BACKGROUND
The cornea is the most important refractive element of the human eye, providing approximately two-thirds of its optical power, accounting for about 43–44 diopters at the corneal apex.1 Since its surface is irregular and aspherical, it is not radially symmetric, and simple measurement techniques are inadequate.
The great upsurge in refractive surgery led to a need for improved methods to analyze corneal shape since refraction and keratometric data alone were insufficient to predict surgical outcomes. Understanding and quantifying corneal contour or shape has become essential in planning modern surgical intervention for refractive surgery, as well as in corneal transplantation, and it is also very valuable for assessing optical performance of the eye. The different methods for evaluating the anterior surface of the cornea, developed over several centuries, have, in the present era, led to the modern corneal topography.
FIRST STEPS IN CORNEAL MEASUREMENT
In 1619, Scheiner analyzed corneal curvature by matching the image of a window frame reflected onto a subject's cornea with the image produced by one of his calibrated spheres.
Keratometer
In 1854, Helmhotz described the first true keratometer, which he called an ophthalmometer.2 With some minor improvements, it is still being used clinically for calculating refraction, intraocular lens power and contact lens fitting normal corneas.2
This apparatus is based on the tendency of the anterior corneal surface to behave like a convex mirror and reflect light. The projection of four point, mire, onto the cornea, creates a reflected image that can be converted into a corneal radius, ‘r’, using a mathematical equation that considers distance from the mire to cornea (75 mm in the keratometer), image size and mire size (64 mm in the keratometer). The corneal radius can be transformed into dioptric power using the formula:
The standard keratometric index represents the combined refractive index of the anterior and posterior surfaces of the cornea, considers the cornea as a single refractive surface, and is 1.3375. Thus, the equation can be simplified to:
Although keratometers are still common in ophthalmology clinics, they do have specific limitations that need to be considered in order to avoid misleading conclusions.
- Most traditional keratometers measure the central 3 mm of the cornea, which only accounts for 6% of the entire surface.
- It assumes that the cornea is a perfectly spherocylindrical surface, which it is not. The cornea is aspheric in shape, flattening between the center and the periphery. Usually the central corneal curvature is fairly uniform, and this is the reason why it can be used to calculate corneal power in normal patients. However, this is not true in some pathologies like ectatic disorders or after refractive surgery.
- The keratometer provides no information as to the shape of the cornea either inside or outside the contour of the mire. Several corneal shapes can all give the same keratometric value so this apparatus is of little use should it become necessary to reconstruct the whole corneal morphology.
Keratoscopy and Photokeratoscopy
Goode presented the first keratoscope in 1847. Placido was the first to photograph the corneal reflections of a series of illuminated concentric rings (known as Placido's rings) in 1880 (Fig. 1.1). Finally, in 1896, Gullstrand was the first to develop a quantitative assessment of photokeratoscopy.3
The keratoscope, like a keratometer, projects an illuminated series of mires onto the anterior corneal surface, usually consisting of concentric rings. The distance between the concentric rings or mires gives the observer an idea of the corneal shape. A steep cornea will crowd of the mires, while a flat cornea will spread them out. Surface irregularity is seen as mire distortion.3
When a photographic camera is attached to the keratoscope, we have a photokeratoscope, which gives semiquantitative and qualitative information about the paracentral, midperipheral and peripheral cornea.
Based on the mathematical equation, it is possible to calculate corneal power from object size. Still, photokeratoscopy gives limited information on the central area, which is not covered by the mires.
Videokeratoscopy
At the beginning of this century, modern corneal topographers were based on videokeratoscopy.4 A video camera is attached to the keratoscope, and the information is analyzed by a computer that displays a color-coded map of power distribution or corneal curvature of the anterior corneal surface (Fig. 1.2). It overcomes some of the limitations of other methods, since it measures larger areas of the cornea, with a much larger number of points thus increasing resolution. Computer technology makes it possible to create permanent records and do multiple data analyses.
FUNDAMENTALS AND TECHNOLOGICAL APPROACHES TO CORNEAL TOPOGRAPHY
Shape of the Normal Cornea
The anterior corneal surface is a refractive surface characterized by an almost spherical shape. The human cornea is not a perfect sphere and is usually assumed to have a conic section. This model could be represented in a simple way by means of the equation:
X2 +Y2 +(1+Q)Z2 − 2RZ = 0
where the Z-axis is the axis of revolution of the conic, R is the radius at the corneal apex, and Q is asphericity, a parameter that is used to specify the type of conicoid.
For a perfect sphere this parameter takes the value of zero (Q = 0), for an ellipsoid with the major axis in the X-Y plane (oblate surface) the asphericity is positive (Q > 0), for an ellipsoid with the major axis in the Z-axis (prolate surface) asphericity is negative (− 1 < Q < 0), while for a paraboloid with its axis along the Z-axis the value is − 1, and it is less than − 1 for a hyperboloid.
Other parameters have been defined to classify the conicoid form of the cornea: ‘P,’ the shape factor (P = Q + 1), or the eccentricity value, ‘e,’ defined as 
Several studies have shown that the anterior corneal configuration tends to be prolate, i.e., the cornea progressively flattens out periphery by 2–4 diopters of flattening.5 The asphericity of the normal cornea depends on the study ranges from − 0.26 to − 0.11.
This tendency can be detected in the topographic map. Toward the periphery, dioptric power appears to decline, and the nasal area flattens more than the temporal area (Fig. 1.3). This could be helpful in distinguishing right eye topography from the left eye topography. The topographic patterns of the two corneas of the same individual often show mirror-image symmetry.
Corneal topographic patterns (Figs. 1.4A to D) have been studied in normal eyes and the following shapes have been found:5 round (23%), oval (21%), symmetric bow-tie typical for regular astigmatism (18%), asymmetric bow-tie (32%) and irregular astigmatism (7%). In the round and oval shapes there is an area of uniform dioptric power close to 43 diopters (D) in the center of the cornea. The bow-tie configuration reflects the existence of corneal astigmatism.5
Fig. 1.3: Corneal topography in a normal right eye. There is a flattening toward the periphery, more pronounced at the nasal area.
Depending on the position of the axes, corneal astigmatism is defined as against-the-rule (the steepest axis is horizontal), with-the-rule (the steepest axis is vertical) or oblique (the steepest axis is near the meridian angles of 45° or 135°).
CORNEAL TOPOGRAPY: CURRENT TECHNOLOGIES
Corneal topography is a noninvasive exploratory technique that graphically describes the geometric characterization of the morphology of the cornea, that permits us differentiating standard normal patterns form the pathological cornea.6 Current topographers are based on either systems based on the light reflection on the cornea, or systems based on the projection of a slit light into the cornea with different technology.
