling in this ophthalmometer wasachieved using two weak prisms with their apices inopposite directions, as proposed by Landolt(Fig. 6b).29 This ophthalmometer was the fore-runner of the American Optical ophthalmometers.

Soon after Chambers and Inskeep introducedtheir ophthalmometer, John Sutcliffe devised an

t (1894). (Haag-Streit Company Archive, Koeniz, Switzer--Streit Company Archive, Koeniz, Switzerland). (d ) Topcong-Streit Company Archive, Koeniz, Switzerland).

http://www.rimc.net

Fig. 5. Reid’s portable ophthalmometer. The illuminatedaperture itself in the iris diaphragm (D) serves as the mire.The object size is thus varied by adjusting the irisdiaphragm.90


ophthalmometer that would allow measurements ofboth perpendicular meridians of the cornea simul-taneously. The Sutcliffe ophthalmometer (Fig. 7a),invented in 1906,114,A introduced a novel method ofdoubling the image of the mire using two movableperpendicular cylindrical lenses, each flanked bytwo stationary cylindrical lenses. Prism effect couldthen be introduced independently in perpendiculardirections by decentering the respective movablecylindrical lenses (Fig. 7b). This type of ophthal-mometer is referred to as a ‘‘one-position ophthal-mometer’’ because it does not have to be rotatedbetween measurements of the two principal merid-ians. The mire design and one-position principlewere subsequently adopted for the Bausch & Lomb--style keratometers (Fig. 8b).

The Bausch & Lomb--style keratometers employhorizontal and vertical prisms that move along the

Fig. 6. Chambers-Inskeep ophthalmometer. (a) Patientand examiner views of the Chambers-Inskeep ophthal-mometer (1899).32 (b) Detail of eye-piece (10) anddoubling prisms (h) of the Chambers-Inskeepophthalmometer.E

axis of the instrument, instead of the perpendicularcylindrical lenses being decentered transverse to theaxis that Sutcliffe used, in order to create thevariable doubling effect in perpendicular directions.This keratometer (Fig. 8a), also borrowed an opticalarrangement used in the Sutcliffe ophthalmometer,known as the Scheiner disc principle, to improvefocusing accuracy and thus improve the adjustmentof the testing distance. The Scheiner disc arrange-ment creates a slightly doubled central image of themire when the instrument is at the wrong distancefrom the cornea and is not focused appropriately.87

Although the keratometer’s general design andprinciples remained the same, a number ofvariations on the original concept emerged overthe years. Some variations were made to addressdifficulties in focusing the keratometer mires,which led to error in the proper distance of themires from the eye. The Bausch & Lomb keratom-eter, for example, as noted earlier, employs theScheiner disk principle to improve focusing accu-racy and thus improve the adjustment of the testingdistance.87 Another method to reduce focusingerror is the use of collimated mires, as employed inthe Zeiss telecentric ophthalmometer, which elim-inates the change in magnification that wouldotherwise accompany errors in testing distancefrom the eye.B

Other design variations improved the keratome-ter’s ease of use, particularly for pediatric applica-tions. Performing keratometric measurements inpediatric patients can be difficult because of therequirement that the patient remain relatively still ata fixed distance from the device. Automatedkeratometers increase the speed with which accuratemeasurements can be taken.77 Hand-held keratom-eters eliminate the need for head fixation and canbe operated by only one hand.125 Hand-heldkeratometers also facilitate measurements in theoperating room,2 useful in children who are un-willing to cooperate in the office124 or for ongoingassessment of corneal astigmatism during cataract orcorneal surgery.3,70,74,105

Utilization of the Keratometer during theMajor Eras in Ophthalmology

THE ERA OF OPTICS AND REFRACTION, AND

ASTIGMATISM

In addition to examining the mechanisms ofaccommodation, Young’s experiments in 1801 alsoled to the discovery of astigmatism of the eye. Hedescribed that particular experiment as follows:

Fig. 7. Sutcliffe ophthalmometer. (a) Drawing of Sutcliffe ophthalmometer.114 (b) Mire design of Sutcliffeophthalmometer (Sutcliffe reports borrowing this mire design from Rudyard Kipling’s monogram).114

