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Contribution of the ocular surface to visual optics
Experimental Eye Research 78 (2004) 417–425 www.elsevier.com/locate/yexer
Review
Contribution of the ocular surface to visual optics C.B. Courville, M.K. Smolek, S.D. Klyce* Lions Eye Research Laboratories, LSU Eye Center, Louisiana State University Health Sciences Center, New Orleans, LA, USA Received 15 September 2003; accepted 13 October 2003
Abstract The air/tear interface contributes 70% of the vergence in the eye and, because of this, even minor variations in its shape can produce significant visual deficit. Placido disc-based corneal topographers measure the precise characteristics of the corneal surface, transforming shape into color-coded dioptric power maps and topography indexes related to optical quality and specific patterns associated with pathology. Artificial intelligence-based methods are used to classify corneal topography and these are used as screening tools. Coupling corneal topography measurements with aberrometry measurements permits the display of the internal aberrations of the eye. Together, these data provide the opportunity to extend refractive correction beyond sphere and cylinder to the higher order aberrations as well. q 2003 Elsevier Ltd. All rights reserved. Keywords: cornea; topography; wavefront; aberrometry; refractive surgery; visual optics
1. Introduction The transparent cornea in the human is some 12 mm in diameter and approximates in cross-section the shape of a negative meniscus lens, being thicker in the periphery (, 0·70 mm) than in the center (, 0·55 mm). As a result, the convex anterior surface is less curved than the concave posterior surface. The anterior radius of curvature of the eye may vary from 7·0 to 8·5 mm and still be consistent with normal vision, but on average, the radius of curvature is , 7·8 mm. The anterior curvature of the cornea in combination with the change in refractive index from air ðn ¼ 1·000Þ to stroma ðn < 1·376Þ generates a large positive refractive effect on light entering the cornea, giving it a power of , 48 diopters (D). The concave posterior curvature contributes about 2 5 D of power due to its negative curvature and the nearly matching refractive indexes of the aqueous humor ðn < 1·336Þ and the stroma. In all, the typical cornea contributes about 43 D to the total 60 D power of the eye, or about 70% of the total refraction. This level of ocular power is necessary to produce a clear image on the retina because the axial length of the eye is only about 24 mm in the average emmetropic * Corresponding author. Dr Stephen D. Klyce, LSU Health Sciences Center, LSU Eye Center, 2020 Gravier Street, Suite B, 70112-2234 New Orleans, LA, USA. E-mail address: [email protected] (S.D. Klyce). 0014-4835/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. DOI:10.1016/j.exer.2003.10.012
eye (range of 22 – 26 mm). Refractive power is supplemented by the crystalline lens. Altering the shape of the lens through the action of the ciliary muscle and processes allows the visual system to accommodate for near vision tasks where more power is needed to overcome the additional negative vergence of light entering the cornea. It should be remembered that the range of corneal power in emmetropia can actually be fairly broad; anywhere from 39 to 47·5 D can still be consistent with normal vision, depending on the power of the lens and the axial length. Beyond age 40, the visual system gradually loses accommodative ability due to protein changes that cause hardening of the crystalline lens. The cornea itself contributes essentially nothing to accommodation, although it may be possible with a sensitive topography device to measure some minor distortions to the corneal shape due to traction on the globe by the ciliary muscle. All normal corneas tend to share certain topographical features in common. The central 3 –4 mm of the cornea tends to have a nearly constant curvature and this region has been referred to as the apical cap. Its location and diameter is a fairly good match to the approximately 4 mm diameter of the entrance pupil under photopic (daylight) conditions. In other words, the optimum aberration-free region of the cornea is optically matched with the pupil and should therefore provide a high quality retinal image. Refractive surgeons take great care in centering procedures with
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respect to the entrance pupil in order to minimize high order aberrations, ghosting, and glare from light scatter that would accompany decentration of the optical zone with respect to the pupil. If the optical zone is displaced with respect to the pupil, night vision complaints increase substantially. The initial refractive element in the eye is actually the tear film which smoothly coats the anterior surface of the cornea. The presence of the tears is critical for vision as the outer membranes of the epithelial squamous cells are reticulated with projections that are 0·5 mm in height and with a similar spacing. Without the tears to smooth these projections, severe degradation in the optics of the cornea would result. The 7 mm thick tear layer is stabilized by a mucin-rich fuzzy surface coat with an outer evaporationblocking lipid layer. Tear film breakup from dry eyes can produce dellen and severe reduction in visual acuity. Because even very minor distortions in the shape of the tear-coated cornea can degrade visual acuity, efforts to characterize the corneal topography in detail have been made for centuries. Direct observation of curvature is not of much value; it was the reflection of a window frame from the corneal surface in the 15th century that provided clues to the eventual development of the Placido disc – the basis for accurate measurement of corneal shape in modern times.
2. Basic principles of measurement 2.1. Keratometry Stemming from the development of the ophthalmometer by Hemholtz (1909) with refinements by Javal and Schiotz, keratometry measures corneal curvature by projecting an illuminated pattern of light of known dimensions onto the corneal surface. Changes in the size of the reflected image follow the traditional formula for a convex mirror to calculate the radius of curvature; accuracy in the past had been given as 0·25 – 0·75 D (Swinger, 1987). Modern keratometers take measurements by using four positions on the corneal surface lying approximately 3 or 4 mm apart. The radius of curvature, Rc ; along the orthogonal steep and flat principal meridians can be converted to power in diopters, P; using the standard keratometric index, 1·3375, less the refractive index of air, 1·000 (Rogers et al., 1997) P ¼ 0·3375=Rc : As noted above, the power given by the keratometry formula is that of the total cornea, not the tear/air interface alone. Since the keratometer reports only the powers of the two principal meridians, the cornea is modeled as a sphere or ellipsoid. Therefore, keratometers cannot be used to measure irregular corneal shapes. Because they make their measurements generally at the pupil margins, they are not effective for assessing the optics of the central cornea. Even 50, keratometry continues to be valuable for anterior
segment applications, including intraocular lens (IOL) calculations and contact lens fitting for corneas lacking disease or trauma. 2.2. Placido disc The Placido disc, originally introduced by Antonio Placido, consists of a circular target of alternating concentric light and dark rings, or mires, with a central aperture through which the virtual image of the target reflected from the tear film surface can be observed. As with keratometry, the size of the image relates directly to power of the corneal surface; steep surfaces minify the image while flat surfaces magnify it. However, unlike keratometry, mires can be projected over a broad area of the cornea, and changes in curvature can be assessed at many locations. Since its inception, the Placido disc concept has been adapted and improved and is now the most widely used technology in modern corneal topographers. 2.3. Corneal topographers As corneal transplantation grew in medical practice, surgeons increasingly became aware that the procedure induced a significant amount of astigmatism. In an attempt to counter this, Troutman (1970) and others developed a surgical keratometer which mounted directly on the operating microscope (Troutman et al., 1977). Although this helped to reduce astigmatism, it became apparent that most patients lost best spectacle-corrected vision more from induced corneal irregularities than from increased cylinder. To allow measurement of corneal irregularities, better ways to measure shape than modified keratometry needed to be developed. The photokeratoscope, which photographed Placido disc images, was developed to compensate for this limitation. By projecting a series of mires onto the corneal surface and capturing the reflection with an instant film camera, surgeons were able to analyze by visual inspection 70– 95% of the total corneal surface, including paracentral and peripheral areas (Rowsey et al., 1981). This approach was utilized in the first widely distributed photokeratoscopes developed by Nidek (Nidek PKS-1000; Riss et al., 1991) and by Kera Corp (Corneascope; Rowsey et al., 1981). These devices provided details of the cornea’s topography, but were limited to the management of relatively severe irregularities in the corneal surface such as occur in corneal grafts, moderately advanced keratoconus, and trauma. They were limited because visual inspection of misshapen mires was too insensitive to pick out all the corneal aberrations of significance to vision. The introduction of radial keratotomy into clinics in 1979 spurred the need for a more accurate analysis of corneal topography. Utilizing advances in digital computers and modeling algorithms, corneal topographers evolved to meet
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the needs of refractive surgeons in pre-operative screening and investigation of postoperative complications. As the number of commercial corneal topographers continues to grow due to market demand, the underlying optical principles and techniques have varied somewhat; the most widespread approach is based on Placido disc technology. The measurement of corneal curvature with the scanning slit, laser holographic interferometry, and rasterstereography have not enjoyed productive clinical use, but it is instructive to view the different approaches that have been tried. 2.4. Placido disc-based corneal topographers The first technology applied by corneal topographers to measure corneal power was the Placido disc, and this approach remains the most viable approach due to its sensitivity, reproducibility, relative freedom from movement artifact, and non-invasiveness. The first commercially successful corneal topographer was the Corneal Modeling System (CMS; Computed Anatomy, Inc, New York, USA) (Gormley et al., 1988), which captured the reflected Placido target image with a CCD digital camera, automatically measured mire shapes, and transformed these into the threedimensional shape and power of the corneal surface. Parenthetically, the CMS was the first device to use a scanning slit to measure the back surface of the cornea as well as the front, but this approach was abandoned owing to cost and lack of accuracy. Several computer algorithms have been developed to reconstruct a model of the corneal surface shape, but since there is no exact solution, approximations can lead to inaccuracies. Fortunately, these are usually confined to the corneal periphery (Maguire et al., 1987; Wilson and Klyce, 1991b). Some of the algorithms have serious deficiencies that can lead to the false indication of keratoconus (Mandell et al., 1996). Placido target-based topographers are available in two general forms distinguished by the diameter of the target. Large diameter targets are less sensitive to magnification errors due to their long working distance, but these devices tend to lose data from the periphery because of shadows caused by the nose and the brow. The small diameter, coneshaped targets do not suffer the same shadow-induced data loss and can project mires far onto the peripheral cornea and sclera, but must perform extremely accurate range compensation to maintain their precision. As a result of their better performance in the corneal periphery, the small cone Placido devices may be more appropriate for contact lens fitting. 2.5. Stereographic corneal topographer A separate approach that avoids the uncertainties of the approximations inherent in Placido based topographers is rasterstereography (Warnicki et al., 1988; Arffa et al., 1989;
