Eye motion correction algorithm for OCT-based corneal topography

: With its sequential image acquisition, OCT-based corneal topography is often susceptible to measurement errors due to eye motion. We have developed a novel algorithm to detect eye motion and minimize its impact on OCT topography maps. We applied the eye motion correction algorithm to corneal topographic scans acquired using a 70 kHz spectral-domain OCT device. OCT corneal topographic measurements were compared to those from a rotating Scheimpflug camera topographer. The motion correction algorithm provided a 2-4 fold improvement in the repeatability of OCT topography and its agreement with the standard Scheimpflug topographer. The repeatability of OCT Zernike-based corneal mean power, cardinal astigmatism, and oblique astigmatism after motion detection was 0.14 D, 0.28 D, and 0.24 D, respectively. The average differences between the two devices were 0.19 D for simulated keratometry-based corneal mean power, 0.23 D for cardinal astigmatism, and 0.25 D for oblique astigmatism. Our eye motion detection method can be applied to any OCT device, and it therefore represents a powerful tool for improving OCT topography.


Introduction
The cornea is the first layer of transparent tissue through which light enters the front of the eye. Its primary function is to focus incoming light onto the retina, a light-sensitive layer lining the inside of the back of the eye. The cornea is responsible for approximately 2/3 of the eye's refractive power, and it can bend light due in part to its refractive index which differs from the refractive indices of air and the aqueous humor [1,2]. The cornea's refractive power is also directly related to its shape, so the curvatures of the anterior and posterior corneal surfaces are critical to visual acuity. Alteration of the normal corneal shape can cause significant visual impairment and is a characteristic of multiple pathologies [3,4].
One of the most well-known diseases associated with changes in corneal shape is keratoconus. It is a progressive disorder which causes the cornea to thin and take on a cone-like shape as it bulges outward [5]. Due to the irregular shape of the cornea, light may not be focused on the retina properly, causing blurred and distorted vision in keratoconic eyes. Screening for the early signs of keratoconus is crucial for evaluating a refractive surgery candidate's risk for post-surgical ectasia [6][7][8]. Diseases affecting the epithelium and endothelium, the outer and inner cellular layers of the cornea, can also significantly influence corneal shape. For example, contact lens warpage changes the surface profile of the anterior cornea by inducing localized variations in epithelial thickness [9]. Other epithelial disorders which impact the anterior surface of the cornea include dry eye and epithelial basement membrane dystrophy (EBMD) [10,11]. In Fuch's dystrophy, the endothelium fails to function properly, and the shape of the posterior cornea changes as a result of corneal edema [12].
Corneal topography is an important technology for measuring the shape of the cornea, and a number of methods and devices have been developed. Early technologies used a Placido disc approach which involves constructing the shape of the anterior cornea by measuring how concentric rings of light reflect off of its surface (e.g. Topolyzer Vario, Alcon Laboratories Inc., Fort Worth, Texas and Atlas, Carl Zeiss Meditec Inc., Jena, Germany) [13]. These devices have limitations, however, including being affected by tear film breakup and the inability to measure the posterior surface of the cornea. Measurement of both anterior and posterior corneal topography was made possible by the application of the scanning slit technique (e.g. Orbscan, Bausch & Lomb, Bridgewater, New Jersey) or the Scheimpflug imaging principle (e. g. Pentacam, Oculus, Wetzlar, Germany) [14].
More recently, topographers based on optical coherence tomography (OCT) have been developed, including the CASIA and CASIA2 (Tomey Corporation, Nagoya, Japan), the Optopol T-OCT (Optopol Technology, Zawiercie, Poland) and the Anterion (Heidelberg Engineering GmbH, Heidelberg, Germany) [15]. An important advantage of OCT is its high resolution which makes it possible to not only detect the faint boundary of the posterior cornea, but also to measure epithelial thickness [16]. Additionally, advances in OCT scanning speeds make it possible to complete topography scans faster than the nearly 2 seconds required by the Pentacam [17].