Fig. 8.Lomb


I take.a double convex lens. fixed ina socket one-fifth of an inch in depth.I dropinto it a little water.till it is three-fourths full,and apply it to my eye, so that the cornea.iseverywhere in contact with the water. My eyeimmediately becomes presbyopic, and therefractive power of the lens.is not sufficientto supply the place of the cornea, renderedinefficacious by the intervention of the water;but the addition of another lens.restores myeye to its natural state, and somewhat more.Ifind the same inequality in the horizontal andvertical refractions as without the water.126

His experiment showed that immersion in water,which neutralized the refraction of his cornea, didnot correct his astigmatism (i.e., the difference inthe horizontal and vertical refractions), which led

‘‘One--position’’ keratometer. (a) Bausch & Lomb kerkeratometer.

him to conclude that his astigmatism must havebeen located primarily in his crystalline lens.126

Soon after Young’s discovery, others describedcorneal astigmatism, including Gerson, Wilde, andJones, but their descriptions were not based on anyophthalmometric measurements.8 It was not until1846 when Senff made measurements of the corneawith a spider web apparatus, as described previously,that corneal astigmatism was proven quantitatively.Upon measuring the cornea for the first time, it wasimmediately apparent to Senff that the cornea wasnot spherical in cross section as the keratometricequations had assumed.18,118,119 Rather, it was anellipsoid. Following Senff, others such as Knapp andDonders18 made further measurements and showedthat the cornea was indeed an ellipsoid with anelongated horizontal meridian. Also, their measure-

atometer. (www.pemed.com). (b) Mire design of Bausch &

http://www.pemed.com


ments demonstrated that astigmatism primarily, butnot exclusively, arose in the cornea, contrary to whatYoung had initially described.126

In 1827, shortly after Young’s discoveries, a Britishastronomer, George Airy, detected his own astigma-tism after noticing that he often did not use his lefteye, but when he did, circular objects appeared ovalto him. He determined that a spherocylindrical lenswould correct this defect and commissioned theproduction of such a lens.1

Because it was now known that astigmatismprimarily arose in the cornea, it was not a far leapfor ophthalmologists to begin using the keratometerto aid in refraction by determining the correctionneeded for astigmatism. The idea of using thekeratometer to measure the necessary correction forastigmatism was incorporated into the design ofJaval and Schiøtz’s keratometer. The mires on theirkeratometer (Fig. 9) constitute two rectangles, onedivided in the middle by a line and the secondhaving staggered steps removed from one edge.

Javal and Schiøtz designed their instrument sothat each step was 5 mm wide, which whencalculated with the parameters of their keratometeris the width that corresponds to 1 diopter of cornealastigmatism. By properly aligning the mire images ineach principal meridian, the amount of cornealastigmatism could be read directly from the numberof steps of overlap of the mire images. It isimportant to note that as Weiland points out, Javaland Schiøtz’s calculation of a 5 mm step size tocorrelate with 1 diopter of corrective cylinder ismisleading, as it is valid only when the correctivespectacle lens is placed in contact with the eye,which at the time was not possible.122

Ophthalmologists quickly realized that becausethe majority of astigmatism arose in the cornea, thekeratometer would be a powerful tool in refractionby determining the orientation and power ofastigmatism, thus yielding the cylinder and axisportions of the refraction. In spite of these facts,there were several features of the keratometer thatwould lead to patients rejecting correcting cylindersthat were based directly on keratometry measure-

Fig. 9. Stepped and solid mires of Javal and Schiøtzophthalmometer.15 Each step on the stepped mire wasdesigned to represent 1 diopter of astigmatism.