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Naufal et al., 1997). With this technology, a drop of fluorescein is instilled into the cul de sac and a grid or raster pattern of cobalt blue light is then projected onto the anterior surface of the eye. The captured stereo images are processed using triangulation to reconstruct the cornea’s topography without approximating algorithms. Surface area coverage is excellent with analysis proceeding out onto the sclera. Rasterstereography can also measure corneal shape in very distorted corneas (e.g. advanced keratoconus and early postoperative corneal grafts) on which Placido mires become indistinct and are not discernable. However, these advantages are balanced with the limitation that direct measurement of surface position does not yield the same sensitivity of measurement as reflected mire image positions. This diminished sensitivity, together with the uncertain effects of fluorescein on tear film stability and structure, reduces the utility of rasterstereography in the clinic. 2.6. Interferometric corneal topographer The method with the highest potential sensitivity for measuring corneal shape is interferometry (MacRae et al., 1989; Rottenkolber and Podbielska, 1996; Smith, 1997). Similar techniques have long been used by the optical industry to detect lens and mirror aberrations with submicron accuracy. With this method a reference surface, or its hologram, and the measured corneal surface are optically compared and the resulting interference fringes are used to determine the difference between the two shapes. Due to the wide variation in corneal shapes, however, it is difficult to represent every variation with a single interference reference. Although multiple studies have been conducted employing different forms of this technology, including laser-based devices (Shack et al., 1979; Burris et al., 1993; Smolek, 1994), this approach has not enjoyed clinical acceptance. 2.7. Scanning slit corneal topographer Scanning slit technology facilitates the measurement of both the anterior and posterior surfaces of the cornea. Since both surfaces, along with corneal thickness, are needed to accurately calculate total corneal power, directly measuring the relative positions of the surfaces would seem to grant scanning slit devices a major advantage over other types of corneal topographer. This technique not only eliminates the need for elevation or shape measurement approximations, but it is also able to measure corneal thickness over a broad area. Scanning slit technology does have its limitations, however. One major drawback is that measurement requires over 1 sec for completion, leaving the data muddled with motion artifact from fixation drift, muscle tremor, pulse, and nystagmus, all of which occur when the data is not captured in 30 msec or less. This problem can be reduced with a tracking system or post-capture registration
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techniques, though only with great expense and difficulty since landmarks, which are necessary for registration, are lacking on the normally transparent cornea. Lack of sensitivity when reconstructing corneal topography from direct surface measurement is also a problem. To overcome this, corneal topography is measured with a traditional Placido target in the Orbscan II model (Bausch and Lomb, Rochester, NY, USA). Though scanning slit technology alone is not practical for measuring topography, it appears to have some value in generating thickness profiles.
3. Presentation formats and standards Once computer-assisted corneal topography was available and it was possible to create an accurate visual representation of the cornea, it became necessary to devise ways in which this newfound data source could be precisely evaluated and applied. Doss et al. (1981) pioneered a method for reconstructing corneal shape from mire patterns and from this corneal power. Klyce (1984) built on this work to create data display methods starting with threedimensional wire-mesh plots. The final outcome of such studies was the introduction of the color-coded contour map of corneal powers (Maguire et al., 1987), which soon became the international standard display format for corneal topography. With this development, clinicians have been able to view pertinent topographic information through color association and pattern recognition. The palette of colors associates normal powers with shades of green, lower powers as cool colors, and higher than normal powers as warm colors. Using the contour map concept allows characteristic patterns in corneal topography to be recognized. For example, corneal cylinder displays as a ‘bow tie’ pattern, keratoconus as a local area of steepening, and pellucid marginal degeneration with its characteristics of a claw or ‘C’-shaped pattern of steepening and ‘negative’ bow tie. Likewise, the contour map permits evaluation of refractive surgical results including optical zone size, centration relative to the entrance pupil, and the occasional defect such as a central island. Due in part to the rapid advance of computer technology, modern corneal topographers are now equipped with the computational power to statistically analyze topography data, making it possible to display many different forms of clinically significant information. The main display formats include axial power (recommended for routine clinical use), refractive power, tangential power, and elevation maps. These are supplemented with a background video image of the eye to relate scale and position, the display of multiple exams simultaneously for viewing the progression of a disease or post-surgical results, and the construction of difference maps that aid in such aspects as showing early postoperative effects of a surgical procedure or the evolution of specific topographic features.
3.1. Units of measure Corneal topographers measure corneal surface curvature. When these devices are used in specific clinical applications, such as contact lens fitting, the measured curvature may be suitably expressed in units of millimeters. More often, when used to evaluate pathology, the optics of the eye, and refractive errors, it is more convenient for the clinician that these devices represent corneal curvature as a power in units of diopters (D). As noted above, this power represents the combined power of both corneal surfaces, and because of this may not be an accurate reflection of the change in refraction following refractive surgery (Swinger and Barker, 1984; Arffa et al., 1986). This is because tissue subtraction procedures such as LASIK change the anterior corneal curvature and corneal thickness, but not that of the posterior surface. To calculate the refractive effect of changing corneal anterior surface curvature by itself, one should use the corneal refractive index, 1·376, while for general use, the keratometric index 1·3375 is preferred. 3.2. ANSI display standards In 1999, the American National Standards Institute (ANSI) released a report pertaining to standards in corneal topography development, research, and practice. The report, ‘Corneal Topography Systems-Standard Terminology, Requirements’ (ANSI, 1999), defines terminology, requirements for measurement and testing, and display standards. In anticipation of its release it was assumed the standard would define a single color palette with specific fixed intervals to facilitate the accurate comparison of data obtained with corneal topographers from different manufacturers. Unfortunately, the specifications for topography displays failed to define a single specific scale and instead proposed a variety of suggestions as to what the parameters of such a scale should be. The ANSI Standard specifies that curvature maps should use one of three corneal diopter intervals: 0·5, 1·0, or 1·5 D. This leaves the user a choice in scale interval, which is contrary to the goal of standardization, and makes the comparison of color topography maps between different manufacturers unreliable. The same problem is encountered in the selection of a proper range of powers, where the ANSI Standard states that the number of interval-representing colors should be between 21 and 25. Three choices of interval size and five choices of color range define numerous possibilities for scales. Further, when discussing which colors should be used to represent these scale intervals, the ANSI Standard states ‘the hue should be monotonically decreasing from green to red and shall be monotonically increasing from green to blue.’ The first problem with this statement lies in the difficulty of defining what ‘blue’ or ‘green’ means simply by its color name, since the interpretation of such color names
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can vary considerably among eras and cultures (Kaiser and Boynton, 1996b). Secondly, the term ‘monotonically’ can refer to any number of step interval changes, such as changes in hue, saturation, and brightness (HSB), changes in wavelength, or the observer’s personal impression of equal changes in hue. Another ambiguity present in this ANSI Standard is the lack of any mention of varying brightness or saturation. It is typically understood that hue is the characteristic of color that varies most with changes in wavelength (Cornsweet, 1970), but color is not defined simply by changes in hue. Changes in saturation and brightness should also be taken into account when determining which colors allow optimum contrast and legibility of grayscale reproductions, but these variables were never considered. Nor does the standard consider the effects of viewing conditions, even though perceived color is dependent on the illumination and surrounding environment (Kaiser and Boynton, 1996a). 3.3. ANSI alternative To combat the ambiguity inherent in the ANSI Standard, Smolek and coworkers set out to define a single scale and color palette that takes into account all of these complications and could be universally adopted by all topographer manufacturers (Smolek et al., 2002). In this standard, referred to as the Universal Standard Scale (USS), first a central power value was established by finding the mean and standard deviation (SD ) of 27 normal corneas. This value was 42·76 ^ 1·59 D; therefore the central power value was set to 42·75 D and the interval size was set to the optimal value of just under 1 SD , or the widely used 1·5 D. This contour interval has been proven to be small enough to capture all topographical characteristics of clinical importance (Wilson et al., 1993), and through clinical experience it has been found that smaller intervals can often lead to misinterpretations of non-existent conditions like irregular corneal topography or keratoconus. In order to associate familiar color recognition with normal and abnormal corneas, the corneal powers lying within ^ 2SD of the determined mean for normals were set to green hues. Therefore, four contour intervals, two above and two below the mean, are displayed as green colors in this standard. Powers immediately above this þ 2SD limit are displayed as yellow, whereas powers immediately below the 2 2SD limit are displayed as cyan. Through the study of 388 topographical maps representing a wide variety of conditions, the optimal range of power values was determined to be 30·0– 67·5 D. This range encompassed 99·9% of the powers present in the trial data set, better than the ANSI standard using each suggested interval size (Smolek et al., 2002). The associated palette of colors used in the USS was arrived at by meticulous subjective adjustment of brightness, saturation, and hue to establish easy to distinguish color contours. The final color palette is a specifically defined range of colors that enable the observer
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to quickly determine clinically important topographical aspects of a color map without confusion. The advantage of adopting a single standard scale like the USS lies not only in the ease of comparison between differing corneal topographers, but more importantly in the accuracy of clinical examination and practice. In the absence of such a scale, the variation between displays given by separate topographers will undoubtably lead to confusion, misinterpretation, and problematic outcomes. 3.4. Self-adapting scales Self-adapting or normalized scales have also produced confusion in the correct interpretation of a color-coded corneal topography map. With this approach, the computer is programmed to search out the range of powers in a given corneal map and then to adjust the range and power interval of the scale so that the full range of colors are used to display topography. With this scheme, the color association concept is defeated as even normal corneas will contain regions that have warm colors usually related to abnormally high powers as well as regions that have the cool colors that usually signify lower than normal powers. A concern is that a normal cornea viewed with the self-adapting scale will usually show an area of red which often signifies the presence of keratoconus in the fixed standard scale. Conversely, a highly irregular cornea with a wide range of powers will be condensed in appearance with the selfadapting scale, potentially masking a major source of visual disability. Most if not all of the corneal topographers commercially available have a certain flexibility as to which scale is used routinely. It is strongly advised that the Universal Standard Scale (Smolek et al., 2002), or one closely similar to that specification be adopted for general use.