One of the primary challenges that OCT topography methods must overcome is the eye motion that can occur during serial image acquisition. Even during fixation, eye movements such as drift and microsaccades occur [18]. Given that the speed of ocular drift is low (∼1 deg/s) [19], it does not have a large impact during the short time period needed to complete a scan. Microsaccades, on the other hand, are larger (0-2 deg) and more rapid (∼40 deg/s) eye movements which occur at a rate of 1-2 times per second [20,21]. If this type of eye motion is not handled properly, it will cause significant distortions in topography maps and adversely impact measurement accuracy and repeatability. It is therefore crucial to detect microsaccades and remove the meridians impacted by them in order to produce accurate topography maps.
There is currently a sparsity of information in the literature regarding the underlying eye motion detection algorithms that are used for OCT topography. In this paper, we describe an algorithm which detects eye motion and strategically builds corneal topography maps to minimize the related distortions. Metrics of corneal mean power and astigmatism were measured for 20 normal eyes and compared to measurements from a rotating Scheimpflug camera topographer. We also present the topography maps for an eye with keratoconus to demonstrate the ability of our technique to capture the topographical features of corneal pathology.

Data collection
Participants were recruited for this study at the Casey Eye Institute (Oregon Health & Science University, Portland, Oregon). Informed consent was obtained from all participants, and the study protocol was approved by the institutional review board of Oregon Health & Science University. The study adhered to the tenets of the Declaration of Helsinki and the Health Insurance Portability and Accountability Act. Participants with no history of ocular surgery or rigid gas permeable contact lens usage were included in the study. Soft contact lens users were asked to refrain from wearing lenses for at least one week prior to data collection.
Both eyes of each participant were scanned using a commercial spectral-domain OCT system (Avanti; Optovue, Inc., Fremont, CA) and a commercial rotating Scheimpflug camera system (Pentacam; OCULUS, Inc., Wetzler, Germany). The scans from the two devices were taken within 30 minutes of each other to minimize the effect of diurnal changes in the cornea. The OCT device operates at a wavelength of 840 nm and has a scan speed of 70,000 axial scans per second. OCT scans were acquired using a "Pachymetry + Cpwr" scan which is a radial pattern composed of 8 sequential and equally spaced meridians, each with 1,020 axial scans and a scan length of 6 mm. This 8-meridian pattern is repeated 5 times during a single scan with a total scan time of approximately 0.6 seconds. The Pentacam's rotating Scheimpflug camera takes 50 radial cross-sectional images, each with a scan length of 9 mm, acquiring 25,000 data points in roughly 2 seconds [17]. Each eye was scanned 5 times using both devices in order to evaluate measurement repeatability. The first 3 scans were taken without asking the participant to sit back. Participants were asked to sit back and were repositioned for scans 4 and 5 to assess the impact of repositioning on repeatability.
Topography maps from the rotating Scheimpflug camera were generated automatically using the embedded Pentacam software. OCT topography maps were generated using a custom algorithm (MATLAB, MathWorks Inc., Natick, MA). Edge detection and dewarping methods were employed to obtain the profiles of the anterior and posterior corneal surfaces ( Fig. 1) [22]. Corrections were applied to the surface profiles to account for the image dimensions (width and depth) [23], the linearity of the meridional line scans, the optical curvature of the field, and the hysteresis of the galvanometers.

Eye motion detection
If large eye movements occur during the OCT scan, the measured shape of the corneal surface will be distorted. Our approach to detecting this eye motion relied on the repeated scans of each meridian during a single topography scan. This allowed for the measured corneal surface profile from the same meridian to be compared across the 5 repeats. If there was no eye motion, the profile would be the same for all 5 repeats. In contrast, if significant eye movement did occur, either during a meridional scan or during the time interval between the repeated meridional scans, a difference in the measured shape of the corneal surface would be observed. Thus, by detecting differences in the surface shape across the repeats, the meridians affected by significant eye movements could be identified and removed before constructing the topography maps.
