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survey of ophthalmology volume 55 number 5 september­october 2010 history of ophthalmology michael marmor editor origins of the keratometer and its evolving role in ophthalmology ron gutmark md,1 and david l guyton md2 the johns hopkins university school of medicine baltimore maryland usa and 2the wilmer eye institute the johns hopkins hospital baltimore maryland usa 1 abstract the keratometer or ophthalmometer as it was originally known had its origins in the attempt to discover the seat of accommodation in the eye since that early beginning it has been reinvented a number of times with improvements and modifications made in the original principles of its design for new applications that arose as ophthalmology advanced the cornea is not only responsible for the majority of the refraction in the eye but is also readily accessible for measurement and modification the keratometer s ability to measure the cornea has allowed it to play a central role in critical advances in ophthalmic history this review describes the origins and principles of this instrument the novel applications that led to the keratometer s continued resurgences over its nearly 250-year history and the modern devices that have borrowed its basic principles and are beginning to replace it in common clinical practice surv ophthalmol 55:481 497 2010 Ó 2010 elsevier inc all rights reserved key words astigmatism contact lens cornea power calculation keratometer ophthalmic surgery doubling mechanism history iol devices ophthalmometer refractive keratometer development and origins as early as the late 1700s scientists attempted to develop techniques of measuring the cornea s curvature because of their interest in determining the mechanism of visual accommodation jesse ramsden and everard home were among those who proposed that accommodation occurred primarily from changes in the cornea to prove their theory ramsden and home attempted to measure its curvature in 1779 after trying several designs they settled on one that consisted of a telescope that examined a doubled reflected image in the cornea.88 this enabled them to measure whether the curvature of the cornea changed during 481 Ó 2010 by elsevier inc all rights reserved accommodation.68 eventually they concluded that no significant changes occurred but maintained this notion as one of three mechanisms acting concurrently to allow accommodation of the eye 1 change in the cornea s radius 2 change in the distance between the crystalline lens and the retina and 3 change in the shape of the crystalline lens.68 in 1801 thomas young described experiments that he conducted on himself in an attempt to clarify which of the three mechanisms was actually occurring during accommodation he wrote i shall take the range of my own eye as being probably about the medium and inquire what changes will be necessary in order to produce 0039-6257 see front matter doi:10.1016/j.survophthal.2010.03.001

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482 surv ophthalmol 55 5 september october 2010 gutmark and guyton it [accommodation whether we suppose the radius of the cornea to be diminished or the distance of the lens from the retina to be increased or these two causes to act conjointly or the figure of the lens itself to undergo an alteration.126 basic principles and early designs early attempts at measuring the cornea relied on rulers and compasses,122,126 but the accuracy of these methods was not sufficient the first important step that led to the creation of the modern keratometer was the realization that reflections of objects in the eye could be utilized as an accurate way to measure the corneal curvature by treating the cornea as a spherical convex mirror one can easily determine the radius of curvature of this mirror by employing the laws that govern reflections and the geometric relations of similar triangles details in appendix a the first task in designing the keratometer was to measure the size of the reflected image of the object on the cornea this issue had already been addressed by astronomers attempting to measure the sizes of celestial bodies such as the sun and the distances between stars by the use of two threads of a spider web placed in the image plane of an astronomical telescope these threads were then aligned with two points whose distance was being measured in the mid-1800s kohlrausch and senff119 applied this technique to the cornea however accurate measurements were still difficult because of the constant movements of the eye and head the inaccuracies caused by these small movements were addressed by optically doubling the image this idea was first employed in 1753 by savary106 in developing a heliometer to measure the apparent diameter of the sun in apogee and perigee to accomplish this savary adjusted the magnified doubled images of the sun in perigee closest to earth larger image so they touched and later measured the distance needed to cause the images to touch when the sun was in apogee farthest from the earth smaller image ramsden88 borrowed this concept to develop a keratometer in 1779 seventyfour years later in 1853 hermann von helmholtz118,119 used the ideas of the astronomer clausen12 to create a keratometer that doubled images with two glass plates instead of prisms in von helmholtz s design fig 1 the two images are displaced from one another by tilting two movable glass plates fig 2a in opposite directions until the extremities of the images touch one another this amount of displacement equals the size of the image fig 1 von helmholtz s original ophthalmometer a von helmholtz s sketches of his ophthalmometer b drawings of enclosure for glass plates used to double image vertical and horizontal cross sections 120 c sketch of the mires of the von helmholtz ophthalmometer illuminated from behind by candles.118 fig 2b and 2c because the doubled images move together head or eye movements have an equal effect on both and do not affect the measurement therefore the first keratometer was created on the foundation of two fundamental principles 1 assuming the cornea to be a spherical reflecting surface the radius of curvature of the cornea can be calculated from measuring the image produced by the reflection in the cornea of an object of known size and distance from the cornea 2 an accurate measurement of the image size even with some movement of the eye can be determined using the image-doubling concept following von helmholtz others sought to improve upon it but the basic principles remained the same among subsequent ´ designers louis emile javal and hjalmar august schiøtz deserve special mention in 1881 they converted von helmholtz s original design which was primarily useful as a laboratory instrument into a device that could be more easily used in clinical practice fig 3 56 their instrument included mires illuminated from the front by candles rather than trans-illuminated from behind to create the