4. Corneal topography indexes Though standardized color-coded contour maps can greatly improve the clinician’s ability to properly diagnose corneal conditions, these displays alone cannot produce the numerical values essential in clinical management. Further, the optical quality of a corneal surface cannot be directly determined from visualization of the color map. Therefore, quantitative indexes have been developed to supplement graphical representations. Simulated keratometery (SimK) values, one of the first corneal topography indexes developed, are designed to simulate the curvature measurements given by a typical keratometry exam (Dingeldein et al., 1989a). Simulated Keratometry and clinical keratometry correlate well (Wilson and Klyce, 1991a). However, it should be taken into account that refractive astigmatism does not necessarily agree with corneal astigmatism since the lens can contribute part if not all of the refractive astigmatism,
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although this appears to be rare. SimK values describe the powers and axes of the steepest and flattest meridians and are designated SimK1 and SimK2, respectively; they are calculated using the corneal topographer data from points on the cornea corresponding to those used for keratometry readings. Cylinder and spherical equivalent can be easily calculated using SimK indexes and are therefore often displayed alongside color maps. SimK values prove extremely useful when applied to determine the amount and axis of astigmatism or eyes with irregular corneas and in the fitting of contact lenses. 4.1. Corneal eccentricity index The ‘Corneal Eccentricity Index’ (CEI) was created to act as an indicator of the degree of eccentricity in the cornea (Maeda et al., 1994a). This value is typically determined by fitting an ellipse to the elevation data provided by the topographer. In a study of 22 normal corneas, the CEI obtained was 0·33 ^ 0·26 (mean ^ 1SD ), corresponding to the prolate shape of the normal central cornea. Use of this index is helpful when fitting contact lenses and differentiating between normal prolate corneas and oblate corneas flattened by myopic refractive surgery. 4.2. Average corneal power The ‘Average Corneal Power’ (ACP) is an area-corrected average of corneal power lying ahead of the entrance pupil (Maeda et al., 1997). There is a good correlation between the average keratometric power and ACP (r 2 ¼ 0·96; P , 0·001; Dingeldein et al., 1989b). However, ACP gives a better estimate of central corneal power than can be obtained from keratometry-like values as it obtains its measure from the whole pupillary area rather than four points near the margin of the pupil. The value of this can be appreciated when analyzing corneal curvature after refractive surgery. With a small optical zone or a decentered treatment area, the use of keratometry can lead to errors greater than 1 D (Maeda et al., 1997). In these cases, it is preferable to use ACP or its equivalent for intraocular lens power calculations. 4.3. Surface regularity index The first index developed to measure the impact of corneal irregularities on optical quality was the ‘Surface Regularity Index’ (SRI; Wilson and Klyce, 1991a). This index sums the meridional mire-to-mire power changes over the apparent entrance pupil, increasing as topographic irregularities increase. SRI was correlated to visual acuity for a group that contained normals, keratoconus, and corneal transplants. This correlation allows the clinically useful prediction of the ‘Potential Visual Acuity’ (PVA) in Snellen chart format, which as noted above, can not be determined from visual inspection of a topography map.
Different approaches were taken by Maloney et al. (1993) and Holladay (1997). They chose to first determine the best-fitting ellipsoid for the central cornea, then calculate the difference between this surface and corneal elevation. Correlating these distortions with clinical data, the results are displayed as color-coded maps of predicted regional Snellen acuity (Holladay, 1997). 4.4. Screening tools and neural networks Even with training, interpretation of corneal topography can often be equivocal, particularly in establishing threshold values between normal corneas and those with very early pathology. As well, there are situations with confounding diagnoses where the similarity between two possible conditions (for example, contact lens molding and early keratoconus) makes interpretation difficult. Because of this, several classification schemes have been developed to run on corneal topographers that aid in classification of corneal topography. 4.5. Indexes for keratoconus detection Ever since the introduction of keratorefractive surgery, the presence of keratoconus has generally been considered as a contraindication. The incidence of keratoconus is very small in the general population, perhaps 0·01% or less, but among refractive surgical candidates rises to 8% or more. Corneal topography is the most sensitive method for the detection of keratoconus where it appears as a localized area of steepening, generally displaced inferiorly, but a firm diagnosis must be accompanied by the clear indication of thinning near the cone apex. Vogt’s striae, Munson’s sign, and a Fleischer ring may also be observed, but these often accompany keratoconus at its more advanced stages. The Orbscan II scanning slit topographer can also be used to detect the pattern of corneal thinning, but most studies find it insensitive to detect the thinning that can be measured with ultrasound in early keratoconus. In the absence of any detectable thinning, an area of topographic steepening may be classified as keratoconus suspect (Waring, 1993), whereas clinical keratoconus is recognized by localized steepness along with thinning. The conundrum for the clinician has been to differentiate between normal variations in corneal steepness and asymmetry and true pathology. Methods based on measurements made from corneal topography data have been developed to meet this challenge. Rabinowitz and McDonnell (1989) were the first to use numerical methods to detect keratoconus using corneal topography data. They developed indexes to measure power differences between the superior and inferior paracentral corneal regions (designated I – S values), the central corneal power (Max K), and the power differences between the left and right eyes. Their corresponding analysis showed that a central corneal power greater than 47·2 D or an I – S value
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greater than 1·4 D is consistent with keratoconus suspect, whereas central corneal powers greater than 48·7 D or I – S values greater than 1·9 D are consistent with clinical keratoconus. This is enough to distinguish the topography of keratoconus corneas from that of normal corneas, but unfortunately the specificity of the method is problematic. Several additional topography studies have appeared in the literature that suffer the same weakness. Using strategies that only differentiate between keratoconus and normal corneas can incorrectly identify conditions such as contact lens molding and corneal transplant topography as keratoconus. Therefore, Maeda et al. (1994b, 1995a)) developed the Keratoconus Prediction Index (KPI) that was able to differentiate between keratoconus and most of the common classes of corneal topography. The KPI value is derived from topographic indices that include the Differential Sector Index (DSI), the Opposite Sector Index (OSI), the Center/Surround Index (CSI), the Surface Asymmetry Index (SAI), the Irregular Astigmatism Index (IAI), and the percent Analyzed Area (AA). These indexes were designed to register decisive characteristics of keratoconus such as local abnormal elevations in corneal power. This method was fairly successful to overcome the limitations in specificity of previous work, and importantly, it provided a cutoff point that was useful for differentiating clinical keratoconus from other conditions. 4.6. Classification with neural networks Though the development of KPI achieved much for keratoconus screening, an all-encompassing corneal topography classification and topographic abnormality detection scheme was still necessary to facilitate interpretation. This search led to the development of an artificial intelligence neural network model by Maeda et al. (1995b), which performs automated corneal topography pattern interpretation. Smolek and Klyce (1997) further improved this approach by introducing a method claiming 100% accuracy, specificity, and sensitivity. These methods have used straight forward indexes derived empirically for the purpose of capturing unique characteristics of corneal pathology. Additional techniques that have been explored for the purpose of pattern recognition include mathematical techniques such as wavelet analysis, Taylor Series expansion, Zernike decomposition, and Fourier analysis. The ultimate classification scheme will not be biased by differences among corneal topographers and will use an artificial intelligence approach that will provide an accurate interpretation for nearly all corneal topographies.