Polynomial fitting of the anterior corneal surface was used to quantify changes in shape across the repeated meridional scans. A 3 rd order polynomial function was used, and the 2 nd and 3 rd order polynomial terms were recorded for each of the 5 repeats of a given meridian. To determine if eye motion occurred, the polynomial terms from the 5 repeats were compared to the average polynomial term for that meridian. The average polynomial terms were calculated as the average value from the 3 most similar repeats. Repeated meridians with a large difference from the average polynomial term were deemed to be contaminated by eye motion and were excluded when building the topography maps. The cutoff value for exclusion was established based on the distribution of polynomial coefficient differences for scans of 82 normal eyes not included in this study. The polynomial coefficient difference corresponding to the 90 th percentile was selected as the cutoff.

Map construction
After microsaccade detection, each of the 40 OCT images from the scan (8 meridians × 5 repeats) were marked as either usable (unaffected by eye motion) or unusable (distorted by eye motion). To build a topographic map, a "set" of 8 consecutive meridians was required to form a complete 8-radial set ( Fig. 2(C)). These sets could be composed of one complete repeat (meridian sequence: 1-2-3-4-5-6-7-8) or meridians across successive repeats (e.g. meridian sequence: 6-7-8-1-2-3-4-5). Preference was given to using 8 meridians from the same repeat in order to maximize the number of sets for a given scan. If more than one combination of meridians was available for building a set across successive repeats, the combination with the smallest sum of polynomial differences (used to detect microsaccades) was selected.

Fig. 2.
A) Illustration of the polynomial fitting approach used to detect eye motion during OCT scans. The meridional scan from Repeat 4 would not be used due to the large difference from the average polynomial fit. The illustrated differences are exaggerated for clarity. B) OCT images from the 8 meridional scans of a single repeat. 1 = usable scan, 0 = unusable scan. Differences in the polynomial fits are more subtle in the OCT images compared to the illustration. C) Example of how to build 8-radial sets with only meridional scans which were not affected by eye motion.
Although the meridians distorted by large eye movements were excluded using polynomial fitting of the anterior cornea, eye motion of smaller magnitudes could still cause errors in the topography maps. For this reason, registration of the anterior and posterior surface profiles from the 8 meridians was needed. For registration in the z-direction, the 8 surface profiles were aligned at the scan center. Lateral registration (in the x-y plane) was performed by shifting each meridional surface profile to be aligned at the center of a sphere fitted to the 3D coordinates of the corneal surface. After registration, elevation maps were generated for the anterior and posterior cornea, and Zernike smoothing was used to remove surface aberrations higher than 4 th order.
The elevation maps from all of the good 8-radial sets (up to 5) within a scan were averaged to generate a final elevation map for the scan. The set maps were first aligned so that the location of the anterior corneal vertex for each map was coincident with the vertex location from the first set. Sets which required a shift larger than 0.2 mm to align the vertices were excluded. Sets with float (sphere-fit subtracted) elevation maps that exhibited weak agreement with the float elevation maps from the other sets in the scan were also excluded. Agreement was evaluated by computing the cross-correlation coefficient of each set map with the average map (computed using all of the sets). Candidate set maps were iteratively removed until all of the remaining maps had a correlation above 0.8 with the average map. Scans with only one remaining set were omitted from any further analyses. All of the set maps were cropped to retain the central 5.5 mm, centered at the vertex, to ensure that a consistent map area was used when computing the average map for the scan. The final average elevation map was used to generate maps of axial power, tangential power, and float elevation for each scan.

Comparison with Pentacam topographic measurements
To analyze the performance of our OCT topography algorithm, the float elevation and corneal power maps were compared to Pentacam maps from the same eye. Agreement between the maps was evaluated qualitatively by comparing the map patterns and quantitatively by measuring corneal mean power and the cardinal and oblique components of corneal astigmatism.
For the Pentacam, these topographic metrics were calculated from the simulated keratometry (SimK) values. SimK is a measure of the curvatures along the flat (K1) and steep (K2) meridional axes of the corneal surface and is analogous to the measurements provided by a manual keratometer. In this study, the axes were determined using the central 4 mm zone of the axial power map centered at the corneal vertex. The steep axis is the axis with the largest average axial power, and the flat axis is defined to be orthogonal to the steep axis. Mean power and the cardinal (A C ) and oblique (A O ) components of astigmatism were computed using Eqs. (1)-(3) [24]: where K2 -K1 is the magnitude of corneal astigmatism (in diopters) and θ is the angle of the steep axis measured counterclockwise from the Cartesian + x axis.