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origins of the keratometer 483 fig 2 a diagram of von helmholtz s double-plate setup where a is the near plate b is the far plate c is the image of the of the mire on the cornea and c1 and c2 are the doubled images of c that the observer would see b explanation of doubling principle the displacement required to move the second images so that it just touches the primary image x is equal to the size of image x c representation of the doubling principle using mires of the bausch lomb keratometer reflections from the cornea this allowed the device to be rotated around its axis to enable measurements in multiple meridians.22 the creation of the von helmholtz ophthalmometer keratometer and the improvements thereafter allowed ophthalmologists and scientists to use the device for various applications particularly the quantitative measurement of corneal astigmatism which thomas young had described half a century earlier fig 3 javal-schiøtz ophthalmometers a original javalschiøtz ophthalmometer using two candles to frontilluminate two movable mires.8 b later design of the javal-schiøtz ophthalmometer using electric lamps for illumination of a printed protractor mire.16 keratometric refractive index the keratometer provides the information necessary to determine the radius of curvature of the external surface of the cornea see equation a.1 in appendix a although this is a useful quantity for the characterization of the shape of the cornea and has its applications as we will see ophthalmologists were more interested in determining the power of the cornea to this end it is necessary to convert radius of curvature to power this conversion can be performed easily for a single spherical refracting surface given the radius of curvature of the surface and the indices of refraction on either side of the surface performing this conversion for a two-sided refracting element such as the cornea requires knowledge of the radius of curvature of both the anterior and posterior faces see appendix b mathematical methods exist for accurately calculating the refractive dioptric power of an optical system such as the cornea with two refractive surfaces.30 however the keratometer measures only the radius of curvature of anterior surface of the cornea thus calculations based only on the refractive index of the cornea and that of air will lead to over-estimation of the corneal power as they will not consider the negative refractive power of the posterior corneal surface direct measurements of the corneal posterior surface are difficult so in order to correct for this error it is necessary to estimate the posterior corneal curvature based on the curvature of the anterior surface this is done by assuming that the anterior and posterior surfaces of the cornea relate to each other by a constant factor.23,24,78,79 this assumption has been shown to

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484 surv ophthalmol 55 5 september october 2010 gutmark and guyton be accurate in the majority of eyes.30 once the constant factor is determined the value of the radius of curvature of the posterior surface of the cornea can be easily computed the mathematical relationships for an optical system with two refractive surfaces can be used to calculate the correct power or alternatively a compensated index of refraction for the cornea can be used which takes into account the constant relationship between the two surfaces this compensated index of refraction is known as the keratometric index of refraction the true index of refraction of the corneal stroma is approximately 1.376.78,79 in order to account for the 5.00 to 7.00 diopter refractive power of the posterior surface of the cornea,21,65 there have historically been a number of different values of the keratometric index used based on the reduced schematic eye of listing,67 von helmholtz considered the whole corneal system as a lens like a watch-crystal surrounded by aqueous humor on both sides and consequently we may just as well consider the aqueous humor as extending clear out to the anterior surface of the cornea 118,119 he went on to say that this assumption is almost necessary for the reason that while the measurements of the outer surface of the cornea are accurate enough the data with respect to the inner surface are not sufficiently reliable 118,119 von helmholtz used the value of 1.3365118,119 as the keratometric index later javal and schiøtz used 1.337 which they ascribe to a value determined by ludwig mauthner.52 subsequently javal used a value of 1.3375 because according to marius tscherning who worked in the same laboratory as javal it allowed for an expedient calculation of 45 d given a radius of curvature of 7.5 mm see equation b.1 in appendix b 116,117 although this was the original proposed keratometric index other values were proposed later by various clinicians and scientists and by the manufacturers of different keratometers for example whereas the haag-streit and bausch lomb keratometers use the original 1.3375 american optical chose 1.336 and zeiss chose 1.332.78,79 others attempted to offer more accurate estimations of the keratometric index based on various methods of calculation some of these values and the methods of calculation are summarized in table 1 improvements in the design of the keratometer over the years numerous additions and modifications have been made to the keratometer the differences among most early keratometers were in the method of doubling and the method by which the images of the mires were aligned with one another.114 there are two basic ways of adjusting the alignment of the mire images 1 doubling apparatus remains fixed and mire location is varied 2 doubling apparatus is variable and mire location is fixed since the introduction of the first keratometers basic keratometer designs have employed variations on one of these two principles the original von helmholtz model employed variable doubling where the position of the two mire images is adjusted by changing the position of the doubling device while the mires remain stationary when it was introduced the javal-schiøtz ophthalmometer incorporated a fixed doubling device in which the doubling device is stationary while the mire separation is adjusted in order to adjust the alignment of the images in a fixed doubling device the size of the object must be changed this can be done in a number of ways such as by moving the keratometer mires laterally javal-schiøtz ophthalmometer55 or by employing an iris diaphragm in the plane of the object to reduce the object size reid portable ophthalmometer 90,114 table 1 estimations of the keratometric index of refraction source ho et al dunne et al23 dubbelman et al21 edmund24 olsen et al79 fam et al30 45 estimated keratometric index 1.3281 1.3283 1.329 1.3300 1.3315 1.33273 source of calculation rotating scheimpflug camera pentacam oculus 221 subjects purkinje image reflection from anterior and posterior corneal surfaces 80 subjects scheimpflug imaging of anterior and posterior curvature 114 subjects photokeratoscopy and pachymetry gullstrand s exact schematic eye orbscan ii bausch lomb measurements of anterior and posterior curvature 2429 subjects

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origins of the keratometer 485 the manner in which doubling is accomplished was also an important distinction between early ophthalmometers the javal-schiøtz ophthalmometer for instance was the first to incorporate a wollaston prism for doubling this prism s birefringence properties create two equally intense diverging light paths differing only in their polarization.56,87 among the first to produce a javal-schiøtz style ophthalmometer were pfister and streit later to become haag-streit who have since produced a number of javal-schiøtz style ophthalmometers fig 4a,c,e at approximately the same time 1888 leroy and dubois devised an ophthalmometer that was a hybrid of the helmholtz and javalschiøtz instruments fig 4b this ophthalmometer used two glass plates to create the doubling effect as in von helmholtz s device but was a fixed doubling instrument with movable mires like the javal-schiøtz device this device was said to be more accurate than the original javal-schiøtz device and was also considerably cheaper 4 subsequent models of the javal-schiøtz style ophthalmometer maintained the fixed doubling principle and have remained largely unchanged even retaining the same mire design fig 4c e the other method of adjusting the alignment of the mire images in a fixed-doubling ophthalmometer is to employ an adjustable iris diaphragm as the object thomas reid devised a portable ophthalmometer based on this principle fig 5 this portable ophthalmometer was positioned so that the iris diaphragm d was directed toward an external light source this light passing through the iris diaphragm was directed toward the patient s eye by a beam splitter prism p and would be seen as a disk reflected from the patient s cornea whose image was doubled with a wollaston prism bp 90 ophthalmometers employing variable doubling were developed in parallel to the fixed doubling instruments described earlier in 1899 the chambers-inskeep ophthalmometer was introduced.e it was based on the von helmholtz model design with stationary mires and varied doubling by moving the doubling apparatus prisms longitudinally fig 6 doubling in this ophthalmometer was achieved using two weak prisms with their apices in opposite directions as proposed by landolt fig 6b 29 this ophthalmometer was the forerunner of the american optical ophthalmometers soon after chambers and inskeep introduced their ophthalmometer john sutcliffe devised an fig 4 javal-schiøtz style ophthalmometers a pfister-streit 1894 haag-streit company archive koeniz switzerland b leroy-dubois 1888 66 c haag-streit 1950 haag-streit company archive koeniz switzerland d topcon omte-1 www.rimc.net e haag-streit om-900 1997 haag-streit company archive koeniz switzerland