5. Wavefront analysis With the introduction of aberrometry to measure the characteristics of the wavefront from the whole eye, there
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is now a powerful adjunct to corneal topography that permits the determination of the interplay between the powerful optics of the corneal surface and the optics of the lens in particular. For example, it is well established that the cornea and the lens together compensate for some of the lower order aberrations, in particular spherical aberration. Aberrometers have a lower spatial resolution than corneal topographers and can analyze a limited diameter, usually 6 mm compared to some topographers that measure surface shape out to 10 mm or so. However, in combination, whole eye aberrometry and corneal topography provide an enormous opportunity for understanding the optics of the eye and improving its refractive status. While most aberrations arise from ocular surface distortions, measuring these with corneal topography, and then subtracting these from whole eye wavefront will provide a measure of internal ocular aberrations. Such data should be helpful to assess internal lens function in both the phakic and pseudophakic eye. There are three principle technologies employed in ocular wavefront sensing devices: Shack – Hartmann, ray tracing, and skiascopy. 5.1. Shack – Hartmann The Shack – Hartmann method is most widely used and has been applied to eliminate the aberrations caused by turbulence in the earth’s atmosphere to improve telescopes used in astronomy (Hartmann, 1900). Liang et al. (1994) saw the opportunity to use this approach to evaluate the eye and were the first to reduce the concept to practice. The device uses a grid of micro-lenslets that each independently observe a laser ray projected onto the retina at a unique angular location. The resulting light, aberrated by the eye’s optics, is focused as an array of spots onto a CCD detection array. The distance of each spot from its ideal position is measured and related to the local distortions in the pupil due to the eye’s optics. The main advantage of this approach is that all points can be measured simultaneously, thus greatly reducing errors from movement. A limiting factor is that only a few hundred points can be measured with confidence inside the pupil, confining spatial resolution to the measurement of lower order aberrations. 5.2. Ray tracing Tscherning (1894) introduced a method to describe the eye’s monochromatic aberrations that was adapted by Howland and Howland (1977), and subsequently modified by Seiler’s group (Mierdel et al., 1997). In this approach a known pattern, typically a grid, is projected onto the retina and the amount of resulting shape distortion is used to calculate the specific aberrations of the eye. The Tracey Ray Tracing system (Tracey Technologies, Houston, TX, USA) is an extension of this concept, though instead of a grid, the projection is in the form of a programmable laser that
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serially forms spots on the retina. Their positions are determined and a ray tracing algorithm is used to reconstruct the eye’s wavefront pattern. The fact that the projected pattern is programmable, allows the spatial resolution to be increased, which may be an advantage over Shack – Hartmann devices. However, the increase in spatial density leads to an increase in the time needed for measurement; the correct balance to minimize movement artifact and maximize spatial resolution must be obtained for optimal utility. 5.3. Skiascopy A third approach in wavefront sensing uses the principles embodied in refractometry based on the approach conceived by Scheiner (Smirnov, 1961) and modified by Webb and Burns (He et al., 1998). The Emory Spatially Resolved Refractometer uses this principle with subjective patient responses. The measurement takes substantially longer to complete than any of the other devices and may not prove to be practical in clinical use. An objective version of this concept, dynamic skiascopy, is used by the NIDEK OPDScan (Nidek Co, Gamagori, Japan), which collects 1440 points from within the pupil to produce a refraction map for the eye. This device achieves higher spatial resolution than other wavefront instruments and has a Placido disc corneal topographer incorporated to measure corneal topography along with the wavefront measurement. This feature allows wavefront and corneal topography to be closely registered during surgery for customized corneal treatments and simplifies the calculation of the internal optics of the eye. 5.4. Frontiers These are exciting times in our ability to further understand the optics of the ocular surface and its contribution to visual acuity. Corneal topographers have evolved to accurate, state of the art systems that are now the standard in the practice of medicine. Aberrometers are fast revealing their capabilities to assess the internal optics of the eye. With new methods of analysis whose development has been driven in great part by the desire to customize refractive surgical procedures, it is now possible to go beyond the traditional simple spherocylindrical prescription. Soon contact lenses and intraocular lenses will be available that deal with spherical aberration and coma as well as sphere and cylinder. New data will be forthcoming that will provide not only extremely accurate optical characteristics of the corneal surface, but also good estimates of the internal aberrations of the eye. Just as good standards have been proposed for corneal topography, standardized displays will be presented for the easy clinical use of aberrometry data. Already corneal topographers can provide high resolution, unambiguous characterization of corneal first surface optics and these data along with wavefront information can
now be used to optimize vision in normal eyes. With the accurate measurement of higher order aberrations, soon excellent vision even in highly aberrated eyes might be achieved.
Acknowledgements This work was supported in part by USPHS grants EY03311 and EY02377 from the National Eye Institute, National Institutes of Health, Bethesda, Maryland.
References American National Standard Ophthalmics-Corneal Topography SystemsStandard Terminology. Requirements. ANSI Z80.23-1999. Optical Laboratories Association, American National Standards Institute, 1999. Arffa, R.C., Klyce, S.C., Busin, M., 1986. Keratometry in epikeratophakia. J. Refract. Corneal Surg. 2, 61–64. Arffa, R.C., Warnicki, J.W., Rehkopf, P.G., 1989. Corneal topography using rasterstereography. J. Refract. Corneal Surg. 5, 414 –417. Burris, T.E., Baker, P.C., Ayer, C.T., et al., 1993. Flattening of central corneal curvature with intrastromal corneal rings of increasing thickness: an eye-bank eye study. J. Cataract Refract. Surg. (Suppl) 19, 182–187. Cornsweet, T.N., 1970. Visual Perception. Academic Press, New York, pp. 234 –236. Dingeldein, S.A., Klyce, S.D., Wilson, S.E., 1989a. Quantitative descriptors of corneal shape derived from computer assisted analysis of photokeratographs. Refract. Corneal Surg. 5, 372 –378. Dingeldein, S.A., Klyce, S.D., 1989b. The topography of normal corneas. Arch. Ophthalmol. 107, 512 –518. Doss, J.D., Hutson, R.L., Rowsey, J.J., et al., 1981. Method for calculation of corneal profile and power distribution. Arch. Ophthalmol. 99, 1261–1265. Gormley, D.J., Gersten, M., Koplin, R.S., et al., 1988. Corneal modeling. Cornea 7, 30–35. Hartmann, J., 1900. Bemerkungen uber den bau die justierung von spektrographen. Z. Instrumenterkd. 20, 47. He, J.C., Marces, S., Webb, R.H., Burns, S., 1998. Measurement of the wavefront aberration of the eye by a fast psychophysical procedure. J. Opt. Soc. Am. A 15, 2449–2456. Helmholtz, Hv., 1909. Handbuch der physiologicschen Optik. Leopold Voss, Hamburg, Germany. Holladay, J.T., 1997. Corneal topography using the Holladay Diagnostic Summary. J. Cataract Refract. Surg. 23, 209– 221. Howland, H.C., Howland, B., 1977. A subjective method for the measurement of monochromatic aberrations of the eye. J. Opt. Soc. Am. A 67, 1508–1518. Kaiser, P.K., Boynton, R.M., 1996a. Human Color Vision, Second Ed, Optical Society of America, Washington, DC, pp. 312 –356. Kaiser, P.K., Boynton, R.M., 1996b. Human Color Vision, Second Ed, Optical Society of America, Washington, DC, pp. 485 –524. Klyce, S.D., 1984. Computer-assisted corneal topography: high resolution graphical presentation and analysis of keratoscopy. Invest. Ophthalmol. Vis. Sci. 25, 1426– 1435. Liang, J., Grimm, W., Geolz, S., Bille, J.F., 1994. Objective measurement of the wave aberrations of the wave aberrations of the human eye using Shack –Hartmann wavefront sensor. J. Opt. Soc. Am. A 11, 949–957. MacRae, S., Rich, L., Phillips, D., et al., 1989. Diurnal variation in vision after radial keratotomy. Am. J. Ophthalmol. 107, 262–267.