In addition to the SimK method, OCT corneal power and astigmatism were also calculated based on Zernike analysis of the reconstructed corneal surface. Mean power and the components of astigmatism were calculated using the following equations [25]: where Z 0 2 is the normalized Zernike polynomial coefficient for the defocus term (in µm), Z 2 2 and Z −2 2 are the normalized Zernike polynomial coefficients for cardinal and oblique astigmatism, n 1 and n 2 are the refractive indices on either side of the refracting surface, and r is the radius of the Zernike analytical zone (in mm, centered at the corneal vertex). For the anterior cornea, n 1 is the refractive index of air (1.0) and n 2 is the keratometric index of the cornea (1.3375). For the posterior cornea, n 1 is the refractive index of the cornea (1.376) and n 2 is the refractive index of the aqueous humor (1.336). A 4 mm analytical zone was used so that the same map area was used for both the SimK-based and the Zernike-based measurements. For a comparison of traditional topographic metrics, K1 and K2 were also calculated from the OCT axial power maps and compared to the Pentacam values.

Statistical analyses
The measurements of mean power and corneal astigmatism from the OCT and Pentacam scans were compared. Bland-Altman analyses were used to evaluate the agreement between the keratometric measures from the two devices. Pearson correlation coefficients were also calculated to assess the relationship between the devices. The repeatability of the measurements across the 5 consecutive scans was quantified by calculating the pooled standard deviation. The repeatability of the OCT measurements and their differences from the Pentacam with and without the motion detection algorithm were evaluated. To determine if repositioning of the participant between scans had an impact on our measurements, an additional analysis was performed to compare the repeatability of scans 1-3 (taken without asking the participant to sit back) and scans 3-5 (taken with repositioning of the participant between scans). The repeatability across the 3 measurements was again calculated as the pooled standard deviation. All statistical analyses were carried out in MedCalc (MedCalc Software, Ostend, Belgium).

Results
Differences in the polynomial fits of the anterior corneal surface were used to identify meridians that were distorted by eye motion. The cutoffs (90 th percentile values) used to designate meridians as usable or unusable were 0.0030 mm for differences in the 2 nd order polynomial coefficient and 0.0013 mm for the differences in 3 rd order polynomial coefficient. For the example illustrated in Fig. 2(A), the difference in the 2 nd order polynomial term was above the threshold for the 4 th repeat of meridian 1. It was therefore flagged as a meridional scan that was distorted by eye motion. Images of a cornea for each of the 8 meridians in the radial scan pattern are shown in Fig. 2(B). Our polynomial fitting approach was successful in detecting blinking (meridians 3-5, OCT interference from the eyelid and eyelashes) and more subtle differences related to eye motion (meridians 2 and 7) or weak signal. Figure 2(C) depicts a scan from which 3 complete sets of 8 radials were able to be constructed from the 5 repeats after the unusable meridians were removed.
The average number of usable sets per scan after the polynomial fit screening was 4.4 ± 0.8 across all of the scans in the study. After removing sets which required a large shift for vertex alignment or exhibited a low correlation with the float elevation maps of other sets, the average number of usable sets was reduced to 3.5 ± 1.1. Only one scan had less than two sets remaining after the quality control criteria were applied. This scan was omitted from further analyses.