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486 surv ophthalmol 55 5 september october 2010 gutmark and guyton fig 5 reid s portable ophthalmometer the illuminated aperture itself in the iris diaphragm d serves as the mire the object size is thus varied by adjusting the iris diaphragm.90 ophthalmometer that would allow measurements of both perpendicular meridians of the cornea simultaneously the sutcliffe ophthalmometer fig 7a invented in 1906,114,a introduced a novel method of doubling the image of the mire using two movable perpendicular cylindrical lenses each flanked by two stationary cylindrical lenses prism effect could then be introduced independently in perpendicular directions by decentering the respective movable cylindrical lenses fig 7b this type of ophthalmometer is referred to as a one-position ophthalmometer because it does not have to be rotated between measurements of the two principal meridians the mire design and one-position principle were subsequently adopted for the bausch lomb-style keratometers fig 8b the bausch lomb style keratometers employ horizontal and vertical prisms that move along the axis of the instrument instead of the perpendicular cylindrical lenses being decentered transverse to the axis that sutcliffe used in order to create the variable doubling effect in perpendicular directions this keratometer fig 8a also borrowed an optical arrangement used in the sutcliffe ophthalmometer known as the scheiner disc principle to improve focusing accuracy and thus improve the adjustment of the testing distance the scheiner disc arrangement creates a slightly doubled central image of the mire when the instrument is at the wrong distance from the cornea and is not focused appropriately.87 although the keratometer s general design and principles remained the same a number of variations on the original concept emerged over the years some variations were made to address difficulties in focusing the keratometer mires which led to error in the proper distance of the mires from the eye the bausch lomb keratometer for example as noted earlier employs the scheiner disk principle to improve focusing accuracy and thus improve the adjustment of the testing distance.87 another method to reduce focusing error is the use of collimated mires as employed in the zeiss telecentric ophthalmometer which eliminates the change in magnification that would otherwise accompany errors in testing distance from the eye.b other design variations improved the keratometer s ease of use particularly for pediatric applications performing keratometric measurements in pediatric patients can be difficult because of the requirement that the patient remain relatively still at a fixed distance from the device automated keratometers increase the speed with which accurate measurements can be taken.77 hand-held keratometers eliminate the need for head fixation and can be operated by only one hand.125 hand-held keratometers also facilitate measurements in the operating room,2 useful in children who are unwilling to cooperate in the office124 or for ongoing assessment of corneal astigmatism during cataract or corneal surgery.3,70,74,105 utilization of the keratometer during the major eras in ophthalmology the era of optics and refraction and astigmatism fig 6 chambers-inskeep ophthalmometer a patient and examiner views of the chambers-inskeep ophthalmometer 1899 32 b detail of eye-piece 10 and doubling prisms h of the chambers-inskeep ophthalmometer.e in addition to examining the mechanisms of accommodation young s experiments in 1801 also led to the discovery of astigmatism of the eye he described that particular experiment as follows:

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origins of the keratometer 487 fig 7 sutcliffe ophthalmometer a drawing of sutcliffe ophthalmometer.114 b mire design of sutcliffe ophthalmometer sutcliffe reports borrowing this mire design from rudyard kipling s monogram 114 i take.a double convex lens fixed in a socket one-fifth of an inch in depth.i drop into it a little water.till it is three-fourths full and apply it to my eye so that the cornea.is everywhere in contact with the water my eye immediately becomes presbyopic and the refractive power of the lens.is not sufficient to supply the place of the cornea rendered inefficacious by the intervention of the water but the addition of another lens.restores my eye to its natural state and somewhat more.i find the same inequality in the horizontal and vertical refractions as without the water.126 his experiment showed that immersion in water which neutralized the refraction of his cornea did not correct his astigmatism i.e the difference in the horizontal and vertical refractions which led him to conclude that his astigmatism must have been located primarily in his crystalline lens.126 soon after young s discovery others described corneal astigmatism including gerson wilde and jones but their descriptions were not based on any ophthalmometric measurements.8 it was not until 1846 when senff made measurements of the cornea with a spider web apparatus as described previously that corneal astigmatism was proven quantitatively upon measuring the cornea for the first time it was immediately apparent to senff that the cornea was not spherical in cross section as the keratometric equations had assumed.18,118,119 rather it was an ellipsoid following senff others such as knapp and donders18 made further measurements and showed that the cornea was indeed an ellipsoid with an elongated horizontal meridian also their measure fig 8 one position keratometer a bausch lomb keratometer www.pemed.com b mire design of bausch lomb keratometer.