C.B. Courville et al. / Experimental Eye Research 78 (2004) 417–425 Maeda, N., Klyce, S.D., Hamano, H., 1994a. Alteration of corneal asphericity in rigid gas permeable contact lens induced warpage. CLAO J. 20, 27–31. Maeda, N., Klyce, S.D., Smolek, M.K., 1995a. Comparison of methods for detecting keratoconus using videokeratography. Arch. Ophthalmol. 113, 870 –874. Maeda, N., Klyce, S.D., Smolek, M.K., 1995b. Neural network classification of corneal topography. Preliminary demonstration. Invest. Ophthalmol. Vis. Sci. 36, 1327–1335. Maeda, N., Klyce, S.D., Smolek, M.K., et al., 1994b. Automated keratoconus screening with corneal topography analysis. Invest. Ophthalmol. Vis. Sci. 35, 2749–2757. Maeda, N., Klyce, S.D., Smolek, M.K., et al., 1997. Disparity of keratometry-style readings and corneal power within the pupil after refractive surgery for myopia. Cornea 16, 517 –524. Maguire, L.J., Singer, D.E., Klyce, S.D., 1987. Graphic presentation of computer analyzed keratoscope photographs. Arch. Ophthalmol. 105, 223–230. Maloney, R.K., Bogan, S.J., Waring, G.O., 1993. Determination of corneal image-forming properties from corneal topography. Am. J. Ophthalmol. 115, 31 –41. Mandell, R.B., Chiang, C.S., Yee, L., 1996. Asymmetric corneal toricity and pseudokeratoconus in videokeratography. J. Am. Optom. Assoc. 67, 540 –547. Mierdel, P., Wiegard, W., Krinke, H.E., Kaemmerer, M., Seiler, T., 1997. Measuring device for determining monochromatic aberrations of the human eye. Ophthalmology 6, 441–445. Naufal, S.C., Hess, J.S., Friedlander, M.H., et al., 1997. Rasterstereography-based classification of normal corneas. J. Cataract Refract. Surg. 23, 222 –230. Rabinowitz, Y.S., McDonnell, P.J., 1989. Computer assisted corneal topography in keratoconus. Refract. Corneal Surg. 5, 400–408. Riss, I., Hoyston, P., Kuhne, F., et al., 1991. Fiabilite´ et reproductibilite´ de photokeratoanlyseur de Nidek. J. Fr. Ophtalmol. 14, 451–454. Rogers, M.J., McCally, R.L., Roberts, C.J., Azar, D.T., 1997. Corneal Topography: Basic Principles. In: Azar, D.T., (Ed.), Refractive Surgery, Stamford, Appleton and Lange, pp. 153 –167. Rottenkolber, M., Podbielska, H., 1996. High precision Twyman-Green interferometer for the measurement of ophthalmic surfaces. Acta Ophthalmol. Scand. 74, 348–353.
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Rowsey, J.J., Reynolds, A.E., Brown, R., 1981. Corneal topography. Corneascope. Arch. Ophthalmol. 99, 1093– 1100. Shack, R., Barker, R., Buchroeder, R., et al., 1979. Ultrafast laser scanner microscope. J. Histochem. Cytochem. 27, 153–159. Smirnov, H.S., 1961. Measurement of the wave aberration in the human eye. Biophysics 6, 52–66. Smith, T.W., 1997. Corneal topography. Doc. Ophthalmol. 43, 249–276. Smolek, M.K., 1994. Holographic interferometry of intact and radially incised human eye-bank corneas. J. Cataract Refract. Surg. 20, 277– 286. Smolek, M.K., Klyce, S.D., 1997. Current keratoconus detection methods compared with a neural network approach. Invest. Ophthalmol. Vis Sci. 38, 2290–2299. Smolek, M.K., Klyce, S.D., Hovis, J.K., 2002. The Universal Standard Scale: Proposed improvements to the American National Institute (ANSI) scale for corneal topography. Ophthalmology 109, 361– 369. Swinger, C.A., 1987. Postoperative astigmatism. Surv. Ophthalmol. 31, 219– 248. Swinger, C.A., Barker, B.A., 1984. Prospective evaluation of myopic keratomileusis. Ophthalmology 91, 785–792. Troutman, R.C., 1970. Surgical correction of high astigmatic corneal errors after successful keratoplasty. In: Troutman, R.C., (Ed.), Microsurgery of Ocular Injuries. Advances in Ophthalmology, vol. 27. S. Karger, Basel, pp. 170 –179. Troutman, R.C., Kelly, S., Kaye, D., 1977. The use and preliminary results of the Troutman surgical keratotomer in cataract and corneal surgery. Trans. Am. Acad. Opthalmol. Otolaryngol. 83, 232–238. Tscherning, M., 1894. Die monochromatischen Aberrationen des menschlichen Auges. Z. Psychol. Physiol. Sinn. 6, 456–471. Waring, G.O. III, 1993. Nomenclature for keratoconus suspects. Refract. Corneal. Surg. 9, 220. Warnicki, J.W., Rehkopf, P.G., Curtin, D.Y., et al., 1988. Corneal topography using computer analyzed rasterstereographic images. Appl. Optics 27, 1135. Wilson, S.E., Klyce, S.D., 1991a. Quantitative descriptors of corneal topography: a clinical study. Arch. Ophthalmol. 109, 349–353. Wilson, S.E., Klyce, S.D., 1991b. Advances in the analysis of corneal topography. Surv. Ophthalmol. 35, 269–277. Wilson, S.E., Klyce, S.D., Husseini, Z.M., 1993. Standardized color-coded maps for corneal topography. Ophthalmology 100, 1723–1727.
Review
Contribution of the ocular surface to visual optics C.B. Courville, M.K. Smolek, S.D. Klyce* Lions Eye Research Laboratories, LSU Eye Center, Louisiana State University Health Sciences Center, New Orleans, LA, USA Received 15 September 2003; accepted 13 October 2003
Abstract The air/tear interface contributes 70% of the vergence in the eye and, because of this, even minor variations in its shape can produce significant visual deficit. Placido disc-based corneal topographers measure the precise characteristics of the corneal surface, transforming shape into color-coded dioptric power maps and topography indexes related to optical quality and specific patterns associated with pathology. Artificial intelligence-based methods are used to classify corneal topography and these are used as screening tools. Coupling corneal topography measurements with aberrometry measurements permits the display of the internal aberrations of the eye. Together, these data provide the opportunity to extend refractive correction beyond sphere and cylinder to the higher order aberrations as well. q 2003 Elsevier Ltd. All rights reserved. Keywords: cornea; topography; wavefront; aberrometry; refractive surgery; visual optics
1. Introduction The transparent cornea in the human is some 12 mm in diameter and approximates in cross-section the shape of a negative meniscus lens, being thicker in the periphery (, 0·70 mm) than in the center (, 0·55 mm). As a result, the convex anterior surface is less curved than the concave posterior surface. The anterior radius of curvature of the eye may vary from 7·0 to 8·5 mm and still be consistent with normal vision, but on average, the radius of curvature is , 7·8 mm. The anterior curvature of the cornea in combination with the change in refractive index from air ðn ¼ 1·000Þ to stroma ðn < 1·376Þ generates a large positive refractive effect on light entering the cornea, giving it a power of , 48 diopters (D). The concave posterior curvature contributes about 2 5 D of power due to its negative curvature and the nearly matching refractive indexes of the aqueous humor ðn < 1·336Þ and the stroma. In all, the typical cornea contributes about 43 D to the total 60 D power of the eye, or about 70% of the total refraction. This level of ocular power is necessary to produce a clear image on the retina because the axial length of the eye is only about 24 mm in the average emmetropic * Corresponding author. Dr Stephen D. Klyce, LSU Health Sciences Center, LSU Eye Center, 2020 Gravier Street, Suite B, 70112-2234 New Orleans, LA, USA. E-mail address: [email protected] (S.D. Klyce). 0014-4835/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. DOI:10.1016/j.exer.2003.10.012
eye (range of 22 – 26 mm). Refractive power is supplemented by the crystalline lens. Altering the shape of the lens through the action of the ciliary muscle and processes allows the visual system to accommodate for near vision tasks where more power is needed to overcome the additional negative vergence of light entering the cornea. It should be remembered that the range of corneal power in emmetropia can actually be fairly broad; anywhere from 39 to 47·5 D can still be consistent with normal vision, depending on the power of the lens and the axial length. Beyond age 40, the visual system gradually loses accommodative ability due to protein changes that cause hardening of the crystalline lens. The cornea itself contributes essentially nothing to accommodation, although it may be possible with a sensitive topography device to measure some minor distortions to the corneal shape due to traction on the globe by the ciliary muscle. All normal corneas tend to share certain topographical features in common. The central 3 –4 mm of the cornea tends to have a nearly constant curvature and this region has been referred to as the apical cap. Its location and diameter is a fairly good match to the approximately 4 mm diameter of the entrance pupil under photopic (daylight) conditions. In other words, the optimum aberration-free region of the cornea is optically matched with the pupil and should therefore provide a high quality retinal image. Refractive surgeons take great care in centering procedures with
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respect to the entrance pupil in order to minimize high order aberrations, ghosting, and glare from light scatter that would accompany decentration of the optical zone with respect to the pupil. If the optical zone is displaced with respect to the pupil, night vision complaints increase substantially. The initial refractive element in the eye is actually the tear film which smoothly coats the anterior surface of the cornea. The presence of the tears is critical for vision as the outer membranes of the epithelial squamous cells are reticulated with projections that are 0·5 mm in height and with a similar spacing. Without the tears to smooth these projections, severe degradation in the optics of the cornea would result. The 7 mm thick tear layer is stabilized by a mucin-rich fuzzy surface coat with an outer evaporationblocking lipid layer. Tear film breakup from dry eyes can produce dellen and severe reduction in visual acuity. Because even very minor distortions in the shape of the tear-coated cornea can degrade visual acuity, efforts to characterize the corneal topography in detail have been made for centuries. Direct observation of curvature is not of much value; it was the reflection of a window frame from the corneal surface in the 15th century that provided clues to the eventual development of the Placido disc – the basis for accurate measurement of corneal shape in modern times.