Representative anterior and posterior topography maps for OCT and Pentacam scans of a normal eye are shown in Fig. 3. The Pentacam maps were cropped to match the size of the OCT maps to allow for an easier visual comparison of the map patterns. Overall, the OCT map patterns agreed well with the patterns displayed by the Pentacam for each type of map. The float elevation magnitudes were different for the OCT and Pentacam maps due to the difference in the map diameter used to calculate the best-fit sphere (OCT = 5.5 mm, Pentacam = 8 mm). The average values for the 2 nd to 4 th order Zernike coefficients measured from the anterior and posterior cornea are presented in Table 1. The Zernike terms describing piston (Z 0 0 ) and tilt (Z −1 1 , Z 1 1 ) are not reported given that they describe bulk translation of the eye rather than characterizing the shape of the corneal surface. The coefficients corresponding to the defocus term (Z 0 2 ) were much larger than the coefficients for the other terms. The only additional Zernike coefficient with a magnitude larger than 1µm corresponded to the vertical astigmatism term (Z 2 2 ) for both the anterior and posterior surfaces of the cornea. Table 1 also contains the repeatability of the Zernike coefficients across the 5 repeated scans of each eye. The variation between the repeated scans of the same eye was small, with repeatability better than 1 µm for each of the Zernike coefficients. When OCT measurements of mean power were made using the SimK method (Eq. (1)), the average across all eyes was 43.4 ± 1.7 D for the anterior cornea and -6.1 ± 0.2 D for the posterior cornea. The Zernike method (Eq. (4)) produced anterior mean power values that were about 0.5 D higher on average (43.9 ± 1.7 D). The average posterior mean power calculated by the Zernike method (-6.2 ± 0.2 D) was similar to the average value from the SimK method. The cardinal and oblique astigmatism components were generally small, with average Zernike-based magnitudes of 0.6 ± 0.4 D and 0.3 ± 0.2 D for the anterior cornea and 0.3 ± 0.1 D and 0.1 ± 0.0 D for the posterior cornea.
Differences in the topographic measurements made by the OCT and Pentacam devices were evaluated using Bland-Altman plots (Figs. 4 and 5). OCT measurements of K1 and K2 showed good agreement with measurements from the Pentacam, resulting in a small difference in SimK-based mean power of 0.19 D (p = 0.004, paired t-test, Fig. 4). For the anterior cornea, OCT measurements of mean power based on the defocus Zernike term were higher than the Pentacam values by an average of 0.68 D (p < 0.001, paired t-test, Fig. 5). The Zernike-based calculation of mean power for the posterior cornea was slightly higher compared to the Pentacam, although the difference was small (0.07 D on average; p = 0.001, paired t-test).
The components of astigmatism demonstrated good agreement between OCT and Pentacam measurements (Fig. 5). For the anterior cornea, OCT values for the cardinal and oblique components were 0.03 D and 0.13 D lower than the Pentacam values on average, respectively. The average differences were 0.01 D and 0.02 D for the cardinal and oblique components of the posterior cornea.
Strong correlations between the OCT and Pentacam measurements of mean power and astigmatism were confirmed. The Pearson correlation coefficients were nearly equal to one for both anterior and posterior mean power (0.99 and 0.98, respectively). Correlations were also high for SimK at 0.98 for K1 and 0.99 for K2. The correlations ranged from 0.67 to 0.84 for the astigmatism components. All correlations were statistically significant (p < 0.05).  OCT topography measurement repeatability (Table 2) and agreement with Pentacam measurements (Table 3) were greatly improved by the eye motion correction algorithm. The components of anterior astigmatism exhibited the largest improvements in both measurement difference and repeatability, with 3-fold and 4-fold changes, respectively.  The measurements used to assess the impact of repositioning on repeatability are listed in Table 4. Without repositioning between the scans, the OCT measurements of anterior mean power were slightly less repeatable than the measurements from the Pentacam (0.13 D vs 0.07 D). The differences in repeatability between the two devices were larger for the anterior astigmatism components, but the variation was still small for the OCT measurements at around 0.25 D. The repeatability measurements for the posterior cornea were nearly equivalent for OCT and Pentacam and all better than 0.05 D. Repositioning did not cause a significant change in repeatability for any of the metrics.  Topography maps generated from the scans of a keratoconus patient are displayed in Fig. 6. Compared to normal corneas, the keratoconic cornea had a higher surface curvature which was illustrated by the corneal power maps. The axial and tangential power maps displayed good agreement between OCT and Pentacam. As in Fig. 3, the float elevation map values differed between OCT and Pentacam because of the different fitting zone diameters that were used to calculate the best-fit sphere. The region of high curvature in the inferior region of the cornea corresponded roughly with the area of large positive float elevation.