Systems Based on the Light Reflection on the Cornea: Curvature Based Topographers
Placido Disk System
A Placido disk system consists of a series of concentric illuminated rings or mires that are reflected off of the cornea and recorded by video-computerized systems.4 The topographer uses an algorithm to translate these reflected images into radial curvature of the corneal surface. Height and slope data derived from the radial curvature of the anterior corneal surface are represented as a corneal keratometric map that follows a color scale developed by the University of Louisiana.6
Figs. 1.4A to D: Normal corneal topographic patterns: (A) Oval topographic pattern, (B) bow-tie pattern that shows an against-the-rule astigmatism, (C) with-the-rule astigmatism and (D) oblique astigmatism.
Flat curves are represented with cool colors (blue or violet), while warm colors (red or orange) correspond to high curvature. Mild colors (green or yellow) correspond to medium curvature equal to the reference sphere.
Currently, several companies manufacture instruments called videokeratoscopes that picture corneal shape based on the Placido disk method, and, in fact, this approach has been the most clinically and commercially successful up to the last decade. Two types of Placido targets have been used:
- Large diameter target (disk-shaped): This is less sensitive to misalignment due to a long working distance, but there can be a loss of data due to interference by the patient's brow and nose.
- Small diameter target (cone-shaped): This is designed for a short working distance and can be influenced by automatic alignment and focusing or compensation of misalignment for accuracy. It does not present data loss due to shadows.
Limitations:
- Placido-based apparatus creates a 3D system by making geometric assumptions about the cornea since the apparatus does not measure corneal surface directly. These assumptions are not accurate for irregular and aspheric corneas.
- The reflection technique depends on the integrity and normality of the tear layer.
Interferometric Method-based Systems
In essence, a reference surface (or its hologram) is compared to the tested surface, the corneal surface and interference fringes are produced as a result of differences between the two shapes, which can be interpreted as a contour map of surface elevations.7
Interference techniques are used in the optical industry to detect lens and mirror aberrations of subwavelength dimensions. High accuracy is theoretically possible, but clinical use has not been very wide-spread as yet.
Moire Deflectometry-based Systems
The deflections of the rays reflected off the corneal surface are analyzed to build up a surface elevation map.7
Systems Based on the Projection of a Slit Light onto the Cornea: Elevation-based Topographers
The common denominator of this technology is the projection of a slit light onto the cornea. Interestingly many of these corneal topographies integrate a dual technology, and in a first stage they use light reflection on the cornea by means of a Placido disk to obtain curvature and refractive power data, followed by capturing the image of the scattered light from the slit light to measure corneal elevations of the entire corneal segment. From these8 two-dimensional (2D) cross-sections, it is possible to create a reliable three-dimensional model.
Depending on the spatial arrangement of the photographic systems, we can distinguish the following two different systems.
Systems Based on the Principle of Normal Photography
Its main feature is that the plane of the camera lens is located parallel with the image.8 When the slit image is on the cornea, it splits into a specular reflection and a refracted beam that penetrates the corneal surface and is scattered by the tissue of the cornea. An image of this scattered light within the corneal tissue is captured by an imaging system, which consists of a camera lens located in parallel with the image. It uses triangulation to measure the elevation of the anterior and posterior corneal surface with respect to a reference plane.8
The most popular system using this principle is the Orbscan (Bausch & Lomb Incorporated, USA) (Fig. 1.5), which was the first commercial device that was able to assess the posterior corneal surface.8 It has dual technology as it uses Placido disk and slit-based systems to obtain 40 slit images of the cornea. These images are captured over one second and are then recorded providing different maps of the anterior and posterior corneal surfaces, and also pachymetric data.
Systems Based on the Principle of Scheimpflug Photography
Its main feature is that the plane of the camera lens is placed sideways to the image. Scheimpflug imaging is based on the Scheimpflug principle, which occurs when a planar subject is not parallel to the image plane.
In this scenario, an oblique tangent can be drawn from the image, object and lens planes, and the point of intersection is the Scheimpflug intersection, where the image is in best focus.9 With a rotating Scheimpflug camera, the devices can obtain many Scheimpflug images in seconds. The main commercial systems based on this principle are Pentacam (Oculus, USA), Galilei (Ziemer, Switzerland) and Sirius (CSO, Italy), which offer repeatable measurements of the corneal curvature and other anatomical measurements of the anterior segment (Fig. 1.6).
Although the instruments based on rotating Scheimpflug cameras are considered the most comprehensive and accurate, they also have some limitations. Lower imaging speed can increase the risk of motion artifacts, even though there is an inbuilt second camera to control for eye movements. For example, commercially available Pentacam uses a rotating Scheimpflug camera (180°) to provide a 3D scan of the anterior segment of the eye. It requires 2 seconds to complete 25 radial scans. Moreover, radial scanning may not provide sufficient scan density of the corneal periphery, needing interpolation. Another limitation is that the instruments using the Scheimpflug principle are less accurate in comparison to Placido-based ones in providing traditional curvature maps of the anterior surface, and only show moderate agreement in simulated keratometry values. The Sirius system has a dual technology and combines Scheimpflug camera and a small-angle Placido disk topographer with 22 rings. The data for the anterior surface are finally determined by merging the Placido image and the Scheimpflug image using a proprietary method.
Systems with a single Scheimpflug channel use a mathematical equation to estimate compensation for an off-center measurement, however, to10 properly compensate for an off-center measurement, a dual Scheimpflug technology is needed.9 Galilei uses a monochromatic slit-light source which combines dual Scheimpflug cameras and a Placido disk to measure both anterior and posterior corneal surfaces.
Systems Based on Optical Coherence Tomography
Optical coherence tomography (OCT) of the cornea and anterior segment is an optical method of cross-sectional scanning based on reflection and scattering of light from the structures within the cornea.10 Measuring different reflectivity from structures within the cornea by a method of optical interferometry produces the cross-section image of the cornea and other anterior segment structures.
In optical interferometry, the light source is split into the reference and measurement beams. The measurement beam is reflected from ocular structures and interacts with the reference light reflected from the reference mirror, a phenomenon called interference. The coherent or positive interference characterized by an increased resulting signal is measured by the interferometer, and, subsequently, the position of the reflecting structure of the eye can be determined.10
In this way, the structures of the anterior segment can be visualized with a high degree of resolution (currently 18 microns axial and 60 microns transverse).
In 2005, a commercial 1310 time-domain OCT system for anterior segment imaging was launched under the name Visante OCT (Carl Zeiss, Inc.). Currently although it is widely used OCT device for dedicated in vivo anterior segment imaging and creates pachymetry maps, it cannot perform topographic analysis of the cornea, mostly because of limitations in acquisition time. The introduction of Fourier domain OCT in 2002 with the primary advantage of increased sensitivity or speed and the possibility of 3D imaging promised to improve the ability of OCT to quantitatively assess the corneal topography.10 Nowadays, commercial high speed 3D anterior segment OCT based on swept source OCT provide higher resolution cross-sectional images that can be used to obtained OCT-based corneal topography. The commercially available OCT-based topographer is SS-1000 CASIA (Tomey Corporation, Inc., Nagoya, Japan) (Fig. 1.7).