ments. At the time, it was thought by some that thereason for this was that the patient could nottolerate seeing so clearly. In reality, one of thereasons for this discrepancy, alluded to ealier, is thatthe keratometer measures the amount of astigma-tism at the corneal plane. Therefore, the vertexdistance of spectacle lenses would need to beaccounted for. For example, in an aphakic eye,2.00 diopters of astigmatism at the cornea isproperly corrected by a cylinder of approxi-mately1.50 diopters of power in the spectacle plane.Additionally, the keratometer uses only small areasof the cornea for the measurement, smaller than theaverage pupil. The measurements obtained, there-fore, may not be representative of the averagerefraction across the pupil. Other reasons for thedifference between the keratometrically measuredastigmatism and the subjective refraction includeerror due to the contribution of the posteriorsurface of the cornea, as well as the presence oflenticular astigmatism.3

Different ‘‘rules’’ were proposed to adjust theamount of astigmatism measured by a keratometerto best correlate with values obtained by subjectiverefraction.55,3,29 The best known of these rules isJaval’s rule,55 shown in equation 1.3,26

AstigmatismTotal 5 pðAstigmatismCornealÞ þ k ð1Þ

Javal chose p to equal 1.25 to adjust for the vertexdistance of the spectacle lenses, and k to equal 0.50D (against the rule) to account for a supposedaverage lenticular astigmatism.26 Javal’s rule hasmany exceptions. For example, the p value of 1.25 ismore appropriate for astigmatism accompanyingmyopia than accompanying hyperopia.

Despite the accuracy and ease with which thekeratometer was able to measure the curvature ofthe cornea, it could not be depended upon solely,and subjective refraction with an optometer and/ortrial lenses remained necessary for best accuracy.122

Edward Jackson wrote about the use of thekeratometer for refraction. He stated that thekeratometer approximated the corneal astigmatismand:

in the majority of cases the ’approximation’ isnot so close as may be rightfully demanded ofthe ophthalmic surgeon . . . and that inexceptional cases . . . the difference betweenthe corneal and total astigmatism is so greatthat the former can hardly be regarded as inany proper sense a guide to the latter . . . Whatit does, then, places it clearly among theapproximate tests. But among such tests thedefiniteness with which it indicates what itdoes indicate, the fact that its indications are


entirely objective, and the rapidity with whichthey may be obtained, all give it high rank . . .52

As mentioned previously, lenticular astigmatismwas considered to be a problem, as it could not beaccounted for with this device. This disadvantage forthe normal eye, though, was not present with theaphakic eye. Because the crystalline lens was nolonger present, any astigmatism in the aphakic eyecould be attributed to the cornea. This, as Weilandremarks, led to ‘‘the ideal field for keratometry.’’122

Jackson wrote of ‘‘the scientific value of the simpledetermination of the corneal astigmatism, and of itspractical value in the determination of astigmatismin the aphakic eye, either of which amply justify itsroutine use.’’52

Despite this theoretical advantage of keratometryin the aphakic eye, the other inaccuracies remain,and one in particular—the vertex distanceproblem—is significant.

As a plus corrective lens is moved away from theeye, less plus power is needed to maintain the samecorrection. In other words, changing the spectaclevertex distance can have a substantial effect on theeffective power of a correcting lens. Equation 2, anapproximation, illustrates this point.

D z D2d ð2Þ

Where D is the change in power due to vertexdistance change, D is the power of the lens, andd the distance the lens moves (in meters). As can bededuced from this formula, aphakic eyes, whichrequire very high power lenses (large D), will beeven more susceptible to error due to a change inthe vertex distance of the spectacle lens. Whenastigmatism is present accompanying aphakia, therefraction in the two principal meridians changes bydifferent amounts with changes in vertex distance,leading to significant changes in the power ofcorrecting cylinder needed. It became commonwisdom to reduce the power of the cylinder for anaphakic eye, as determined by the keratometer, byone-fourth to one-third, before prescribing it, sothat the patient could ‘‘tolerate’’ it. In actuality, thepower decrease was necessary to provide the correctcylinder at the spectacle vertex distance!

This vertex distance problem was eventually un-derstood. By that time, however, the lens could beplaced directly in contact with the eye. Cornealcontact lenses had been invented.