Discussion
In this paper, we have described a novel method for constructing corneal topography maps from OCT images. Our algorithm identifies the anterior and posterior boundaries of the cornea, detects eye motion during image acquisition, and builds maps of corneal elevation and curvature. The repeatability of our OCT measurements and their differences from the Pentacam, a standard clinical corneal topographer, were evaluated.
A variety of other methods for generating corneal topography maps from OCT images have been reported in the literature. In one study, ray tracing and Zernike analyses were used to construct topographic maps of the anterior cornea from the Triton swept-source OCT scanner [26]. The OCT measurements of keratometry and surface aberrations from the Triton device were higher than those from the Pentacam for both normal and keratoconic eyes. Ortiz et al. focused on the curvature of field optical distortion, showing that failing to correct it causes significant errors in measurements of corneal curvature and float elevation maps [27]. Another group described a modified wavelength scanning interferometry technique for nanometer-precision topography, though in vivo application of the method remains untested [28]. Zernike reconstruction has also been paired with a recursive half searching algorithm to build topography maps [29], and while this method did attempt to correct for axial eye motion, our polynomial fitting approach instead focused on minimizing the impact of any type of eye motion by simply removing the images that were affected by large eye movements.
For any OCT-based approach to corneal topography, eye motion is a significant obstacle to overcome. Possible methods for dealing with eye motion include pupil tracking [30][31][32][33] and specialized scan protocols [34][35][36][37]. For example, McNabb et al. designed a novel radial scan pattern to reduce the effects of eye motion by acquiring successive subsampled corneal volumes [35]. Using orthogonal raster scans, Kraus et al. detected eye motion and corrected the related distortions in volumetric OCT data [37]. Draelos et al. made use of both RGB-D cameras and scanner-integrated pupil tracking to detect eye motion in real-time [33]. Another approach described by Malone et al. used spectrally encoded reflectance imaging for retinal motion tracking [38].
However, like many commercial OCT devices, the device used in our study does not possess the capability to track eye movement or implement custom scan patterns. We therefore developed a novel motion detection method, which can be applied to any OCT machine, using only the corneal shape measured from images acquired with existing radial scan patterns. The apparent shape of the cornea in the OCT image can be affected by motion that occurs either during a line scan or in the time period between the repeated line scans along the same meridian. Motion during the line scan distorts the shape of the cornea because its position in the OCT image changes during the acquisition of the successive axial scans that make up the 2D frame. The measured shape of the cornea is impacted by motion between repeated meridional scans because the scan is no longer acquired along the same cross-section of the cornea. Furthermore, these changes in measured corneal shape can occur as a result of either translational or rotational eye movement, and our algorithm did not attempt to differentiate between these two types of motion. Blinking was also easily identified since the shadows created by eyelash or eyelid interference led to highly irregular surface profiles (Fig. 2).
After the motion correction operations, the anterior and posterior surfaces of the cornea were constructed using Zernike polynomials up to and including the 4 th order terms. The predominantly parabolic shape of the cornea was indicated by the large coefficient for the defocus term (Z 0 2 ). Astigmatism was uncommon in this set of eyes, with an exception being the vertical astigmatism of the posterior cornea which was reflected in the coefficient for the Z 2 2 term. Because our sample was composed of normal eyes, they did not exhibit significant higher order surface aberrations, and the 3 rd and 4 th order Zernike terms were generally small. The 2 nd order terms (used to compute the mean power and components of astigmatism) demonstrated variation across repeated scans that was small compared to their respective sample standard deviations across different eyes. This low within-subject variability relative to the between-subject variability is evidence that the Zernike-based measurements are sensitive in detecting differences in corneal shape between eyes.