PERFORMING A GOOD TOPOGRAPHY EXAMINATION
Corneal topography is a noninvasive imaging technique for mapping the surface curvature of the cornea. The specific method varies depending on the device used, but some aspects are common. The patient is seated facing a bowl containing an illuminated pattern which is focused on the anterior surface of his cornea. The reflected pattern is analyzed by a computer that calculates the shape of the cornea by means of different graphic formulae.1111
Although computer programs are created to be very accurate, they cannot recognize, and account for, every problem. Critical points for precise measurement are accurate alignment, centring and focusing. They depend on the ability of the examiner to take a good measurement. Another potential source of error is tear film irregularities, for example focal flattening over a dry patch. These may be most easily identified on the raw image.
Tear film breakup causes mistracking of the mires and artefacts in the topography pattern and will apparently look like significant irregularities (Fig. 1.8). These corneal irregularities could suggest a corneal pathology, such as keratoconus, and result in wrong diagnosis (Figs. 1.9A and B).12
Figs. 1.9A and B: (A) Raw image and (B) topographic irregularities and patches of the map in the same eye because of a tear film with large instability.
To avoid disturbing the tear film, corneal topography should be performed before administering dilating drops and taking intraocular pressures.
In addition, one must avoid artefacts induced by the nose or the eyelids, which can lead to a loss of information in certain areas (Figs. 1.10A and B). These errors are transformed into black areas or areas without data on the topographic map.13
Figs. 1.10A and B: Loss of information of certain areas of the cornea due to eyelids not opened enough. (A) Topographic map (B) Scheimpflug image.
Correct positioning of the head, eyes and eyelid opening should be ensured to avoid these problems.
INTERPRETATION OF CORNEAL TOPOGRAPHY MAPS
Accurate interpretation of corneal shape using color-coded topographic maps is difficult and confusing for many clinicians, even experienced cornea specialists. In order to obtain the best performance in the analysis of corneal maps, several important points must be taken into consideration.14
It is critical to check the raw image first. After that it is necessary to focus on the scale and step intervals with which the color-coded topographic map is built up. It is also important to review different topographic displays, especially when evaluating irregular or postsurgery corneas.
Raw Photoqueratoscope Image
The photokeratoscope image displays the Placido's rings projected onto the cornea (Fig. 1.11). When considering a color-coded map, the clinician must check that the unprocessed data upon which it is based are reliable. If the videokeratoscope image is irregular, data cannot be processed by the instrument in a meaningful way.
Thus, for Placido disk-based computerized videokeratoscopes, the videokeratoscope image should not be ignored. In fact, it is recommended to check this map before referring to any of the other topographic displays, and to go back to it when there are any doubts regarding the accuracy of the displayed data. This image provides important information for assessing tear film quality, mire centring on the cornea, lid opening, or the causes of local irregularities, and other artefacts. If the device used displays computer tracking of the Placido mires it is important to rule out tracking errors.
Devices that rely only on scanning slit technology to analyze the anterior corneal surface lack of the valuable information provided by the raw-videokeratoscope image.12 Whether the resulting map is based on reliable primary data or not is impossible to verify without the raw image. Some instruments identify regions of uncertainty, showing mire distortions that cannot be reliable, by leaving blank areas on the color-coded map. Other15 instruments merely extrapolate onto the uncertain regions information gathered from adjacent regions with reliable data.
For Scheimpflug technology, its images should also be checked before looking at the resulting maps, and correct centration and focus should be assured.
Color-coded Scales
The shape of a cornea can be measured and represented by color-coded maps in which a given color indicates a different curvature or elevation. The usual color spectrum for corneal powers shows near-normal power as green, lower-than-normal power as cool colors (blues) and higher-than-normal powers as warm colors (reds). Most topographers offer absolute as well as normalized scales to allow the clinician to customize the information for maximal clinical value (Figs. 1.12A and B):
- Normalized scale (variable scale) uses a given color for different curvatures or elevations on each cornea analyzed, depending on the range for that particular cornea, determined by its flattest and steepest values. These maps are difficult to interpret and can lead to an incorrect diagnosis since they may magnify subtle changes in corneal surface if the scale is too narrow, or minimize large distortions if the scale is too wide. In addition, color recognition, one of the primary clues used to interpret on corneal topography, is lost with a variable scale, since it uses different colors for different eyes.
- Absolute scale (fixed scale) uses the same color for the same curvature or elevation no matter which eye is examined. However, there are many different absolute scales since the examiner can choose different variables such as range or step size (intervals in color changes). For the specified scale, however, each display will use the same colors, steps and range. In order to facilitate comparisons over time and between patients, it is recommended to stick with a given fixed scale for routine examinations and to change the scale in the particular cases in which this becomes necessary. As an example, the popular Klyce/Wilson scale ranges from 28 D to 65 D in equal 1.5 D intervals. Currently, there is no consensus as to the best absolute scale, but in general, dioptric scales with intervals smaller than 0.5 D are not clinically useful and provide details that are not relevant and may complicate map interpretation. For corneas with large dioptric ranges, for instance in advanced keratoconus intervals greater than 0.5 D are recommended. Regarding scales for elevation maps, elevation steps of approximately 5 microns appear to be clinically useful.
As mentioned earlier, color pattern recognition makes it possible to identify common topographic patterns such as the corneal cylinder (Fig. 1.13), keratoconus (local area of inferonasal steepening) or pellucid marginal degeneration (butterfly pattern or inferior arcuate steepening), as well as features associated with refractive surgery (Fig. 1.14), such as optical zone size, centration and central islands.16
Figs. 1.12A and B: Corneal topography map represented using (A) a normalized relative scale and (B) an absolute scale.
Topographic Displays: Corneal Maps
Maps can be obtained from the anterior and posterior surface except in the case of pure Placido disk technology.
- Axial map (sagittal map): Although this is the original and most commonly used map, its values only provide a good approximation for the paracentral cornea (Fig. 1.15A).20Figs. 1.15A to D: Different kinds of topography maps for the same cornea: (A) Sagittal axial map, (B) instantaneous or tangential map, (C) elevation map and (D) pachymetry map.The axial map measures the radius of curvature for a comparable sphere (with the same tangent as the point in question) with a center of rotation on the axis of the videokeratoscope. Localized changes in curvature and peripheral data are poorly represented, because of the spherical bias of the reference optical axis.4 However, newer algorithms in some devices (e.g., arc-step method) have improved the accuracy of curvature measurements in the peripheral region.