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488 surv ophthalmol 55 5 september october 2010 gutmark and guyton ments demonstrated that astigmatism primarily but not exclusively arose in the cornea contrary to what young had initially described.126 in 1827 shortly after young s discoveries a british astronomer george airy detected his own astigmatism after noticing that he often did not use his left eye but when he did circular objects appeared oval to him he determined that a spherocylindrical lens would correct this defect and commissioned the production of such a lens.1 because it was now known that astigmatism primarily arose in the cornea it was not a far leap for ophthalmologists to begin using the keratometer to aid in refraction by determining the correction needed for astigmatism the idea of using the keratometer to measure the necessary correction for astigmatism was incorporated into the design of javal and schiøtz s keratometer the mires on their keratometer fig 9 constitute two rectangles one divided in the middle by a line and the second having staggered steps removed from one edge javal and schiøtz designed their instrument so that each step was 5 mm wide which when calculated with the parameters of their keratometer is the width that corresponds to 1 diopter of corneal astigmatism by properly aligning the mire images in each principal meridian the amount of corneal astigmatism could be read directly from the number of steps of overlap of the mire images it is important to note that as weiland points out javal and schiøtz s calculation of a 5 mm step size to correlate with 1 diopter of corrective cylinder is misleading as it is valid only when the corrective spectacle lens is placed in contact with the eye which at the time was not possible.122 ophthalmologists quickly realized that because the majority of astigmatism arose in the cornea the keratometer would be a powerful tool in refraction by determining the orientation and power of astigmatism thus yielding the cylinder and axis portions of the refraction in spite of these facts there were several features of the keratometer that would lead to patients rejecting correcting cylinders that were based directly on keratometry measure ments at the time it was thought by some that the reason for this was that the patient could not tolerate seeing so clearly in reality one of the reasons for this discrepancy alluded to ealier is that the keratometer measures the amount of astigmatism at the corneal plane therefore the vertex distance of spectacle lenses would need to be accounted for for example in an aphakic eye 2.00 diopters of astigmatism at the cornea is properly corrected by a cylinder of approximately1.50 diopters of power in the spectacle plane additionally the keratometer uses only small areas of the cornea for the measurement smaller than the average pupil the measurements obtained therefore may not be representative of the average refraction across the pupil other reasons for the difference between the keratometrically measured astigmatism and the subjective refraction include error due to the contribution of the posterior surface of the cornea as well as the presence of lenticular astigmatism.3 different rules were proposed to adjust the amount of astigmatism measured by a keratometer to best correlate with values obtained by subjective refraction.55,3,29 the best known of these rules is javal s rule,55 shown in equation 1.3,26 astigmatismtotal 5 pðastigmatismcorneal Þ þ k ð1Þ javal chose p to equal 1.25 to adjust for the vertex distance of the spectacle lenses and k to equal 0.50 d against the rule to account for a supposed average lenticular astigmatism.26 javal s rule has many exceptions for example the p value of 1.25 is more appropriate for astigmatism accompanying myopia than accompanying hyperopia despite the accuracy and ease with which the keratometer was able to measure the curvature of the cornea it could not be depended upon solely and subjective refraction with an optometer and/or trial lenses remained necessary for best accuracy.122 edward jackson wrote about the use of the keratometer for refraction he stated that the keratometer approximated the corneal astigmatism and in the majority of cases the approximation is not so close as may be rightfully demanded of the ophthalmic surgeon and that in exceptional cases the difference between the corneal and total astigmatism is so great that the former can hardly be regarded as in any proper sense a guide to the latter what it does then places it clearly among the approximate tests but among such tests the definiteness with which it indicates what it does indicate the fact that its indications are fig 9 stepped and solid mires of javal and schiøtz ophthalmometer.15 each step on the stepped mire was designed to represent 1 diopter of astigmatism.

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origins of the keratometer 489 entirely objective and the rapidity with which they may be obtained all give it high rank .52 as mentioned previously lenticular astigmatism was considered to be a problem as it could not be accounted for with this device this disadvantage for the normal eye though was not present with the aphakic eye because the crystalline lens was no longer present any astigmatism in the aphakic eye could be attributed to the cornea this as weiland remarks led to the ideal field for keratometry 122 jackson wrote of the scientific value of the simple determination of the corneal astigmatism and of its practical value in the determination of astigmatism in the aphakic eye either of which amply justify its routine use 52 despite this theoretical advantage of keratometry in the aphakic eye the other inaccuracies remain and one in particular the vertex distance problem is significant as a plus corrective lens is moved away from the eye less plus power is needed to maintain the same correction in other words changing the spectacle vertex distance can have a substantial effect on the effective power of a correcting lens equation 2 an approximation illustrates this point d z d2d ð2Þ where d is the change in power due to vertex distance change d is the power of the lens and d the distance the lens moves in meters as can be deduced from this formula aphakic eyes which require very high power lenses large d will be even more susceptible to error due to a change in the vertex distance of the spectacle lens when astigmatism is present accompanying aphakia the refraction in the two principal meridians changes by different amounts with changes in vertex distance leading to significant changes in the power of correcting cylinder needed it became common wisdom to reduce the power of the cylinder for an aphakic eye as determined by the keratometer by one-fourth to one-third before prescribing it so that the patient could tolerate it in actuality the power decrease was necessary to provide the correct cylinder at the spectacle vertex distance this vertex distance problem was eventually understood by that time however the lens could be placed directly in contact with the eye corneal contact lenses had been invented the era of contact lenses numerous versions of contact lenses were proposed since the 15th century leonardo da vinci is often credited with describing the first contact lens.14,75,81,110 what is referred to as his design for a contact lens was an enlarged model of the eye that was filled with water he would place his eye in the model as part of his experiments in an attempt to explain why the world was not seen upside-down as expected based on the optics of the eye there is no evidence however that leonardo had intended ´ to create a contact lens.27 rene descartes was the first to propose a device that had contact with the eye to correct refractive errors.17,28 his contact lens consisted of a tube open at one end with a lens mounted at the other end which was to be filled with water and placed in contact with the eye herschel in 183043 and fick in 1888 were the first to describe afocal contact shells.34 august muller was ¨ the first to describe a powered contact lens in 1889.81 with the introduction of modern-type plastic corneal contact lenses by tuohy in 1950,c contact lenses evolved from an optical curiosity into a widely accepted visual aid 110 early in the development of glass contact lenses there appeared to be a major problem contact lenses that were ground as those described by august muller were uncomfortable and could not ¨ be worn for an extended period of time,14,75,81 whereas contact lenses that were blown as those produced by f a muller were comfortable and ¨ could be worn continuously for extended periods of time but the latter were of unknown power fitting was generally done with trial sets or by making molds of the eye.14 joseph dallos was a major proponent of fitting contact lenses by taking molds of the eye and he perfected this technique.14 as contact lenses gained popularity and acceptance the keratometer gained a new application by 1936 in his textbook visual optics emsley had already written that when fitting some contact glasses.the keratometer is definitely necessary 27 the keratometer found a number of different roles in contact lens management these included the fitting of the contact lens monitoring changes of the cornea and of the contact lens and ensuring accurate parameters of the finished contact lens.104 the fitting of contact lenses requires the determination of several parameters to ensure an effective lens and comfortable fit these parameters include the base curve and diameter of the contact lens as well as the refraction and the amount of corneal astigmatism.35 base curve refers to the radius of the spherical back surface of the contact lens because the keratometer measures the curvature of the anterior corneal surface which is the surface that will be adjacent to the posterior lens surface it is perfectly suited for determining the proper base curve the appropriate lens diameter can also be estimated from the keratometric