THE ERA OF CONTACT LENSES

Numerous versions of ‘‘contact lenses’’ wereproposed since the 15th century. Leonardo da Vinciis often credited with describing the first contactlens.14,75,81,110 What is referred to as his design for

a ‘‘contact lens’’ was an enlarged model of the eyethat was filled with water. He would place his eye inthe model as part of his experiments in an attemptto explain why the world was not seen upside-downas expected based on the optics of the eye. There isno evidence, however, that Leonardo had intendedto create a contact lens.27 Rene Descartes was thefirst to propose a device that had contact with theeye to correct refractive errors.17,28 His ‘‘contactlens’’ consisted of a tube, open at one end witha lens mounted at the other end, which was to befilled with water and placed in contact with the eye.Herschel in 183043 and Fick in 1888 were the first todescribe afocal contact shells.34 August Muller wasthe first to describe a powered contact lens in1889.81 With the introduction of modern-typeplastic corneal contact lenses by Tuohy in 1950,C

contact lenses ‘‘evolved from an optical curiosityinto a widely accepted visual aid.’’110

Early in the development of glass contact lensesthere appeared to be a major problem: contactlenses that were ground, as those described byAugust Muller, were uncomfortable and could notbe worn for an extended period of time,14,75,81

whereas contact lenses that were blown, as thoseproduced by F. A. Muller, were comfortable andcould be worn continuously for extended periods oftime. But the latter were of unknown power. Fittingwas generally done with trial sets or by makingmolds of the eye.14 Joseph Dallos was a majorproponent of fitting contact lenses by taking moldsof the eye, and he perfected this technique.14 Ascontact lenses gained popularity and acceptance,the keratometer gained a new application. By 1936,in his textbook Visual Optics, Emsley had alreadywritten that ‘‘when fitting some contact glasses.thekeratometer is definitely necessary.’’27

The keratometer found a number of differentroles in contact lens management. These includedthe fitting of the contact lens, monitoring changes(of the cornea and of the contact lens), andensuring accurate parameters of the finished con-tact lens.104

The fitting of contact lenses requires the de-termination of several parameters to ensure aneffective lens and comfortable fit. These parametersinclude the base curve and diameter of the contactlens, as well as the refraction and the amount ofcorneal astigmatism.35 Base curve refers to theradius of the spherical back surface of the contactlens. Because the keratometer measures the curva-ture of the anterior corneal surface, which is thesurface that will be adjacent to the posterior lenssurface, it is perfectly suited for determining theproper base curve. The appropriate lens diametercan also be estimated from the keratometric


readings by employing a nomogram created by Dyer,based on the measurements of a large series ofpatients.3 Measurement of the shape or toricity ofthe corneal surface is also achieved by the kera-tometer and is vital in choosing a properly fittingcontact lens. Depending on the toricity of thecornea, different lens designs may be selected(e.g., spheric, aspheric, bitoric).25

As contact lenses became more popular and thetechnology improved, it became more and moreimportant to obtain accurate measurements ofa larger area of the cornea. The keratometer in itsoriginal configuration could only measure approx-imately 2.5 mm of the central cornea.113 As contactlens diameters extended beyond this range, clini-cians became interested in ways to extend thecapability of the keratometer. Several methods ofmeasuring the periphery of the cornea were pro-posed, thus allowing further study of the cornea aswell as affording the ability to construct a crudetopographical map of the entire cornea. Someclinicians made peripheral measurements of thecornea with the ordinary keratometer by alteringthe fixation of the subject, with eccentric fixationtargets in the plane of the mires.123 Others createddevices with small single mires6 or reduced mireseparation69,104 that could allow for examination ofsmall areas on the peripheral corneal surface whencombined with fixation targets that guided thesubject to look to the side. However, these small-mire keratometers suffered from decreased pre-cision because the decreased movement of the miresreduced the precision of measurements.20

TABLE 2

Refractive Error as a Function of Various OcularMeasurements

Variable Error Rx error

Corneal radius 1.0 mm 5.7 DAxial length 1.0 mm 2.7 DPostoperative anterior

chamber depth1.0 mm 1.5 D

Data from Olsen.79

THE ERA OF INTRAOCULAR LENS IMPLANTATION

AND REFRACTIVE SURGERY

With the advent of intraocular lens (IOL)implantation and later refractive surgery, keratom-etry found new applications and new challenges.