- Local tangential curvature map (instantaneous map): The tangential map displays the tangential/instantaneous/local radius of curvature or tangential power, which is calculated by referring to the neighboring points and not to the axis of the videokeratoscope (Fig. 1.15B). Tangential maps reflect local changes and peripheral data better than axial maps. They are very useful in detecting local irregularities, corneal ectatic diseases, or surgically induced changes. For example, in keratoconus corneas with a displaced apex, tangential maps are less influenced by peripheral distortion, and can determine the position and extent of the cone more precisely than axial maps.9
- Refractive map: The refractive map displays the refractive power of the cornea, which is calculated based on Snell's law of refraction, assuming optical infinity. This map correlates corneal shape to vision, and is useful in understanding the effects of surgery.13
- Elevation map: The elevation map displays corneal height or elevation relative to a reference plane (Fig. 1.15C), with a presumed assumption of the shape, which may be the best-fit sphere, best-fit asphere, average corneal shape, or even based on preoperative data. Points above the reference surface are positive (hot colors), and points below the reference surface are negative (cool colors). This map shows the 3D shape of the cornea and is useful in measuring the amount of tissue to be removed by a procedure, assessing postoperative visual problems, or planning and/or monitoring surgical procedure.9
- Difference map: The difference map displays the changes in certain values between two maps (Fig. 1.16). It is used to monitor any type of change, such as recovery from contact lens-induced warpage or surgery-induced changes.
- Relative map: The relative map displays some values by comparing them to an arbitrary standard (e.g., sphere, asphere or normal cornea) and a specific mathematical model. This map enhances or magnifies unique features of the cornea being examined.
- Irregularity map (surface quality maps): The irregularity map uses the same technique as the elevation map, but takes as a reference surface the best-fit spherocylindrical toric surface. The difference between the actual surface and the theoretical surface represents that part of the cornea which cannot be optically corrected. Like refractive power maps, the irregularity map only has clinical meaning when considering the values over the pupillary area.21
- Corneal thickness maps (Fig. 1.15D): Numerous other displays, including 3D maps, astigmatic vector analysis, etc. are available but less used.
QUANTITATIVE DESCRIPTORS OF CORNEAL TOPOGRAPHY: CORNEAL INDEXES
Color-coded maps provide a rapid visual method for clinical diagnosis, but do not supply numerical values that can be used for clinical management. Several corneal indexes describe different features of corneal topography quantitatively and are of great aid in contact lens fitting, for improved assessment of the optical quality of the corneal surface, and can be used in artificial intelligence systems to aid in the diagnosis of corneal shape anomalies. Some of the most useful indexes have been described hereunder.
Basic Topographic Indexes
Simulated Keratometry Reading (SimK Values)
This is a simple descriptor of corneal topography that provides the power and axes of the steepest and flattest corneal curvatures just as K1 and K2 are provided by the classic keratometer, to which it correlates well.3 The cylinder is calculated from the difference between SimK1 and SimK2. Its common uses are:
- Fitting contact lenses
- Refractive surgery calculations
- Supplying a starting point when assessing an irregular corneal shape, since it gives the quantity and axis of astigmatism
Minimum Keratometry Reading
Minimum keratometry reading (MinK) is the minimum meridional power from rings 7, 8 and 9. The average power as well as axis are displayed.
Corneal Eccentricity Index
Corneal eccentricity index (CEI) estimates the eccentricity of the central cornea, and is calculated by fitting an ellipse to the corneal elevation data.12 A positive value is for a prolate surface, negative value for an oblate surface (e.g., flattened corneas after myopic refractive surgery), and zero value for a perfect sphere. Normal central corneas are prolate, meaning they are steeper in the center than in the periphery, and tend to be around 0.30. This value is used for:
- Fitting contact lenses
- Approaching to the global shape factor
Average Corneal Power
This is the area-corrected average of corneal power in front of the pupil. It usually corresponds to the spherical equivalent of the classic keratometer, except after decentered refractive surgery. It may be helpful in determining central corneal curvature when calculating the appropriate intraocular lens.
Surface Regularity Index, and Potential Visual Acuity
Surface regularity index (SRI) measures the regularity of the corneal surface that correlates with the best spectacle-corrected visual acuity assuming the cornea to be the only limiting factor.14 This index adds up the meridional mire-to-mire power changes over the apparent pupil entrance. The SRI value increases with increases in the irregularity of the corneal surface, and its normal value is less than 1.0. It measures optical quality.
Potential visual acuity (PVA) is a range of the expected visual acuity that is achievable based on the corneal topography and can be calculated based on SRI.
Surface Asymmetry Index
Surface asymmetry index (SAI) is a descriptor of the corneal surface that measures the difference between points located 180° apart in a great number of equally spaced meridians.15 Therefore, as the cornea becomes less symmetric, the index differs more from 0.
Other indexes, some of which will be mentioned below, have been developed, and might be exclusive to one particular topographer. The clinician should evaluate the meaning, utility and validity of each index since some indexes have been tested in peer-reviewed literature while others have not.23
Screening Tools and Artificial Intelligence Programs (Neural Networks) for Classification and Auto Diagnosis
As mentioned earlier, even for experienced personnel, interpretation of topography can be difficult, particularly when trying to differentiate the early stages of a disease from a normal cornea (suspected keratoconus), or when trying to differentiate between two similar conditions (contact lens warpage versus early keratoconus). Several mathematical algorithms have been developed to help solve this problem, with high sensitivity and specificity.
Rabinowitz and McDonnell developed the first numerical method for detecting keratoconus using only topographic data.16 They use the I-S value, which measures the differences between the superior and inferior paracentral corneal regions, the central corneal power (MaxK), and the power difference between both eyes. Their study determined the following results:
- Keratoconus suspect: central corneal power > 47.2 D or I-S > 1.4
- Clinical keratoconus: central corneal power > 47.8 D or I-S > 1.9
However, using only these simple measurements for a diagnosis could create specificity problems.
To solve the specificity problem, the new strategy must be able to detect and consider the unique characteristics of keratoconus maps, such as local abnormal elevations. The keratoconus prediction index, developed by Maeda et al.,17 is calculated from the differential sector index (DSI), the opposite sector index (OSI), the center/surround index (CSI), the SAI, the irregular astigmatism index (IAI) and the percent analyzed area (AA). This method partially overcomes the specificity limitation.
Maeda et al. also developed the neural network model, based on artificial intelligence.17 It is a much more sophisticated method for classifying corneal topography and detecting different corneal topographic abnormalities; it employs indexes that were empirically found to capture specific characteristics of the different corneal pathologies, including keratoconus. Further modifications in neural network approach developed by Smolek and Klyce supposedly produce 100% accuracy, specificity and sensitivity in diagnosing keratoconus.