2. Basic principles of measurement 2.1. Keratometry Stemming from the development of the ophthalmometer by Hemholtz (1909) with refinements by Javal and Schiotz, keratometry measures corneal curvature by projecting an illuminated pattern of light of known dimensions onto the corneal surface. Changes in the size of the reflected image follow the traditional formula for a convex mirror to calculate the radius of curvature; accuracy in the past had been given as 0·25 – 0·75 D (Swinger, 1987). Modern keratometers take measurements by using four positions on the corneal surface lying approximately 3 or 4 mm apart. The radius of curvature, Rc ; along the orthogonal steep and flat principal meridians can be converted to power in diopters, P; using the standard keratometric index, 1·3375, less the refractive index of air, 1·000 (Rogers et al., 1997) P ¼ 0·3375=Rc : As noted above, the power given by the keratometry formula is that of the total cornea, not the tear/air interface alone. Since the keratometer reports only the powers of the two principal meridians, the cornea is modeled as a sphere or ellipsoid. Therefore, keratometers cannot be used to measure irregular corneal shapes. Because they make their measurements generally at the pupil margins, they are not effective for assessing the optics of the central cornea. Even 50, keratometry continues to be valuable for anterior
segment applications, including intraocular lens (IOL) calculations and contact lens fitting for corneas lacking disease or trauma. 2.2. Placido disc The Placido disc, originally introduced by Antonio Placido, consists of a circular target of alternating concentric light and dark rings, or mires, with a central aperture through which the virtual image of the target reflected from the tear film surface can be observed. As with keratometry, the size of the image relates directly to power of the corneal surface; steep surfaces minify the image while flat surfaces magnify it. However, unlike keratometry, mires can be projected over a broad area of the cornea, and changes in curvature can be assessed at many locations. Since its inception, the Placido disc concept has been adapted and improved and is now the most widely used technology in modern corneal topographers. 2.3. Corneal topographers As corneal transplantation grew in medical practice, surgeons increasingly became aware that the procedure induced a significant amount of astigmatism. In an attempt to counter this, Troutman (1970) and others developed a surgical keratometer which mounted directly on the operating microscope (Troutman et al., 1977). Although this helped to reduce astigmatism, it became apparent that most patients lost best spectacle-corrected vision more from induced corneal irregularities than from increased cylinder. To allow measurement of corneal irregularities, better ways to measure shape than modified keratometry needed to be developed. The photokeratoscope, which photographed Placido disc images, was developed to compensate for this limitation. By projecting a series of mires onto the corneal surface and capturing the reflection with an instant film camera, surgeons were able to analyze by visual inspection 70– 95% of the total corneal surface, including paracentral and peripheral areas (Rowsey et al., 1981). This approach was utilized in the first widely distributed photokeratoscopes developed by Nidek (Nidek PKS-1000; Riss et al., 1991) and by Kera Corp (Corneascope; Rowsey et al., 1981). These devices provided details of the cornea’s topography, but were limited to the management of relatively severe irregularities in the corneal surface such as occur in corneal grafts, moderately advanced keratoconus, and trauma. They were limited because visual inspection of misshapen mires was too insensitive to pick out all the corneal aberrations of significance to vision. The introduction of radial keratotomy into clinics in 1979 spurred the need for a more accurate analysis of corneal topography. Utilizing advances in digital computers and modeling algorithms, corneal topographers evolved to meet
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the needs of refractive surgeons in pre-operative screening and investigation of postoperative complications. As the number of commercial corneal topographers continues to grow due to market demand, the underlying optical principles and techniques have varied somewhat; the most widespread approach is based on Placido disc technology. The measurement of corneal curvature with the scanning slit, laser holographic interferometry, and rasterstereography have not enjoyed productive clinical use, but it is instructive to view the different approaches that have been tried. 2.4. Placido disc-based corneal topographers The first technology applied by corneal topographers to measure corneal power was the Placido disc, and this approach remains the most viable approach due to its sensitivity, reproducibility, relative freedom from movement artifact, and non-invasiveness. The first commercially successful corneal topographer was the Corneal Modeling System (CMS; Computed Anatomy, Inc, New York, USA) (Gormley et al., 1988), which captured the reflected Placido target image with a CCD digital camera, automatically measured mire shapes, and transformed these into the threedimensional shape and power of the corneal surface. Parenthetically, the CMS was the first device to use a scanning slit to measure the back surface of the cornea as well as the front, but this approach was abandoned owing to cost and lack of accuracy. Several computer algorithms have been developed to reconstruct a model of the corneal surface shape, but since there is no exact solution, approximations can lead to inaccuracies. Fortunately, these are usually confined to the corneal periphery (Maguire et al., 1987; Wilson and Klyce, 1991b). Some of the algorithms have serious deficiencies that can lead to the false indication of keratoconus (Mandell et al., 1996). Placido target-based topographers are available in two general forms distinguished by the diameter of the target. Large diameter targets are less sensitive to magnification errors due to their long working distance, but these devices tend to lose data from the periphery because of shadows caused by the nose and the brow. The small diameter, coneshaped targets do not suffer the same shadow-induced data loss and can project mires far onto the peripheral cornea and sclera, but must perform extremely accurate range compensation to maintain their precision. As a result of their better performance in the corneal periphery, the small cone Placido devices may be more appropriate for contact lens fitting. 2.5. Stereographic corneal topographer A separate approach that avoids the uncertainties of the approximations inherent in Placido based topographers is rasterstereography (Warnicki et al., 1988; Arffa et al., 1989;
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Naufal et al., 1997). With this technology, a drop of fluorescein is instilled into the cul de sac and a grid or raster pattern of cobalt blue light is then projected onto the anterior surface of the eye. The captured stereo images are processed using triangulation to reconstruct the cornea’s topography without approximating algorithms. Surface area coverage is excellent with analysis proceeding out onto the sclera. Rasterstereography can also measure corneal shape in very distorted corneas (e.g. advanced keratoconus and early postoperative corneal grafts) on which Placido mires become indistinct and are not discernable. However, these advantages are balanced with the limitation that direct measurement of surface position does not yield the same sensitivity of measurement as reflected mire image positions. This diminished sensitivity, together with the uncertain effects of fluorescein on tear film stability and structure, reduces the utility of rasterstereography in the clinic. 2.6. Interferometric corneal topographer The method with the highest potential sensitivity for measuring corneal shape is interferometry (MacRae et al., 1989; Rottenkolber and Podbielska, 1996; Smith, 1997). Similar techniques have long been used by the optical industry to detect lens and mirror aberrations with submicron accuracy. With this method a reference surface, or its hologram, and the measured corneal surface are optically compared and the resulting interference fringes are used to determine the difference between the two shapes. Due to the wide variation in corneal shapes, however, it is difficult to represent every variation with a single interference reference. Although multiple studies have been conducted employing different forms of this technology, including laser-based devices (Shack et al., 1979; Burris et al., 1993; Smolek, 1994), this approach has not enjoyed clinical acceptance. 2.7. Scanning slit corneal topographer Scanning slit technology facilitates the measurement of both the anterior and posterior surfaces of the cornea. Since both surfaces, along with corneal thickness, are needed to accurately calculate total corneal power, directly measuring the relative positions of the surfaces would seem to grant scanning slit devices a major advantage over other types of corneal topographer. This technique not only eliminates the need for elevation or shape measurement approximations, but it is also able to measure corneal thickness over a broad area. Scanning slit technology does have its limitations, however. One major drawback is that measurement requires over 1 sec for completion, leaving the data muddled with motion artifact from fixation drift, muscle tremor, pulse, and nystagmus, all of which occur when the data is not captured in 30 msec or less. This problem can be reduced with a tracking system or post-capture registration
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techniques, though only with great expense and difficulty since landmarks, which are necessary for registration, are lacking on the normally transparent cornea. Lack of sensitivity when reconstructing corneal topography from direct surface measurement is also a problem. To overcome this, corneal topography is measured with a traditional Placido target in the Orbscan II model (Bausch and Lomb, Rochester, NY, USA). Though scanning slit technology alone is not practical for measuring topography, it appears to have some value in generating thickness profiles.
3. Presentation formats and standards Once computer-assisted corneal topography was available and it was possible to create an accurate visual representation of the cornea, it became necessary to devise ways in which this newfound data source could be precisely evaluated and applied. Doss et al. (1981) pioneered a method for reconstructing corneal shape from mire patterns and from this corneal power. Klyce (1984) built on this work to create data display methods starting with threedimensional wire-mesh plots. The final outcome of such studies was the introduction of the color-coded contour map of corneal powers (Maguire et al., 1987), which soon became the international standard display format for corneal topography. With this development, clinicians have been able to view pertinent topographic information through color association and pattern recognition. The palette of colors associates normal powers with shades of green, lower powers as cool colors, and higher than normal powers as warm colors. Using the contour map concept allows characteristic patterns in corneal topography to be recognized. For example, corneal cylinder displays as a ‘bow tie’ pattern, keratoconus as a local area of steepening, and pellucid marginal degeneration with its characteristics of a claw or ‘C’-shaped pattern of steepening and ‘negative’ bow tie. Likewise, the contour map permits evaluation of refractive surgical results including optical zone size, centration relative to the entrance pupil, and the occasional defect such as a central island. Due in part to the rapid advance of computer technology, modern corneal topographers are now equipped with the computational power to statistically analyze topography data, making it possible to display many different forms of clinically significant information. The main display formats include axial power (recommended for routine clinical use), refractive power, tangential power, and elevation maps. These are supplemented with a background video image of the eye to relate scale and position, the display of multiple exams simultaneously for viewing the progression of a disease or post-surgical results, and the construction of difference maps that aid in such aspects as showing early postoperative effects of a surgical procedure or the evolution of specific topographic features.