When IOL implantation surgery was initiallyintroduced, surgeons implanted IOLs of a standardpower. It was soon realized that IOL power shouldbe calculated in order to obtain more precise post-surgical results. Various formulas were presented bya number of clinicians and visual scientists includingBinkhorst,5 Colenbrander,13 and Le Grand.65 Theseformulas required several ocular measurementssuch as corneal power, anterior chamber depth,and axial length of the eye. Corneal power wasmeasured by the keratometer, anterior chamberdepth was determined by a slit-lamp attachment, andaxial length was measured by ultrasound. In anaphakic eye, measurement of the axial length couldalso be calculated using the keratometricallydetermined corneal power and the aphakic spectacle

correction near the anterior focal point. Soonadditional formulas were derived, some based onoptical theory (e.g., Haigis, Holladay I, Hoffer Q),whereas others were empirically based regressionformulas (e.g., SRK/I, SRK/II, Binkhorst),112 andstill others applied empirical data to theoreticallyderived formulas (e.g., SRK/T).92

A precise determination of corneal radius is ofvital importance for the accuracy of the IOL powerformulas. Of the relevant optical variables, an errorin corneal radius can have a tremendous effect onpostoperative refractive error, as seen in Table 2.

Following corneal refractive surgery, the measure-ment of corneal radius and the calculation ofdesired IOL power are complicated by additionalfactors.

As discussed previously, the accuracy of thekeratometer relies on several assumptions regardingthe normal cornea. These assumptions, althoughnot entirely accurate, had usually been sufficient forclinical purposes. Once the cornea becomes abnor-mal by disease or surgical intervention, however,these assumptions become even less applicable, anderrors in measurement increase. Because calcula-tions of IOL power require knowledge of thecorneal power, accurate keratometric measurementsare essential. As discussed previously, calculations ofcorneal power are based on the radius of curvatureof the cornea. Without direct measurement of theposterior corneal surface, the conversion fromradius of curvature to a dioptric power relies onestimations and adjustments that are necessarybecause only the anterior corneal curvature ismeasured. Because these corrections are based ona normal corneal shape and on a normal ratiobetween the anterior and posterior corneal surfaces,any alteration in this configuration can introduceerror into the calculations. Refractive surgeries suchas radial keratotomy (RK), photorefractive keratec-tomy (PRK), and laser-assisted in situ keratomileusis(LASIK) alter the form of the normal cornea toachieve specific refractive outcomes. Because ofthese changes, measurement of the cornea withkeratometry and other corneal biometry techniquessuch as corneal topography became problematic.


With RK, radial slits are made in the mid-peripheralcornea. Normal intraocular pressure causes theseweakened areas to bulge, resulting in a flattening ofthe central cornea (Fig. 10a). Errors in RK resultbecause standard keratometric measurements co-incide with the location of the newly formedtransition zone, where the flat central cornea beginsits transition into the peripheral cornea. As this area issteeper than the central cornea, keratometric mea-surement is unreliable.112 Although RK results inchanges to the shape of the cornea, this proceduredoes not significantly alter the thickness of the centralcornea, nor the ratio of the anterior surface toposterior surface radii of curvature.41 In PRK andLASIK, on the other hand, both the thickness of thecornea and the ratio of the anterior to posterior radiiof the cornea change (Fig. 10b).44,76,112,121 Thesechanges in the cornea result in overestimation ofcorneal power in RK, PRK, and LASIK, which leads toundercorrection with subsequent cataract and IOLsurgery.89,96,100,101,102,112 To overcome these inaccur-acies with keratometry after refractive surgery, variousmethods have been devised to estimate corneal power(see Hoffer46 for a more complete review). Thesemethods include: (1) performing calculations basedon known dioptric power values (such as pre- or post-operative refraction), thereby circumventing theneed to convert the radius of curvature of the corneato a dioptric power value; (2) adjusting the conver-sion factor (index of refraction) by estimating thechange that will occur between the anterior andposterior corneal surfaces; and (3) taking directmeasurements of the posterior corneal surface.57

The first such method, often referred to as thespherical equivalent change method112 or clinicalhistory method,47 was published by Guyton37 andHolladay50 in 1989 and was initially intended for eyesafter RK. It proposed subtracting the change in thespherical equivalent due to the refractive surgeryfrom the power measured by the keratometer pre-RK.