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490 surv ophthalmol 55 5 september october 2010 gutmark and guyton readings by employing a nomogram created by dyer based on the measurements of a large series of patients.3 measurement of the shape or toricity of the corneal surface is also achieved by the keratometer and is vital in choosing a properly fitting contact lens depending on the toricity of the cornea different lens designs may be selected e.g spheric aspheric bitoric 25 as contact lenses became more popular and the technology improved it became more and more important to obtain accurate measurements of a larger area of the cornea the keratometer in its original configuration could only measure approximately 2.5 mm of the central cornea.113 as contact lens diameters extended beyond this range clinicians became interested in ways to extend the capability of the keratometer several methods of measuring the periphery of the cornea were proposed thus allowing further study of the cornea as well as affording the ability to construct a crude topographical map of the entire cornea some clinicians made peripheral measurements of the cornea with the ordinary keratometer by altering the fixation of the subject with eccentric fixation targets in the plane of the mires.123 others created devices with small single mires6 or reduced mire separation69,104 that could allow for examination of small areas on the peripheral corneal surface when combined with fixation targets that guided the subject to look to the side however these smallmire keratometers suffered from decreased precision because the decreased movement of the mires reduced the precision of measurements.20 the era of intraocular lens implantation and refractive surgery with the advent of intraocular lens iol implantation and later refractive surgery keratometry found new applications and new challenges when iol implantation surgery was initially introduced surgeons implanted iols of a standard power it was soon realized that iol power should be calculated in order to obtain more precise postsurgical results various formulas were presented by a number of clinicians and visual scientists including binkhorst,5 colenbrander,13 and le grand.65 these formulas required several ocular measurements such as corneal power anterior chamber depth and axial length of the eye corneal power was measured by the keratometer anterior chamber depth was determined by a slit-lamp attachment and axial length was measured by ultrasound in an aphakic eye measurement of the axial length could also be calculated using the keratometrically determined corneal power and the aphakic spectacle correction near the anterior focal point soon additional formulas were derived some based on optical theory e.g haigis holladay i hoffer q whereas others were empirically based regression formulas e.g srk/i srk/ii binkhorst 112 and still others applied empirical data to theoretically derived formulas e.g srk/t 92 a precise determination of corneal radius is of vital importance for the accuracy of the iol power formulas of the relevant optical variables an error in corneal radius can have a tremendous effect on postoperative refractive error as seen in table 2 following corneal refractive surgery the measurement of corneal radius and the calculation of desired iol power are complicated by additional factors as discussed previously the accuracy of the keratometer relies on several assumptions regarding the normal cornea these assumptions although not entirely accurate had usually been sufficient for clinical purposes once the cornea becomes abnormal by disease or surgical intervention however these assumptions become even less applicable and errors in measurement increase because calculations of iol power require knowledge of the corneal power accurate keratometric measurements are essential as discussed previously calculations of corneal power are based on the radius of curvature of the cornea without direct measurement of the posterior corneal surface the conversion from radius of curvature to a dioptric power relies on estimations and adjustments that are necessary because only the anterior corneal curvature is measured because these corrections are based on a normal corneal shape and on a normal ratio between the anterior and posterior corneal surfaces any alteration in this configuration can introduce error into the calculations refractive surgeries such as radial keratotomy rk photorefractive keratectomy prk and laser-assisted in situ keratomileusis lasik alter the form of the normal cornea to achieve specific refractive outcomes because of these changes measurement of the cornea with keratometry and other corneal biometry techniques such as corneal topography became problematic table 2 refractive error as a function of various ocular measurements variable corneal radius axial length postoperative anterior chamber depth data from olsen.79 error 1.0 mm 1.0 mm 1.0 mm rx error 5.7 d 2.7 d 1.5 d