The Pentacam system for instance has developed seven indices of corneal irregularity within the central cornea for the grading and classification of keratoconus (TKC), as well as the postoperative assessment (Fig. 1.17). These indices include index of surface variance (ISV), index of vertical asymmetry (IVA), keratoconus index (KI), central keratoconus index (CKI), index of height asymmetry (IHA), index of height decentration (IHD) and index of minimum radius of curvature (Rmin). This machine also provides with two diagrams that describe the change of corneal thickness in relation to location, and a progression index of this thickness/location relationship to suggest the presence or not of an ectatic disease.24
In addition to this, the Pentacam tomography includes a new software adaptation called the Belin/Ambrosio enhance ectasia display (BAD) that combines both the anterior and posterior elevation data and pachymetric data to orient in the diagnosis of corneal ectasia.
The Sirius system displays a keratoconus summary to aid in the diagnosis and the follow-up of keratoconus combining indices based on curvature, pachymetry and elevation such as the symmetry index of the front and back surface, or the Baiocchi Calossi Versaci front and back index (BCV f and BCV b) to evaluate coma and trefoil aberrations.
The Casia OCT system has a built-in software that estimates ectasia similarity of a scan, and this is calculated as the ectasia similarity score (Fig. 1.18). This score is presented in percentage of similarity.
CORNEAL ABERROMETRY: FUNDAMENTALS AND CLINICAL APPLICATIONS
Whenever a point object does not form a point image on the retina, as it should be in an ideal optical system, one encounters an optical aberration.18 Although one may feel that he is measuring the total refractive error, when refracting a patient, one is actually only considering two components of a whole host of refractive components in the optics of the eye. However, these two components—sphere and cylinder—do constitute the main optical aberrations of an eye. Even in a normal eye with no subjective need for refraction, optical aberrations can be detected.
Since the cornea has the highest refractive power, more than 70% of the eye's refraction, it is the principal site of aberrations, although the lens and the tear film may also contribute to aberrations.1925
MEASURING WAVEFRONT ABERRATION
Measuring Total Wavefront Aberration
It is possible to express ideal image formation by means of waves. An ideal optical system will provide a spherical converging wave centered at the ideal point image. However, in practice, the resulting wavefront differs from this ideal wavefront. The deviation from this ideal wavefront is called wavefront aberration, and the more it differs from zero, the more the real image differs from the ideal image and the worse the image quality. Ocular wavefront sensing devices use five main technologies to determine the resulting or output wave:20
- The Shack-Hartmann method is the most widely used and is inspired by astronomy technology. It consists of analyzing the wave emerging from the eye after directing a small low energy laser beam. This reflected wave is divided by means of a series of small lenses (lenslet array), which generates focused spots. The position of spots is recorded and compared to the ideal one. This type of aberrometer provides reproducible measurements in normal eyes but is limited in eyes with significant amounts of aberrations due to the overlapping of the spots.18
- The Tscherning technique uses typically a grid that is projected onto the retina. The distortion of the pattern is analyzed and used to calculate the wavefront aberration of the eye.21
- The Ray Tracing system is similar to the Tscherning technique. However, instead of a grid, a programmable laser serially projects light beams that form spots on the retina at different locations.21
- The spatially resolved refractometer evaluates the wavefront profile using the subjective patient response. This technology is not practical for clinical use.
- Piramidal aberrometry is a new wavefront sensor based on the Foucault knife edge.22 The Osiris pyramidal aberrometry system bases his working principle on a high-resolution four-faced pyramid wavefront sensor on the focal plane that provides the wavefront gradients in two orthogonal directions and four pupil images (known as sub-pupil) distributed by their intensity: each sub-pupil performs a Foucault knife-edge test to derive slope and shape of the wavefront. Since wavefront is sampled in the very last stage of the optical path, the resolution of the device is extremely high compared to commercial sensors. Finally, the device seems to make possible the analysis of very irregular corneas probably due to his fuzzy dynamic range and to the absence of problems related to sample overlapping, so it might allow higher sensitivity than Hartmann-Shack wavefront sensor.
Measuring Corneal Wavefront Aberration
It is known that 80% of all aberrations of the human eyes occur in the corneal area and only 20% of aberrations originate from the rest of the ocular structures.2327
The effect of corneal aberrations is especially important after corneal surgery such as keratorefractive procedures since the anterior corneal surface is the only one modified.24 The corneal wavefront aberration, which is the component of the total ocular wavefront aberration attributed to the cornea, can be derived from the corneal topographic height data. Specifically, the calculation of wavefront aberrations is performed by expanding the anterior corneal height data into a set of orthogonal Zernike polynomials (Fig. 1.19).
Zernike Polynomials
For a quantitative description of the wavefront shape, there is a need for a more sophisticated analysis than conventional refraction, as the latter only divides the wavefront in two basic terms: sphere and cylinder. One can obtain more information by breaking down the wavefront into terms, which are clinically meaningful, besides the sphere and the cylinder. For this purpose, a standard equation has been universally accepted by refractive surgeons and vision scientists, known as Zernike polynomials.25
Zernike polynomials are equations which are used to fit the wavefront data in a 3D way. The wavefront function is decomposed into terms that describe specific optical aberrations such as spherical aberration, comma, etc. (Fig. 1.20). Each term in the polynomial has two variables, r (rho) and q (theta), where r is the normalized distance of a specific point from the center of the pupil, and q is the angle formed between the imaginary line joining the pupillary center with the point of interest and the horizontal. According to that, we can imagine that aberrations are strongly influenced by pupil size, and, therefore, aberrometric measurements should be related to the diameter of the patient's pupil.28
Zernike terms (
) are defined using a double index notation: (1) a radial order (n) and (2) an angular frequency (m). When talking about first, second, third, etc., aberrations we point to indicate the radial order (n). Each radial order involves n + l terms. There are an infinite number of Zernike terms that can be used to fit an individual wavefront. However, for clinical practice, terms up to the fourth radial order are usually considered:25
- Zernike terms below third order can be measured and corrected by conventional optical means the first order term, the prism, is not relevant to the wavefront as it represents tilt and is corrected using a prism. The second order terms represent low order aberrations that include defocus (spherical component of the wavefront) and astigmatism (cylinder component). Wavefront maps that measure only defocus and astigmatism can be perfectly corrected using spectacles and contact lenses.
- After the second radial order come the high order aberrations. These are not measured by conventional refraction or autorefraction. The aberrometer is the only method available that can quantify these complex kinds of distortions.
- Third order terms describe comma and trefoil defects.
- Fourth order terms represent tetrafoil, spherical aberration and secondary astigmatism components.