Fig. 10. Changes in cornea induced by RK and PRK/LASIK.decreased corneal thickness and change in ratio of anterior tperipheral cornea in RK results in flattening of central cornea,posterior corneal radius of curvature.

This method is accurate,47,48,49,101,111 but requiresthe availability of precise pre-surgical keratometryand refractive error.57 A number of other methodsthat require a variety of pre- and post-refractivesurgery data have been proposed.31,39,53,64,100,102,111

Other methods that require knowledge of clinicalhistory aimed at adjusting the index of refraction tomake it more accurate following refractive sur-gery.10,54,62,63,96,99,101,102 When preoperative mea-surements are not available, or when it is uncertainwhether they were accurate and stable, methods notrequiring knowledge of clinical history are needed. Anumber of such methods have been proposed,including the contact lens method,94,109 methodsthat employ post-operative topography or keratom-etry data,33,38,60,95,98,103,107 a method that relies onpostoperative pachymetry,36 and methods relying onnew ocular scanning devices such as the Pentacam(Oculus, Inc., Wetzlar, Germany)7 or Orbscan II(Orbtek, Bausch and Lomb, Salt Lake City, UT,USA).11,85

Transition to Modern Techniques ofKeratography

Although devices to measure corneal power andcorneal topography have only recently becomecommonplace in ophthalmology clinics, the originfor many of these dates back to the late 1800s. Manyof these new devices are based on the Placido diskprinciple. In 1880, Antonio Placido described theuse of a disk painted with alternating black andwhite rings, with a hole in the center equipped witha plus lens for the examiner to look through(Fig. 11).83,84

The reflection of these rings from the frontsurface of the patient’s cornea gave the examinera qualitative assessment of the contour of thecornea. Placido employed this technique, took

(a) Removal of corneal tissue in PRK and LASIK results ino posterior corneal radii of curvature. (b) Bulging of mid-with no change in corneal thickness or ratio of anterior to


photographs of the reflections, and later calculatedthe radius of curvature of the cornea using theseimages, or compared the images to images reflectedby spheres of known radius.51,120 This was a veryeffective means of describing the corneal surface,but calculations were difficult, and comparisonswere time-consuming. Although other improve-ments were attempted, the method employing thePlacido disk would not allow for easy quantitativemeasurements as were available with the keratom-eter. The advent of computers, however, enabledefficient application of the Placido disk method.

The first device to incorporate computer technol-ogy to automate the use of the Placido disk forperforming corneal topography was the photo-electronic keratoscope described by Reynolds andKratt in 1959.93 In 1981, the corneascope, a new,more advanced version of the photo-electronickeratoscope, was introduced.19,97 Automation ofkeratoscopes allowed keratometric measurementsto be taken rapidly, and this ability, combined withthe application of this technology to handhelddevices40,42,61 allowed for improved measurementof the cornea in children.42,61,77

Recently, more sophisticated devices and tech-niques have been introduced and have the potentialof replacing the traditional keratometer in clinicalpractice. These include videokeratography, opticalcoherence tomography, slit-scanning Scheimpflugphotography, and very high frequency ultrasound.The primary advantages of the newer techniques areautomation, the extended area of measurement, andincreased accuracy. Currently there are a number ofvideokeratography devices that rely on the Placidodisk principle, use computer-based calculations, anddisplay color-coded maps of corneal power.59

Although the Placido-disk-based devices are use-ful, they only measure the anterior corneal surface.Therefore, in order to calculate total corneal power,various assumptions must still be made regardingthe relationship between the anterior and posteriorcorneal surfaces. One of the primary advantages of

Fig. 11. Placido disk. Example of hand-held devicedescribed by Placido (www.phisick.com).

other modern devices is their ability to measure theposterior corneal surface accurately and directly.