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origins of the keratometer 491 with rk radial slits are made in the mid-peripheral cornea normal intraocular pressure causes these weakened areas to bulge resulting in a flattening of the central cornea fig 10a errors in rk result because standard keratometric measurements coincide with the location of the newly formed transition zone where the flat central cornea begins its transition into the peripheral cornea as this area is steeper than the central cornea keratometric measurement is unreliable.112 although rk results in changes to the shape of the cornea this procedure does not significantly alter the thickness of the central cornea nor the ratio of the anterior surface to posterior surface radii of curvature.41 in prk and lasik on the other hand both the thickness of the cornea and the ratio of the anterior to posterior radii of the cornea change fig 10b 44,76,112,121 these changes in the cornea result in overestimation of corneal power in rk prk and lasik which leads to undercorrection with subsequent cataract and iol surgery.89,96,100,101,102,112 to overcome these inaccuracies with keratometry after refractive surgery various methods have been devised to estimate corneal power see hoffer46 for a more complete review these methods include 1 performing calculations based on known dioptric power values such as pre or postoperative refraction thereby circumventing the need to convert the radius of curvature of the cornea to a dioptric power value 2 adjusting the conversion factor index of refraction by estimating the change that will occur between the anterior and posterior corneal surfaces and 3 taking direct measurements of the posterior corneal surface.57 the first such method often referred to as the spherical equivalent change method112 or clinical history method,47 was published by guyton37 and holladay50 in 1989 and was initially intended for eyes after rk it proposed subtracting the change in the spherical equivalent due to the refractive surgery from the power measured by the keratometer pre-rk this method is accurate,47,48,49,101,111 but requires the availability of precise pre-surgical keratometry and refractive error.57 a number of other methods that require a variety of pre and post-refractive surgery data have been proposed.31,39,53,64,100,102,111 other methods that require knowledge of clinical history aimed at adjusting the index of refraction to make it more accurate following refractive surgery.10,54,62,63,96,99,101,102 when preoperative measurements are not available or when it is uncertain whether they were accurate and stable methods not requiring knowledge of clinical history are needed a number of such methods have been proposed including the contact lens method,94,109 methods that employ post-operative topography or keratometry data,33,38,60,95,98,103,107 a method that relies on postoperative pachymetry,36 and methods relying on new ocular scanning devices such as the pentacam oculus inc wetzlar germany7 or orbscan ii orbtek bausch and lomb salt lake city ut usa 11,85 transition to modern techniques of keratography although devices to measure corneal power and corneal topography have only recently become commonplace in ophthalmology clinics the origin for many of these dates back to the late 1800s many of these new devices are based on the placido disk principle in 1880 antonio placido described the use of a disk painted with alternating black and white rings with a hole in the center equipped with a plus lens for the examiner to look through fig 11 83,84 the reflection of these rings from the front surface of the patient s cornea gave the examiner a qualitative assessment of the contour of the cornea placido employed this technique took fig 10 changes in cornea induced by rk and prk/lasik a removal of corneal tissue in prk and lasik results in decreased corneal thickness and change in ratio of anterior to posterior corneal radii of curvature b bulging of midperipheral cornea in rk results in flattening of central cornea with no change in corneal thickness or ratio of anterior to posterior corneal radius of curvature.

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492 surv ophthalmol 55 5 september october 2010 gutmark and guyton photographs of the reflections and later calculated the radius of curvature of the cornea using these images or compared the images to images reflected by spheres of known radius.51,120 this was a very effective means of describing the corneal surface but calculations were difficult and comparisons were time-consuming although other improvements were attempted the method employing the placido disk would not allow for easy quantitative measurements as were available with the keratometer the advent of computers however enabled efficient application of the placido disk method the first device to incorporate computer technology to automate the use of the placido disk for performing corneal topography was the photoelectronic keratoscope described by reynolds and kratt in 1959.93 in 1981 the corneascope a new more advanced version of the photo-electronic keratoscope was introduced.19,97 automation of keratoscopes allowed keratometric measurements to be taken rapidly and this ability combined with the application of this technology to handheld devices40,42,61 allowed for improved measurement of the cornea in children.42,61,77 recently more sophisticated devices and techniques have been introduced and have the potential of replacing the traditional keratometer in clinical practice these include videokeratography optical coherence tomography slit-scanning scheimpflug photography and very high frequency ultrasound the primary advantages of the newer techniques are automation the extended area of measurement and increased accuracy currently there are a number of videokeratography devices that rely on the placido disk principle use computer-based calculations and display color-coded maps of corneal power.59 although the placido-disk-based devices are useful they only measure the anterior corneal surface therefore in order to calculate total corneal power various assumptions must still be made regarding the relationship between the anterior and posterior corneal surfaces one of the primary advantages of other modern devices is their ability to measure the posterior corneal surface accurately and directly the first commercially available device that allowed measurement of the posterior corneal surface was the orbscan originally from orbtek inc currently from bausch lomb 108,115 this device employed a scanning-slit technique for its measurements optical slit-scanning uses a number of slit light beams that scan the cornea the twodimensional images of the cross-sections of the cornea illuminated by the slit beam are captured by a camera and processed to obtain a topographical map of the cornea newer scanning-slit systems orbscan ii bausch lomb combine a placido disk with scanning-slit techniques to take advantage of both technologies.9,58 another modern keratometric technique that allows for direct measurement of the posterior corneal surface is scheimpflug photography employed in the pentacam oculus inc and galilei zeimer group port switzerland 45 this relies on the scheimpflug principle which describes the geometry necessary to produce focused images when the planes of the image lens and object are not parallel with each other see maus et al71 for a complete description an arrangement of the three planes according to this principle results in a larger focal depth than can normally be achieved.21,71,72,73,d this allows the camera to create a three-dimensional model of the anterior segment of the eye using the resulting measurements of the thickness of the cornea the software is able to calculate topographical and power maps of the cornea very high frequency ultrasound originally used in metallurgy has since been adapted for use in corneal imaging.91 this technology employed by artemis arcscan inc allows for direct visualization and measurement of the posterior cornea and the unique ability to generate 3-dimensional maps of individual corneal layers this can be very useful in the planning of corneal refractive surgery as well as in the monitoring of post-surgical results.91 comparative features of the different types of modern keratometry devices and those of the standard keratometer are presented in table 3 conclusions from its early origins in the study of the mechanism of accommodation the keratometer has repeatedly found new applications as ophthalmology has advanced its ease of use for the refraction of the cornea has contributed to its success in diverse applications over generations fig 11 placido disk example of hand-held device described by placido www.phisick.com

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origins of the keratometer table 3 characteristics of a selection of corneal biometry techniques technology keratometer placido disk scheimpflug photography year first described year first commercially available 1779 88 maximum points measured typical operation may be less 4 n/a 25,00086 advantages easy to use inexpensive peripheral corneal measurement direct measurement of posterior corneal surface visualization of anterior chamber structures large depth of focus71 direct measurement of posterior corneal surface mapping of individual corneal layers and anterior chamber91 optical opacities do not affect measurements82 direct measurement of posterior corneal surface9 non-contact imaging anterior segment imaging58 limitations limited area of measurement extrapolates central corneal data difficult to measure small changes in central cornea image distortion due to scheimpflug principle must be compensated by computer71 decreasing field of view with increasing resolution requires experienced examiner82 188084 198572 200486 very high-frequency ultrasound 199080 12,288 scan linesa optical slit-scanning 1995108 199942 9,60058 generation and detection of sufficiently narrow slit for accurate measurements difficult to achieve corneal haze affects measurements9 a maley p artemis information [online e-mail from patrick maley ceo arcscan inc 28 july 2009 493