Because spherical and comma aberrations refer to symmetrical systems and the eye is not rotationally symmetrical, the terms spherical-like and comma-like aberrations are normally used (Fig. 1.21).29
Wavefront Maps
Wavefront map describes the optical path difference between the measured wavefront and the reference wavefront in microns at the pupil entrance.18 The wavefront error is derived mathematically from the reconstructed wavefront by one of the techniques described earlier. It is plotted as a 2D or 3D map for qualitative analysis in a similar fashion to corneal topography maps. In wavefront error maps, each color represents a specific degree of wavefront error in microns (Fig. 1.21) and like in corneal topography maps, it is necessary to consider the range and the interval of the scale.
Optical and Image Quality
In order to evaluate the impact of aberrations on visual quality following quantitative parameters have been defined (Fig. 1.22):
- Peak to valley error (PV error): This is a simple measure of the distance from the lowest point to the highest point on the wavefront and is not the best measurement of optical quality since it does not represent the extent of the defect.25
- Root mean square error (RMS error): This measure is by far the most widely used. In a simple way, the RMS wavefront error is a statistical measure of the deviation of the ocular or corneal wavefront from the ideal25 (Table 1.1). In other words, it describes the overall aberration and indicates how bad individual aberrations are.
- Strehl ratio: This represents the ratio of the maximum intensity of the actual image to the maximum intensity of the fully diffracted limited image, both being normalized to the same integrated flux.25 This ratio measures optical excellence in terms of theoretical performance results and it is linked to the RMS by the Maréchal formula.
- Point spread function (PSF): This is the spread function observed on the retina when the object is a point in infinity.25 PSF measures how well one object point is imaged on the output plane (retina) through the optical system. In the eye, small pupils (~1 mm) produce diffraction-limited PSFs because of the pupil border. In larger pupils, aberrations tend to be the dominant source of degradation.
- Modulation transfer function, phase transfer function and optical transfer function: Sinusoidal gratings greatly simplify the study of optical systems, because irrespective of the amount of eye aberrations, sinusoidal grating objects always produce sinusoidal grating images.26 Consequently, there are only two ways that an optical system can affect the image of a grating, by reducing contrast or by shifting the image at a specific resolution; are called respectively the modulation transfer function (MTF) and the phase transfer function (PTF). The eye's optical transfer function (OTF) is made up of the MTF and the PTF. A high-quality OTF is, therefore, represented by high MTF and low PTF.
Fig. 1.22: Visual quality summary obtained with the Sirius CSO topographer. It is possible to visualize the wavefront map (gray scale), Strehl ratio, point spread function (PSF) and modulation transfer function (MTF) function.
Clinical Applications
Aberrometers allow practitioners to gain a better understanding of vision by measurement of high-order aberrations. These aberrations reflect a refractive error that is beyond conventional spheres and cylinders. There may be a large group of patients whose best-corrected visual acuity (BCVA) may improve significantly by removing the optical aberrations and this new refractive entity has been called aberropia. Reduced optical quality of the eye produced by light scatter and optical aberrations may actually be the root cause of blurred vision associated with dry eye syndrome and tear film disruption. Measurement of these aberrations are also helpful in keratoconus, post-graft fitting, irregular astigmatism or when refractive surgery has reduced the patient's optical quality.20
Customized ablation patterns, currently in constant evolution, are the future step in laser technology that should address not only spherical and cylindrical refractive errors (low-order aberrations), but also high-order aberrations such as trefoil and comma (Figs. 1.23A to C). Thus, vision can be optimized to the limits determined by pupil size (diffraction) and retinal structure and function.
PATHOLOGICAL CORNEA
Corneal topography is a very important tool in the detection of corneal pathologies, especially ectatic disorders. Screening for these anomalies or their potential development is a critical point in preoperative evaluation for refractive surgery. Keratorefractive procedures are contraindicated in these abnormal corneas.
Keratoconus
Keratoconus is characterized by a localized conical protrusion of the cornea associated with an area of corneal stromal thinning, especially at the apex of the cone. The typical associated topographic pattern is the presence of an inferior area of steepening (Fig. 1.24A to D).33
Figs. 1.23A to C: Customized ablation profile designed according to corneal aberrations: (A) Case of early keratoconus with an unaided and corrected distance visual acuity of 0.5, (B) customized transepithelial PRK ablation profile in order to treat only the coma with the minimal possible ablation depth, (C) topographic outcome 6 months after simultaneous transPRK and corneal collagen crosslinking with an unaided vision of 0.8 and corrected distance vision of 1 due to the regularization of the astigmatism.
In advanced cases, the dioptric power at the apex is at or above 55 D.27 In a small group of patients, the topographic alterations may be centered at the central cornea. In these cases, there may be an asymmetric bow-tie configuration, and usually the inferior loop is larger than the superior loop (Figs. 1.23A to C). Keratoconic corneas have three common characteristics that are not present in normal corneas:
- An area of increased corneal power surrounded by concentric areas of decreasing power.
- An inferior-superior power asymmetry.
- A skewing of the steepest radial axes above and below the horizontal meridian.
Keratoconus suspects are problematic. They may signal impending development of a clinical keratoconus, but they may also represent a healthy cornea.
Figs. 1.24A to D: Keratoconus topography pattern. It can be observed the inferior steepening with posterior elevation and corneal thinning.
The lack of ectasia in the fellow cornea does not indicate that the keratoconus suspect will not progress to true keratoconus. In these cases, the ideal management is close follow-up of the signs of keratoconus in order to check on their stability, and a thorough analysis of the videokeratographic indexes.
Pellucid Marginal Degeneration
Pellucid marginal degeneration is characterized by an inferior corneal thinning between 4 and 8 o'clock positions, a narrow band of clear thinned corneal stroma.28 The ectasia is extremely peripheral and it appears just over the36 thinned area, presenting a crescent-shaped morphology. This pattern has a classical ‘butterfly’ appearance that results in a flattening of the vertical meridian and a marked against-the-rule irregular astigmatism (Fig. 1.25A to D).
Keratoglobus
Keratoglobus is a rare bilateral disorder in which the entire cornea is thinned out, most markedly near the corneal limbus, in contrast to the localized central or paracentral thinning of keratoconus. It is very difficult to obtain reliable and reproducible measurements in these cases due to the high level of irregularity and the poor quality of the associated tear film.
Figs. 1.25A to D: Pellucid marginal degeneration topography pattern. It can be observed the crescent-shaped inferior ectasia with posterior elevation and inferior thinning.