The first commercially available device thatallowed measurement of the posterior cornealsurface was the Orbscan (originally from Orbtek,Inc., currently from Bausch & Lomb).108,115 Thisdevice employed a scanning-slit technique for itsmeasurements. Optical slit-scanning uses a numberof slit light beams that scan the cornea. The two-dimensional images of the cross-sections of thecornea illuminated by the slit beam are captured bya camera and processed to obtain a topographicalmap of the cornea. Newer scanning-slit systems(Orbscan II, Bausch & Lomb) combine a Placidodisk with scanning-slit techniques to take advantageof both technologies.9,58

Another modern keratometric technique thatallows for direct measurement of the posteriorcorneal surface is Scheimpflug photography, em-ployed in the Pentacam (Oculus, Inc.) and GALILEI(Zeimer Group, Port, Switzerland).45 This relies onthe Scheimpflug principle, which describes thegeometry necessary to produce focused imageswhen the planes of the image, lens, and object arenot parallel with each other (see Maus et al71 fora complete description). An arrangement of thethree planes according to this principle results ina larger focal depth than can normally be achie-ved.21,71,72,73,D This allows the camera to createa three-dimensional model of the anterior segmentof the eye. Using the resulting measurements of thethickness of the cornea, the software is able tocalculate topographical and power maps of thecornea.

Very high frequency ultrasound, originally used inmetallurgy, has since been adapted for use incorneal imaging.91 This technology, employed byArtemis (ArcScan, Inc.), allows for direct visualiza-tion and measurement of the posterior cornea andthe unique ability to generate 3-dimensional mapsof individual corneal layers. This can be very usefulin the planning of corneal refractive surgery, as wellas in the monitoring of post-surgical results.91

Comparative features of the different types ofmodern keratometry devices and those of thestandard keratometer are presented in Table 3.

Conclusions

From its early origins in the study of themechanism of accommodation, the keratometerhas repeatedly found new applications as ophthal-mology has advanced. Its ease of use for therefraction of the cornea has contributed to itssuccess in diverse applications over generations.

http://www.phisick.com

TABLE 3

Characteristics of a Selection of Corneal Biometry Techniques

TechnologyYear First Described (Year first

commercially available)Maximum Points Measured

(typical operation may be less) Advantages Limitations

Keratometer 177988 4 � Easy to use� Inexpensive

� Limited area ofmeasurement

Placido disk 188084 N/A � Peripheral cornealmeasurement

� Extrapolates central cor-neal data

Scheimpflug photography 198572 (200486) 25,00086 � Direct measurement ofposterior corneal surface� Visualization of anterior

chamber structures� Large depth of focus71

� Difficult to measure smallchanges in central cornea� Image distortion due to

Scheimpflug principlemust be compensated bycomputer71

Very high-frequencyultrasound

199080 12,288 scan linesa � Direct measurement ofposterior corneal surface� Mapping of individual

corneal layers and anteriorchamber91

� Optical opacities do notaffect measurements82

� Decreasing field of viewwith increasing resolution� Requires experienced

examiner82

Optical slit-scanning 1995108 (199942) 9,60058 � Direct measurement ofposterior corneal surface9

� Non-contact imaging� Anterior segment

imaging58

� Generation and detectionof sufficiently narrow slitfor accurate measure-ments difficult to achieve� Corneal haze affects

measurements9

aMaley P. Artemis information [online]. E-mail from Patrick Maley, CEO Arcscan Inc, 28 July 2009.

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Novel devices are now appearing that allow access toareas in the eye, such as the posterior cornealsurface, that were previously difficult or evenimpossible to study. As these new anatomic frontiersare explored, some are proving significant andothers less so. Currently the keratometer is stillwidely used due to its simplicity, minimal expense,and the speed with which measurements can betaken. However, as the costs of new devices aredecreasing, they are becoming more competitive interms of speed and ease of use. Although the use ofthe keratometer is declining as newer and morepowerful devices are replacing it, it remains the‘‘gold standard’’ against which these new instru-ments can be validated.