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494 surv ophthalmol 55 5 september october 2010 gutmark and guyton 6 bonnet r cochet d new method of topographical ophthalmometry its theoretical and clinical applications am j optom physiol opt 1962;39:227 51 7 borasio e stevens j smith gt estimation of true corneal power after keratorefractive surgery in eyes requiring cataract surgery besst formula j cataract refract surg 2006;32:2004 14 8 burnett sm a theoretical and practical treatise on astigmatism st louis jh chambers and co 1887 9 cairns g mcghee cnj orbscan computerized topography attributes applications and limitations j cataract refract surg 2005;31:205 20 10 camellin m calossi a a new formula for intraocular lens power calculation after refractive corneal surgery j refract surg 2006;22:187 99 11 cheng ac ho t lau s et al introducing a new ratio useful in the estimation of preoperative corneal power in patients with myopic lasik based on postoperative corneal data cornea 2009;28:1 4 12 clausen t beschreibung eines neuen micrometers astronomische nachrichten 1841;186 95 6 13 colenbrander mc calculation of the power of an iris clip lens for distant vision br j ophthalmol 1973;56 735 40 14 dallos j contact glasses the invisible spectacles arch ophthal 1936;154 617 23 15 davis ae the refraction of the eye new york the macmillan company 1900 pp 388 16 de schweinitz ge diseases of the eye a handbook of ophthalmic practice for students and practitioners philadelphia wb saunders co 1921 pp 763 17 descartes r discourse on method optics geometry and meteorology translated by paul j olscamp indianapolis hackett publishing co 2001 pp 120 1 18 donders fc moore wd on the anomalies of accommodation and refraction of the eye london jw rooke 1864 19 doss jd hutson rl rowsey jj et al method for calculation of corneal profile and power distribution arch ophthalmol 1981;99:1261 5 20 douthwaite wa evardson wt corneal topography by keratometry br j ophthalmol 2000;84:842 7 21 dubbelman m van der heijde gl the shape of the anterior and posterior surface of the aging human cornea vision res 2006;46:993 1001 22 duke-elder s abrams d the dioptric imagery of the eye in duke-elder s ed system of ophthalmology vol 5 st louis the c.v mosby company 1970 pp 99 100 23 dunne mcm royston jm barnes da normal variations of the posterior corneal surface acta ophthalmol 1992;70 255 61 24 edmund c posterior corneal curvature and its influence on corneal dioptric power acta ophthalmol copenh 1994;72:715 20 25 edrington tb schornack ja initial evaluation in bennett es weissman ba eds clinical contact lens practice philadelphia lippincott 2005 pp 197 214 26 elliott m callender mg elliott db accuracy of javal s rule in determining spectacle astigmatism optom vis sci 1994 711 23 6 27 emsley hh visual optics london hatton press ltd 1936 28 enoch jm descartes contact lens am j optom arch am acad optom 1956;332 77 85 29 ettles w the ophthalmometer trans opt soc 1906;8 53 73 30 fam hb lim kl validity of the keratometric index large population-based study j cataract refract surgery 2007;33 686 91 31 feiz v mannis mj garcia-ferrer f et al intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia a standardized approach cornea 2001;20:792 7 32 ferguson ll optics and opticians the jewelers review 1899;3221 652 novel devices are now appearing that allow access to areas in the eye such as the posterior corneal surface that were previously difficult or even impossible to study as these new anatomic frontiers are explored some are proving significant and others less so currently the keratometer is still widely used due to its simplicity minimal expense and the speed with which measurements can be taken however as the costs of new devices are decreasing they are becoming more competitive in terms of speed and ease of use although the use of the keratometer is declining as newer and more powerful devices are replacing it it remains the gold standard against which these new instruments can be validated method of literature search the literature review for this article was performed through medline embase isi and scopus using the following search terms as well as combinations of the same terms keratometer ophthalmometer history ocular biometry catoptric astigmatism keratometric index contact lens fitting helmholtz javal schiøtz refractive surgery iol placido corneal topography and hand-held u.s and international patent literature was also searched using some of the same search terms as well as others specific to the various devices discussed all available years were covered additional literature was found in the reference lists of other articles various digital libraries including the hathi trust digital library and google search of the listed terms relevant non-english sources were also considered english abstracts for some non-english sources were employed and full or partial translations of text were obtained for other important non-english sources all original sources relevant to the topic were considered for inclusion some sources were excluded to avoid redundancy references 1 airy gb on a peculiar defect in the eye and a mode of correcting it transactions of the cambridge philosophical society 1827;22 267 71 2 amoils sp intraoperative keratometry with the oval comparator astigmometer br j ophthalmol 1986 709 708 11 3 bannon re walsh r on astigmatism three parts am j optom arch am acad optom 1945;222 101 11 224 162 81 225 210 9 4 berry ga ophthalmology a new practical ophthalmometer am j med sci 1888;963 308 9 5 binkhorst cd power of the prepupillary pseudophakos br j ophthalmol 1972;56:332 7