Reliable topographic examinations show an arc of peripheral increase in corneal power (steepening) and a very asymmetrical bow-tie configuration.28
Terrien's Marginal Degeneration
In Terrien's marginal degeneration, there is a flattening over the areas of peripheral thinning. When thinning is restricted to the superior and/or inferior areas of the peripheral cornea, there is a relative steepening of the38 corneal surface approximately 90° away from the midpoint of the thinned area.29 Therefore, high against-the-rule or oblique astigmatism is a common feature, as this disorder involves more frequently the superior and/or inferior peripheral cornea. If the area of thinning is small or if the disorder extends around the entire circumference of the cornea, central cornea may remain relatively spared with a spherical configuration.
Pterygium
Pterygium is a triangular encroachment of the conjunctiva onto the cornea usually near the medial canthus. When the lesion continues to grow out onto the cornea, it could lead to a high degree of astigmatism. When the growth of pterygium is about 2 mm or more, a flattening of the cornea at the axis of the lesion occurs. This produces a marked with-the-rule astigmatism, even of more than 4 D. The evolution of the pathology and the surgical outcome could be monitored by changes in corneal topography.
Postoperative Cornea in Refractive Surgery
Keratorefractive procedures attempt to alter the curvature of the central and midperipheral cornea, and usually have a minimal effect on the corneal periphery. The area in which the curvature is modified is called the optical zone. This tends to be surrounded by a small zone of altered curvature before normal cornea is reached at the periphery. The corneal effect of surgery could be determined by analyzing the difference map between the preoperative and postoperative measurements.30
Postradial Keratotomy
Radial keratotomy (RK) corrects myopia by placing a series of radial incisions (nearly full corneal thickness) leaving a central clear zone (optical zone). These incisions cause a flattening of the central cornea due to retraction of the most anterior collagen fibers and the outward pressure of the intraocular force. This area of flattening is surrounded at an approximately 7 mm zone by a bulging ring of steepening called the paracentral knee or inflection zone. This increases asphericity and corneal irregularity.
A very typical finding in these corneas is a topographic pattern with a polygonal shape.18 Depending on the number of incisions made, squares, hexagons or octagons can be seen. The angles of the polygons correspond closely to the central ends of the incisions (Fig. 1.26A to D).
Postastigmatic Keratotomy
Astigmatic keratotomy (AK) is a simple modification of the RK that is used to correct astigmatism. Rather than placing incisions radially on the cornea, incisions are strategically placed circumferentially on the peripheral cornea at39 the steepest meridian. The incisions induce a flattening in that meridian, but provoke steepening in the perpendicular meridian, in a process called coupling18 (Figs. 1.27A and B). Coupling results from the presence of intact rings of collagen lamellae that run circumferentially around the base of the cornea. With the surgery, these rings become oval in the operated meridian and transmit forces to the untouched meridian. The astigmatic change achieved is the sum of the flattening in one meridian and the steepening on its perpendicular meridian.
Figs. 1.26A to D: Postradial keratotomy cornea. Observe the anterior and posterior circumferential elevation but without any alteration in the corneal pachymetry.
Postphotorefractive Keratectomy
Photorefractive keratectomy (PRK) is a procedure which uses a kind of laser (excimer laser, a cool pulsing beam of ultraviolet light) to reshape the cornea. To correct myopia, the excimer laser flattens the central cornea by removing tissue in that area. However, the optical zone needs to be steepened to correct hyperopia.41
Figs. 1.27A and B: (A) Before and (B) after astigmatic keratotomy. Observe the considerable flattening induced by the keratotomy, in this case excessive, generating a secondary significant astigmatism in the previously flat axis.
This is achieved by removing an annulus of tissue from the midperiphery of the cornea.
The topographic pattern in myopic corrections shows a flattening of the central cornea, an oblate profile (Fig. 1.28A to D). Hyperopic corrections have a pattern of central steepening surrounded by a ring of relative flattening at the edge of the treatment zone, a prolate profile (Fig. 1.29A to D). In astigmatic corrections, the treatment zone is oval.1842
Inadequate ablations during surgery can be detected postoperatively by analyzing the resulting corneal topography. Decentrations can only be identified by a relatively asymmetric location of the treatment area (Fig. 1.30). Other complicated patterns that may lead to severe visual disturbances are the presence of focal irregularities or central islands produced by an inhomogeneous laser beam or an irregular process of corneal healing.
Postlaser in situ Keratomileusis
Laser in situ keratomileusis (LASIK) is an excimer laser procedure like PRK, but in this case, tissue is ablated of under a superficial corneal flap in order to minimize the influence of the epithelium.
The topographic patterns for myopic and hyperopic corrections are the same as in PRK (Figs. 1.28 and 1.29). Although the ablation is covered by a flap of corneal tissue, surface irregularities and central islands may still occur. Decentrations may also occur in a LASIK ablation, depending on the patient's ability to maintain eye fixation during surgery (Fig. 1.30). Epithelial in-growth at the periphery of the flap-stromal interface produces an area of steepening surrounded by an area of marked flattening making the corneal surface more irregular.
Postlaser Thermal Keratoplasty
In laser thermal keratoplasty (LTK), a Holmium laser, is used to heat corneal stromal collagen in a ring around the outside of the pupil. The heat causes the tissue to shrink, producing a zone of localized flattening centered on the spot, and a surrounding zone of steepening. This bulging effect of the central cornea makes it possible to correct hyperopia. The typical topographic pattern shows the central corneal steepening and a ring of flattening overlying the spots (Fig. 1.31).
Figs. 1.29A to D: Topographic pattern after a high-hyperopic ablation. In contrast to a real corneal ectasia, after a hyperopic treatment the posterior corneal surface and the central corneal thickness are normal.
Postintrastromal Corneal Rings Implantation
Intrastromal rings are small segments or rings, made of a plastic-like substance, that are inserted into the periphery of the cornea to correct small degrees of myopia or hyperopia. They act as spacers and by changing the orientation of the collagen lamellae, depending on their shape and position, flatten or steepen the central cornea.46
Nowadays, intrastromal rings are mainly used to reduce the corneal steepening and irregular astigmatism associated with keratoconus (Figs. 1.32A and B).
Postoperative Cornea in Keratoplasty Surgery
Keratoplasty topographies exhibit a wide variety of patterns, depending on the type of keratoplasty performed, the quality of the surgical procedure, whether sutures are still in place in the cornea, and the time elapsed after the procedure.47
Sutures usually induce a central bulge in the corneal graft and its removal results in a decrease of the astigmatic component (Figs. 1.33A and B). The prolate configuration after keratoplasty is the most frequent pattern with a high degree of irregularity. There can be multiple regions of abnormally high or low power, or both simultaneously in the map. Irregular astigmatism over the entrance pupil may be detrimental to optimum visual acuity in the keratoplasty patient.3148
Figs. 1.33A and B: (A) Before and (B) after graft suture removal on a previous penetrating keratoplasty. Observe the significant reduction of the topographic cylinder.