3.1. Units of measure Corneal topographers measure corneal surface curvature. When these devices are used in specific clinical applications, such as contact lens fitting, the measured curvature may be suitably expressed in units of millimeters. More often, when used to evaluate pathology, the optics of the eye, and refractive errors, it is more convenient for the clinician that these devices represent corneal curvature as a power in units of diopters (D). As noted above, this power represents the combined power of both corneal surfaces, and because of this may not be an accurate reflection of the change in refraction following refractive surgery (Swinger and Barker, 1984; Arffa et al., 1986). This is because tissue subtraction procedures such as LASIK change the anterior corneal curvature and corneal thickness, but not that of the posterior surface. To calculate the refractive effect of changing corneal anterior surface curvature by itself, one should use the corneal refractive index, 1·376, while for general use, the keratometric index 1·3375 is preferred. 3.2. ANSI display standards In 1999, the American National Standards Institute (ANSI) released a report pertaining to standards in corneal topography development, research, and practice. The report, ‘Corneal Topography Systems-Standard Terminology, Requirements’ (ANSI, 1999), defines terminology, requirements for measurement and testing, and display standards. In anticipation of its release it was assumed the standard would define a single color palette with specific fixed intervals to facilitate the accurate comparison of data obtained with corneal topographers from different manufacturers. Unfortunately, the specifications for topography displays failed to define a single specific scale and instead proposed a variety of suggestions as to what the parameters of such a scale should be. The ANSI Standard specifies that curvature maps should use one of three corneal diopter intervals: 0·5, 1·0, or 1·5 D. This leaves the user a choice in scale interval, which is contrary to the goal of standardization, and makes the comparison of color topography maps between different manufacturers unreliable. The same problem is encountered in the selection of a proper range of powers, where the ANSI Standard states that the number of interval-representing colors should be between 21 and 25. Three choices of interval size and five choices of color range define numerous possibilities for scales. Further, when discussing which colors should be used to represent these scale intervals, the ANSI Standard states ‘the hue should be monotonically decreasing from green to red and shall be monotonically increasing from green to blue.’ The first problem with this statement lies in the difficulty of defining what ‘blue’ or ‘green’ means simply by its color name, since the interpretation of such color names
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can vary considerably among eras and cultures (Kaiser and Boynton, 1996b). Secondly, the term ‘monotonically’ can refer to any number of step interval changes, such as changes in hue, saturation, and brightness (HSB), changes in wavelength, or the observer’s personal impression of equal changes in hue. Another ambiguity present in this ANSI Standard is the lack of any mention of varying brightness or saturation. It is typically understood that hue is the characteristic of color that varies most with changes in wavelength (Cornsweet, 1970), but color is not defined simply by changes in hue. Changes in saturation and brightness should also be taken into account when determining which colors allow optimum contrast and legibility of grayscale reproductions, but these variables were never considered. Nor does the standard consider the effects of viewing conditions, even though perceived color is dependent on the illumination and surrounding environment (Kaiser and Boynton, 1996a). 3.3. ANSI alternative To combat the ambiguity inherent in the ANSI Standard, Smolek and coworkers set out to define a single scale and color palette that takes into account all of these complications and could be universally adopted by all topographer manufacturers (Smolek et al., 2002). In this standard, referred to as the Universal Standard Scale (USS), first a central power value was established by finding the mean and standard deviation (SD ) of 27 normal corneas. This value was 42·76 ^ 1·59 D; therefore the central power value was set to 42·75 D and the interval size was set to the optimal value of just under 1 SD , or the widely used 1·5 D. This contour interval has been proven to be small enough to capture all topographical characteristics of clinical importance (Wilson et al., 1993), and through clinical experience it has been found that smaller intervals can often lead to misinterpretations of non-existent conditions like irregular corneal topography or keratoconus. In order to associate familiar color recognition with normal and abnormal corneas, the corneal powers lying within ^ 2SD of the determined mean for normals were set to green hues. Therefore, four contour intervals, two above and two below the mean, are displayed as green colors in this standard. Powers immediately above this þ 2SD limit are displayed as yellow, whereas powers immediately below the 2 2SD limit are displayed as cyan. Through the study of 388 topographical maps representing a wide variety of conditions, the optimal range of power values was determined to be 30·0– 67·5 D. This range encompassed 99·9% of the powers present in the trial data set, better than the ANSI standard using each suggested interval size (Smolek et al., 2002). The associated palette of colors used in the USS was arrived at by meticulous subjective adjustment of brightness, saturation, and hue to establish easy to distinguish color contours. The final color palette is a specifically defined range of colors that enable the observer
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to quickly determine clinically important topographical aspects of a color map without confusion. The advantage of adopting a single standard scale like the USS lies not only in the ease of comparison between differing corneal topographers, but more importantly in the accuracy of clinical examination and practice. In the absence of such a scale, the variation between displays given by separate topographers will undoubtably lead to confusion, misinterpretation, and problematic outcomes. 3.4. Self-adapting scales Self-adapting or normalized scales have also produced confusion in the correct interpretation of a color-coded corneal topography map. With this approach, the computer is programmed to search out the range of powers in a given corneal map and then to adjust the range and power interval of the scale so that the full range of colors are used to display topography. With this scheme, the color association concept is defeated as even normal corneas will contain regions that have warm colors usually related to abnormally high powers as well as regions that have the cool colors that usually signify lower than normal powers. A concern is that a normal cornea viewed with the self-adapting scale will usually show an area of red which often signifies the presence of keratoconus in the fixed standard scale. Conversely, a highly irregular cornea with a wide range of powers will be condensed in appearance with the selfadapting scale, potentially masking a major source of visual disability. Most if not all of the corneal topographers commercially available have a certain flexibility as to which scale is used routinely. It is strongly advised that the Universal Standard Scale (Smolek et al., 2002), or one closely similar to that specification be adopted for general use.
4. Corneal topography indexes Though standardized color-coded contour maps can greatly improve the clinician’s ability to properly diagnose corneal conditions, these displays alone cannot produce the numerical values essential in clinical management. Further, the optical quality of a corneal surface cannot be directly determined from visualization of the color map. Therefore, quantitative indexes have been developed to supplement graphical representations. Simulated keratometery (SimK) values, one of the first corneal topography indexes developed, are designed to simulate the curvature measurements given by a typical keratometry exam (Dingeldein et al., 1989a). Simulated Keratometry and clinical keratometry correlate well (Wilson and Klyce, 1991a). However, it should be taken into account that refractive astigmatism does not necessarily agree with corneal astigmatism since the lens can contribute part if not all of the refractive astigmatism,
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although this appears to be rare. SimK values describe the powers and axes of the steepest and flattest meridians and are designated SimK1 and SimK2, respectively; they are calculated using the corneal topographer data from points on the cornea corresponding to those used for keratometry readings. Cylinder and spherical equivalent can be easily calculated using SimK indexes and are therefore often displayed alongside color maps. SimK values prove extremely useful when applied to determine the amount and axis of astigmatism or eyes with irregular corneas and in the fitting of contact lenses. 4.1. Corneal eccentricity index The ‘Corneal Eccentricity Index’ (CEI) was created to act as an indicator of the degree of eccentricity in the cornea (Maeda et al., 1994a). This value is typically determined by fitting an ellipse to the elevation data provided by the topographer. In a study of 22 normal corneas, the CEI obtained was 0·33 ^ 0·26 (mean ^ 1SD ), corresponding to the prolate shape of the normal central cornea. Use of this index is helpful when fitting contact lenses and differentiating between normal prolate corneas and oblate corneas flattened by myopic refractive surgery. 4.2. Average corneal power The ‘Average Corneal Power’ (ACP) is an area-corrected average of corneal power lying ahead of the entrance pupil (Maeda et al., 1997). There is a good correlation between the average keratometric power and ACP (r 2 ¼ 0·96; P , 0·001; Dingeldein et al., 1989b). However, ACP gives a better estimate of central corneal power than can be obtained from keratometry-like values as it obtains its measure from the whole pupillary area rather than four points near the margin of the pupil. The value of this can be appreciated when analyzing corneal curvature after refractive surgery. With a small optical zone or a decentered treatment area, the use of keratometry can lead to errors greater than 1 D (Maeda et al., 1997). In these cases, it is preferable to use ACP or its equivalent for intraocular lens power calculations. 4.3. Surface regularity index The first index developed to measure the impact of corneal irregularities on optical quality was the ‘Surface Regularity Index’ (SRI; Wilson and Klyce, 1991a). This index sums the meridional mire-to-mire power changes over the apparent entrance pupil, increasing as topographic irregularities increase. SRI was correlated to visual acuity for a group that contained normals, keratoconus, and corneal transplants. This correlation allows the clinically useful prediction of the ‘Potential Visual Acuity’ (PVA) in Snellen chart format, which as noted above, can not be determined from visual inspection of a topography map.