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origins of the keratometer 33 ferrara g cennamo g marotta g et al new formula to calculate corneal power after refractive surgery j refract surg 2004;20:465 71 34 fick ae a contact-lens arch ophthalmol 1888;17:215 26 35 gasson a morris j the contact lens manual a practical guide to fitting edinburgh butterworth heinemann ed 3 2006 p 26 36 geggel hs pachymetric ratio no-history method for intraocular lens power adjustment after excimer laser refractive surgery ophthalmology 2009;116:1057 66 37 guyton dl consultations in refractive surgery refract corneal surg 1989;5:202 3 38 haigis w intraocular lens calculation in extreme myopia j cataract refract surg 2009;355 906 11 39 hamed am wang l misra m et al a comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis ophthalmology 2002;109:651 8 40 hammack gg evaluation of the alcon renaissance handheld automated keratometer international contact lens clinic 1997;24:59 65 41 hanna kd jouve fe waring go preliminary computer simulation of the effects of radial keratotomy arch ophthalmol 1989;107:911 8 42 harvey em miller jm dobson v reproducibility of corneal astigmatism measurements with a hand held keratometer in preschool children br j ophthalmol 1995;79:983 90 43 herschel jfw light encyclopedia metropolitana london baldwin cradock 1830 p 398 44 hjortdal jo bohm a kohlhaas m et al mechanical stability of the cornea after radial keratotomy and photorefractive keratectomy j refract surg 1996;12:459 66 45 ho jd tsai cy tsai rj et al validity of the keratometric index evaluation by the pentacam rotating scheimpflug camera j cataract refract surg 2008 341 137 45 46 hoffer kj intraocular lens power calculation after previous laser refractive surgery j cataract refract surg 2009;35 759 65 47 hoffer kj intraocular lens power calculations for eyes after refractive keratotomy j refract surg 1995;11:490 3 48 holladay jt iols in lasik patients how to get them right the first time rev ophthalmol 2000;8:59 49 holladay jt cataract surgery in patients with previous keratorefractive surgery rk prk and lasik ophthalmol pract 1997;15:238 44 50 holladay jt consultations in refractive surgery refract corneal surg 1989;5:202 3 51 horner dg salmon to soni ps corneal topography in benjamin wj ed borish s clinical refraction philadelphia wb saunders 1998 pp 524 58 52 jackson e value of the ophthalmometer in practical refraction work trans am ophthalmol soc 1894;7:177 80 53 jarade ef abi nader fc tabbara kf intraocular lens power calculation following lasik determination of the new effective index of refraction j refract surg 2006;22:75 80 54 jarade ef tabbara kf new formula for calculating intraocular lens power after laser in situ keratomileusis j cataract refract surg 2004;30:1711 5 55 javal l schiøtz h un opthalmometre pratique annales d oculistique 1881;86:5 21 56 javal e memoires d ophthalmometrie paris libraire de l academie de medecine 1890 p 131 57 kalyani sd kim a ladas jg intraocular lens power calculation after corneal refractive surgery curr opin ophthalmol 2008;19:357 62 58 karpecki pm bausch lomb orbscan ii/iiz anterior segment analysis system in wang m ed corneal topography in the wavefront era a guide for clinical application thorofare slack inc 2006 pp 191 206 59 klyce sd computer-assisted corneal topography highresolution graphic presentation and analysis of keratoscopy invest ophthalmol vis sci 1984;25:1426 35 495 60 koch d wang l calculating iol power in eyes that have had refractive surgery [editorial j cataract refract surg 2003;29:2039 42 61 lam akc a hand held keratometer ophthalmic physiol opt 1995;153 227 30 62 langenbucher a haigis w seitz b difficult lens power calculations curr opin ophthalmol 2004;15:1 9 63 langenbucher a scholz k szentmary n et al calculations ´ of corneal power after corneo refractive surgery from keratometry and change of spectacle refraction some considerations on the clinical history method curr eye res 2007;325 421 9 64 latkany ra chokshi ar speaker mg et al intraocular lens calculations after refractive surgery j cataract refract surg 2005;31:562 70 65 le grand yj physiological optics [translated by g sami and sg el hage berlin springer verlag 1980 pp 136 7 66 leroy cja dubois r un nouvel opthalmometre pratique revue generale d ophthalmologie 1888;2:49 62 ´ ´ 67 listing jb mathematische diskussion des ganges der lichtstrahlen im auge in wagner r ed handworterbuch der physiologie leipzig f.c.w vogel 1853 pp 451 504 68 mandell rb jesse ramsden inventor of the ophthalmometer am j optom arch am acad optom 1960;37:633 8 69 mandell rb methods to measure the peripheral corneal curvature part 3 ophthalmometry j am optom assoc 1962;33:889 92 70 masket s correlation between intraoperative and early postoperative keratometry j cataract refract surg 1988 143 277 80 71 maus m krober s swartz t et al pentacam in wang m ed corneal topography in the wavefront era a guide for clinical application thorofare slack inc 2006 pp 281 94 72 mayer h irion km new approach to area image analysis of scheimpflug photos of the anterior eye segment ophthalmic res 1985;172 106 10 73 merklinger hm depth of field in merklinger hm ed focusing the view camera a scientific way to focus the view camera and estimate depth of field dartmouth nova scotia macnab print 1993 pp 49 56 74 morlet n maloof a wingate n et al reliable keratometry with a new hand held surgical keratometer calibration of the keratoscopic astigmatic ruler br j ophthalmol 1998;821 35 8 75 muller a brillenglaser und hornhautlinsen inaugural ¨ dissertation university of kiel 1889 76 naroo sa charman wn changes in posterior corneal curvature after photorefractive keratectomy j cataract refract surg 2000;26:872 8 77 noonan cp mackenzie j chandna a repeatability of the hand-held nidek auto-keratometer in children j aapos 1998;23 186 7 78 olsen t calculation of intraocular lens power a review acta ophthalmol scand 2007;85:472 85 79 olsen t on the calculation of power from curvature of the cornea br j ophthalmol 1986;70:152 4 80 pavlin cj sherar md foster fs subsurface ultrasound microscopic imaging of the intact eye ophthalmology 1990;97:244 50 81 pearson rm efron n hundredth anniversary of august muller s inaugural dissertation on contact lenses surv ¨ ophthalmol 1989;34:133 41 82 pinero dp plaza ab alio jl anterior segment biometry with 2 imaging technologies very-high-frequency ultrasound scanning versus optical coherence tomography j cataract refract surg 2008;34:95 102 83 placido a neue instrumente centralblatt fur praktische augenheilkunde 1881;30 1 84 placido a novo instrumento de esploracao da cornea periodico d oftalmologia pratica 1880;5:27 30 85 qazi ma cua iy roberts cj et al determining corneal power using orbscan ii videokeratography for intraocular lens calculation after excimer laser surgery for myopia j cataract refract surg 2007;33:21 30

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