Method of Literature Search

The literature review for this article was per-formed through Medline, EMBASE, ISI, and Scopususing the following search terms as well as combi-nations of the same terms: keratometer, ophthalmometer,history, ocular biometry, catoptric, astigmatism, keratomet-ric index, contact lens, fitting, Helmholtz, Javal, Schiøtz,refractive surgery, IOL, Placido, corneal topography, andhand-held. U.S. and international patent literaturewas also searched using some of the same searchterms as well as others specific to the various devicesdiscussed.

All available years were covered. Additionalliterature was found in the reference lists of otherarticles, various digital libraries including the HathiTrust Digital Library, and Google search of the listedterms. Relevant non-English sources were alsoconsidered. English abstracts for some non-Englishsources were employed, and full or partial trans-lations of text were obtained for other importantnon-English sources.

All original sources relevant to the topic wereconsidered for inclusion. Some sources wereexcluded to avoid redundancy.

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Other Cited Material

A. Sutcliffe JH, inventor. Ophthalmometer. United States patentUS 890,580. 9 June 1908

B. Edmund Optics Technical Library, ‘‘What is Telecentricity?’’Available at www.edmundoptics.com/technical-support/imaging/what-is-telecentricity/

C. Tuohy KM, inventor. Contact lens. United States patent US2,510,438. 6 June 1950

D. Scheimpflug T, inventor. Improved method and apparatus forthe systematic alteration or distortion of plane pictures andimages by means of lenses and mirrors for photography and forother purposes. Great Britain patent GB 1196. 12 May 1904

E. Inskeep CC, Chambers JE, inventors; Ophthalmometer.United States patent US 631,307. 22 August 1899

The authors reported no proprietary or commercial interest inany product mentioned or concept discussed in this article. Thiswork was supported by a grant from the Doris Duke CharitableFoundation to The Johns Hopkins Medical Institution to fundRon Gutmark, a Doris Duke Clinical Research Fellow.

Reprint address: Ron Gutmark, The Zanvyl Krieger Children’sEye Center, The Wilmer Institute, 233, The Johns HopkinsHospital, 600 North Wolfe Street, Baltimore, Maryland 21287-9028.

http://www.edmundoptics.com/technical-support/imaging/what-is-telecentricity/

http://www.edmundoptics.com/technical-support/imaging/what-is-telecentricity/


Appendix A Appendix B

These laws are illustrated in Figure A.1 and aredescribed by the following equation, when d is muchlarger than r, as is always the case clinically:

r52dI

OðA:1Þ

Where O is the object size, I the image size, d is thedistance of the object from the cornea, and r is theradius of the front surface of the cornea.

Fig. A.1. Illustration of catoptric system with corneaacting as spherical reflecting surface.

According to Gaussian optics, equation B.126 de-scribes the refracting dioptric power (P) of a sphericalsurface of a transparent medium, given the index ofrefraction of the medium (n1), the index of refractionof the optical medium adjacent to the surface (n2), andthe radius of curvature of the surface (r), in meters:

P5ðn1� n2Þ

rðB:1Þ

For the cornea, n1 is the refractive index of the cornea,n2 is the refractive index of air (n2 5 1.000) and r is theradius of curvature, in meters, as measured by thekeratometer. Equation B.1 describes the refraction ata single refractive surface, but the cornea, havinga finite thickness, has two refractive surfaces, theanterior surface in contact with air, and the posteriorsurface, in contact with the aqueous humor. EquationB.226 illustrates how to calculate the combinedrefractive dioptric power of two refractive surfaces.

When; P15n1� n2

r1and P25

n0� n1

r2

P5P1 þ P2 � dn1

P1P2

ðB:2Þ

where, in the case of the cornea, P1 is the dioptricpower of the posterior surface, P2 the dioptric powerof anterior surface, n1 and n2 are as defined above,n0 is the refractive index of the aqueous (1.336), r1 isthe radius of curvature of the posterior surface, r2 isthe radius of curvature of the anterior surface, andd is the thickness of the central cornea.

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