Different approaches were taken by Maloney et al. (1993) and Holladay (1997). They chose to first determine the best-fitting ellipsoid for the central cornea, then calculate the difference between this surface and corneal elevation. Correlating these distortions with clinical data, the results are displayed as color-coded maps of predicted regional Snellen acuity (Holladay, 1997). 4.4. Screening tools and neural networks Even with training, interpretation of corneal topography can often be equivocal, particularly in establishing threshold values between normal corneas and those with very early pathology. As well, there are situations with confounding diagnoses where the similarity between two possible conditions (for example, contact lens molding and early keratoconus) makes interpretation difficult. Because of this, several classification schemes have been developed to run on corneal topographers that aid in classification of corneal topography. 4.5. Indexes for keratoconus detection Ever since the introduction of keratorefractive surgery, the presence of keratoconus has generally been considered as a contraindication. The incidence of keratoconus is very small in the general population, perhaps 0·01% or less, but among refractive surgical candidates rises to 8% or more. Corneal topography is the most sensitive method for the detection of keratoconus where it appears as a localized area of steepening, generally displaced inferiorly, but a firm diagnosis must be accompanied by the clear indication of thinning near the cone apex. Vogt’s striae, Munson’s sign, and a Fleischer ring may also be observed, but these often accompany keratoconus at its more advanced stages. The Orbscan II scanning slit topographer can also be used to detect the pattern of corneal thinning, but most studies find it insensitive to detect the thinning that can be measured with ultrasound in early keratoconus. In the absence of any detectable thinning, an area of topographic steepening may be classified as keratoconus suspect (Waring, 1993), whereas clinical keratoconus is recognized by localized steepness along with thinning. The conundrum for the clinician has been to differentiate between normal variations in corneal steepness and asymmetry and true pathology. Methods based on measurements made from corneal topography data have been developed to meet this challenge. Rabinowitz and McDonnell (1989) were the first to use numerical methods to detect keratoconus using corneal topography data. They developed indexes to measure power differences between the superior and inferior paracentral corneal regions (designated I – S values), the central corneal power (Max K), and the power differences between the left and right eyes. Their corresponding analysis showed that a central corneal power greater than 47·2 D or an I – S value
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greater than 1·4 D is consistent with keratoconus suspect, whereas central corneal powers greater than 48·7 D or I – S values greater than 1·9 D are consistent with clinical keratoconus. This is enough to distinguish the topography of keratoconus corneas from that of normal corneas, but unfortunately the specificity of the method is problematic. Several additional topography studies have appeared in the literature that suffer the same weakness. Using strategies that only differentiate between keratoconus and normal corneas can incorrectly identify conditions such as contact lens molding and corneal transplant topography as keratoconus. Therefore, Maeda et al. (1994b, 1995a)) developed the Keratoconus Prediction Index (KPI) that was able to differentiate between keratoconus and most of the common classes of corneal topography. The KPI value is derived from topographic indices that include the Differential Sector Index (DSI), the Opposite Sector Index (OSI), the Center/Surround Index (CSI), the Surface Asymmetry Index (SAI), the Irregular Astigmatism Index (IAI), and the percent Analyzed Area (AA). These indexes were designed to register decisive characteristics of keratoconus such as local abnormal elevations in corneal power. This method was fairly successful to overcome the limitations in specificity of previous work, and importantly, it provided a cutoff point that was useful for differentiating clinical keratoconus from other conditions. 4.6. Classification with neural networks Though the development of KPI achieved much for keratoconus screening, an all-encompassing corneal topography classification and topographic abnormality detection scheme was still necessary to facilitate interpretation. This search led to the development of an artificial intelligence neural network model by Maeda et al. (1995b), which performs automated corneal topography pattern interpretation. Smolek and Klyce (1997) further improved this approach by introducing a method claiming 100% accuracy, specificity, and sensitivity. These methods have used straight forward indexes derived empirically for the purpose of capturing unique characteristics of corneal pathology. Additional techniques that have been explored for the purpose of pattern recognition include mathematical techniques such as wavelet analysis, Taylor Series expansion, Zernike decomposition, and Fourier analysis. The ultimate classification scheme will not be biased by differences among corneal topographers and will use an artificial intelligence approach that will provide an accurate interpretation for nearly all corneal topographies.
5. Wavefront analysis With the introduction of aberrometry to measure the characteristics of the wavefront from the whole eye, there
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is now a powerful adjunct to corneal topography that permits the determination of the interplay between the powerful optics of the corneal surface and the optics of the lens in particular. For example, it is well established that the cornea and the lens together compensate for some of the lower order aberrations, in particular spherical aberration. Aberrometers have a lower spatial resolution than corneal topographers and can analyze a limited diameter, usually 6 mm compared to some topographers that measure surface shape out to 10 mm or so. However, in combination, whole eye aberrometry and corneal topography provide an enormous opportunity for understanding the optics of the eye and improving its refractive status. While most aberrations arise from ocular surface distortions, measuring these with corneal topography, and then subtracting these from whole eye wavefront will provide a measure of internal ocular aberrations. Such data should be helpful to assess internal lens function in both the phakic and pseudophakic eye. There are three principle technologies employed in ocular wavefront sensing devices: Shack – Hartmann, ray tracing, and skiascopy. 5.1. Shack – Hartmann The Shack – Hartmann method is most widely used and has been applied to eliminate the aberrations caused by turbulence in the earth’s atmosphere to improve telescopes used in astronomy (Hartmann, 1900). Liang et al. (1994) saw the opportunity to use this approach to evaluate the eye and were the first to reduce the concept to practice. The device uses a grid of micro-lenslets that each independently observe a laser ray projected onto the retina at a unique angular location. The resulting light, aberrated by the eye’s optics, is focused as an array of spots onto a CCD detection array. The distance of each spot from its ideal position is measured and related to the local distortions in the pupil due to the eye’s optics. The main advantage of this approach is that all points can be measured simultaneously, thus greatly reducing errors from movement. A limiting factor is that only a few hundred points can be measured with confidence inside the pupil, confining spatial resolution to the measurement of lower order aberrations. 5.2. Ray tracing Tscherning (1894) introduced a method to describe the eye’s monochromatic aberrations that was adapted by Howland and Howland (1977), and subsequently modified by Seiler’s group (Mierdel et al., 1997). In this approach a known pattern, typically a grid, is projected onto the retina and the amount of resulting shape distortion is used to calculate the specific aberrations of the eye. The Tracey Ray Tracing system (Tracey Technologies, Houston, TX, USA) is an extension of this concept, though instead of a grid, the projection is in the form of a programmable laser that
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serially forms spots on the retina. Their positions are determined and a ray tracing algorithm is used to reconstruct the eye’s wavefront pattern. The fact that the projected pattern is programmable, allows the spatial resolution to be increased, which may be an advantage over Shack – Hartmann devices. However, the increase in spatial density leads to an increase in the time needed for measurement; the correct balance to minimize movement artifact and maximize spatial resolution must be obtained for optimal utility. 5.3. Skiascopy A third approach in wavefront sensing uses the principles embodied in refractometry based on the approach conceived by Scheiner (Smirnov, 1961) and modified by Webb and Burns (He et al., 1998). The Emory Spatially Resolved Refractometer uses this principle with subjective patient responses. The measurement takes substantially longer to complete than any of the other devices and may not prove to be practical in clinical use. An objective version of this concept, dynamic skiascopy, is used by the NIDEK OPDScan (Nidek Co, Gamagori, Japan), which collects 1440 points from within the pupil to produce a refraction map for the eye. This device achieves higher spatial resolution than other wavefront instruments and has a Placido disc corneal topographer incorporated to measure corneal topography along with the wavefront measurement. This feature allows wavefront and corneal topography to be closely registered during surgery for customized corneal treatments and simplifies the calculation of the internal optics of the eye. 5.4. Frontiers These are exciting times in our ability to further understand the optics of the ocular surface and its contribution to visual acuity. Corneal topographers have evolved to accurate, state of the art systems that are now the standard in the practice of medicine. Aberrometers are fast revealing their capabilities to assess the internal optics of the eye. With new methods of analysis whose development has been driven in great part by the desire to customize refractive surgical procedures, it is now possible to go beyond the traditional simple spherocylindrical prescription. Soon contact lenses and intraocular lenses will be available that deal with spherical aberration and coma as well as sphere and cylinder. New data will be forthcoming that will provide not only extremely accurate optical characteristics of the corneal surface, but also good estimates of the internal aberrations of the eye. Just as good standards have been proposed for corneal topography, standardized displays will be presented for the easy clinical use of aberrometry data. Already corneal topographers can provide high resolution, unambiguous characterization of corneal first surface optics and these data along with wavefront information can
now be used to optimize vision in normal eyes. With the accurate measurement of higher order aberrations, soon excellent vision even in highly aberrated eyes might be achieved.
Acknowledgements This work was supported in part by USPHS grants EY03311 and EY02377 from the National Eye Institute, National Institutes of Health, Bethesda, Maryland.
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