Contact Lens-induced Corneal Warpage or Molding
Corneal warpage is characterized by topographic changes in the cornea following contact lens wear (most frequently in wearers of hard or RGP lenses) as a result of the mechanical pressure exerted by the lens. There are at least four different forms of noticeable topography changes that usually occur mixed with one another: (1) peripheral steepening, (2) central flattening, (3) furrow depression and (4) central molding or central irregularity.1849
Inferior corneal steepening (pseudokeratoconus) is caused by a superiorly riding contact lens that flattens above the visual axis with an apparent steepening below. The topographic image could appear similar to keratoconus, but both conditions are easily differentiated (Figs. 1.34A and B). In corneal warpage, the shape indexes do not indicate any keratoconic condition, and the steep K is not as steep as it is in keratoconus.
Other Uses of Corneal Topography
Corneal topography is a diagnostic tool, but it is also essential before all refractive procedures, to enable the surgeon to understand the refractive status of an individual eye, and plan the optimum refractive treatment. The corneal topography is also used for the following purposes:
Figs. 1.34A and B: Corneal warpage: (A) soft contact lens removed 1 day before the measurement; (B) same patient 1 week later without using contact lenses. Observe how it disappears the inferior asymmetry on the topographic astigmatism.
- To guide removal of tight sutures after corneal surgery (keratoplasty, cataract surgery, etc.) that are causing steepening of the cornea (Figs. 1.33A and B).
- To help in the AK surgical plan.
- To guide contact lens fitting: election of the probe lens and design of the lens.
- To calculate the keratometry values for the calculation of the required intraocular lens power before cataract surgery or refractive lens exchange. This is an important issue in corneas that have undergone previous refractive surgery, because it is more difficult to estimate the real keratometric values in order to avoid hyper- or hypocorrections.
- To evaluate the effect and evolution of a keratorefractive procedure.
REFERENCES
- Kaufman H, Barron B, McDonald M, Kaufman S. Companion handbook to the cornea. London, Butterworth Heinemann, 1999.
- Dabezies OH, Holladay JT. Measurement of corneal curvature: keratometer (ophthalmorneter). In Contact lenses: the CLAO guide to basic science and clinical practice. Kendall/Hunt Publishing Co. 1995. pp. 253–89.
- Wilson SE, Klyce SD. Advances in the analysis of corneal topography. Surv Ophthalmol. 1991;35:269–77.
- Corbett M, O'Brart D, Rosen E, Stevenson R. Cornea l topography: principles and applications. BMJ Publishing Group, 1999.
- Bogan SJ, Waring GO, Ibrahim O, Drews C, Curtis L. Classification of normal corneal topography based on computerassisted videokeratography. Arch Ophthalmol. 1990;108:945–9.
- Corneal Topography. American Academy of Ophthalmology. Ophthalmol. 1999;106:1628–38.
- Mejia-Barbosa Y, Malacara-Hernandez, D. A review of methods for measuring corneal topography. Optom Vis Sd. 2001;78:240–53.
- Cairns G, McGhee CNJ. Orbscan computerized topography: Attributes, applications, and limitations. J Cataract Refract Surg. 2005;31:205–20.
- Cavas-Martinez F, De la Cruz Sanchez E, Nieto Martinez J, Fernandez-Cañavate FJ, Fernandez-Pacheco D.G. Corneal Topography in Keratoconus: state of the art.
- Steinberg J, Casagrande MK, Frings A, Katz T, Druchkiv V, Richard G, Linke SJ. Screening for Subclinical Keratoconus Using Swept-Source Fourier Domain Anterior Segment Optical Coherence Tomography. Cornea. 2015 Nov;34(11):1413-9.
- Miller D, Greiner JV: Corneal measurements and tests. In Principles and practice of ophthalmology. Philadelphia, WB Saunders, 1994.
- Rao SK, Padmanabhan P. Understanding corneal topography. Curr Opin Ophthalmol. 2000;11:248–59.
- Ambrosio R Jr, Klyce SD, Wilson SE. Corneal topographic and pachymetric screening of keratorefractive patients. J Refract Surg. 2003;19:24–9.
- Courville CB, Smolek MK, Klyce SD. Contribution of ocular surface to visual optics. Exp Eye Res. 2004;78:417–25.
- Klyce SD. Corneal topography and the new wave. Cornea. 2000;19:723–29.
- Rabinowitz YS, Nesbum AB, McDonnell PL Videokeratography of the fellow eye in unilateral keratoconus. Ophthalmol. 1993;100:181–6.
- Maeda N, Klyce SD, Smolek MK. Neural network classification of corneal topography. Preliminary demonstration. Invest Ophthalmol Vis Sci. 1995;36:1327–35.
- Boyd BF, Agarwal A, Alio JL, Krueger RR, Wilson SE (eds). Wavefront analysis, aberrometers and corneal topography. Highlights ofophthalmology, 2003.
- Wilson SE, Ambrosio R. Computerized corneal topography and its importance to wavefront technology. Cornea. 2001;20:441–54.
- Molebny VV, Panagopoulou SI, Molebny SV, Wakil YS, Pallikaris IG. Principles of ray tracing aberrometry. J Refract Surg. 2000;16:S572–575.
- Chamot SR, Dainty C, Esposito S. Adaptive optics for ophthalmic applications using a pyramid wavefront sensor. Opt Express. 2006;14:518–526.
- Vincigerra P, Camesasca FI, Calossi A. Statistical Analysis of phisiological aberrations of the cornea. J Refract Surg. 2003;19(suppl):265–9.
- Joslin CE, Wu SM, McMahon TT, Shahidi M. Higher-order wavefront aberrations in corneal refractive therapy. Optom Vis Sci. 2003;80:805–11.
- Thibos LN, Applegate RA, Schwiergerling JT, Webb R. Standards for reporting the optical aberrations of eyes. J Refract Surg. 2002;18:S652–60.
- Hamam H. A new measure for optical performance. Optom Vis Sci. 2003;80:174–84.
- Rabinowitz YS. Keratoconus. Surv Ophthahnol. 1998;42:297–319.
- Karabatsas CH, Cook SD. Topographic analysis in pellucid marginal corneal degeneration and keratoglobus. Eye. 1996;10:451–55.
- Wilson SE, Lin DT, Klyce SD, Insler MS. Terrien's marginal degeneration: corneal topography. Refract Corneal Surg. 1990;6:15–20.
- Vang L, Koch DD. Corneal Topography and its integration into refractive surgery. Comp Ophthalmol Update. 2005;6:73–81.
- Krachmer JH, Mannis MJ, Holland EJ, (ed). Cornea. Surgery of cornea and conjunctiva. St Louis, Elsevier-Mosby, 2005.