Our motion detection algorithm provided substantial improvement in the difference between OCT and Pentacam measurements of mean power and astigmatism ( Table 2). Bland-Alman plots showed good agreement between OCT and Pentacam measurements after motion correction was implemented. Our results are similar to those from previous studies which compared OCT to other topographers. Mean power and the components of astigmatism were also calculated by Ozyol et al. and compared between the IOLMaster700 and the Pentacam [39]. Their reported differences were similar to the differences in our study, with magnitudes of 0.2 D for mean power, 0.07 D for cardinal astigmatism, and 0.02 D for oblique astigmatism. A study comparing the Galilei G2 (dual rotating Scheimpflug-Placido) to the Casia SS-1000 (swept-source OCT) concluded that the two devices were equivalent in detecting the shape of both the anterior and posterior cornea and could be considered interchangeable [40]. The MS-39 device, which combines OCT imaging and Placido topography, was shown to agree well with two Scheimpflug-based topographers including the Pentacam [41]. A new OCT device released by Optopol (Revo NX) demonstrated differences in simK from the Galilei G6 at levels similar to those found in our study [42]. Karnowski et al. built a custom swept-source OCT device and showed good agreement with the Pentacam for float elevation maps and SimK values [43]. In relation to these studies, the comparable level of agreement that we found between OCT and Pentacam provides further validation of our OCT topography approach.
The only parameter that differed notably between OCT and Pentacam measurements was the Zernike-based anterior mean power (average difference = 0.68 D, Fig. 4). Our results suggest that this difference is related to the methods used to calculate mean power. The Pentacam computes mean power as the average of the flat and steep SimK axes (K1 and K2). The strong agreement between our OCT measurements of SimK-based mean power and the Pentacam values provides evidence that the difference in mean power was not due to differences in the detected shape of the cornea (Fig. 5). The Zernike method for calculating mean power differs from the SimK method in two ways: 1) it takes the entire corneal surface into account rather than measuring along only two axes and 2) it does not rely on the axial power calculation which is based on the refractive power of the equivalent sphere [44]. By measuring the parabolic shape of the corneal surface as a whole, the Zernike method may be able to characterize the optical power of the cornea more precisely [45].
In addition to demonstrating good agreement, the OCT and Pentacam measurements were strongly correlated. While still statistically significant, the correlations were lower for the components of astigmatism relative to mean power. The primary explanation for this is likely that the eyes in this study had small magnitudes of astigmatism. The relationship between OCT and Pentacam measures of astigmatism may be stronger if it is evaluated over a larger range of astigmatism values.
The repeatability of the topographic measurements was analyzed by taking repeated OCT and Pentacam scans of each eye. The implementation of our motion detection algorithm vastly improved the repeatability of the mean power and astigmatism measurements ( Table 3). The repeatability performance of the two devices in our study was comparable to previous reports analyzing various topographers [41,46,47]. For the anterior cornea, the repeatability of the mean power and astigmatism measurements was slightly better for the Pentacam compared to OCT (Table 4), although the OCT values were near or below the clinically acceptable threshold of 0.25 D [48]. This discrepancy in repeatability is likely related to the difference in azimuthal sampling density between the two devices (50 meridians for Pentacam vs. 8 meridians for OCT). This is particularly problematic for measuring astigmatism, which requires a precise determination of the steep and flat axes. With fewer meridians, those with slight segmentation errors or distortions caused by eye motion that did not reach the threshold for removal will have a larger impact on the map patterns. Furthermore, the measurement of astigmatism relies on interpolation between the meridians, which can be done with better precision when data points are sampled more densely.
OCT measurements of the posterior cornea exhibited excellent repeatability on par with the Pentacam. The ability of OCT to reliably detect the faint boundary of the posterior cornea is related to its high resolution [49]. The better repeatability for the posterior cornea compared to the anterior cornea can be explained by the difference between the refractive indices (n 2 − n 1 ) used to calculate the mean power and astigmatism components (Eqs. (4)- (6)). The magnitude of this difference is 0.3375 for the anterior cornea and 0.04 for the posterior cornea. Therefore, the corneal power measurements for the posterior cornea are less influenced by differences in the measured Zernike coefficients.
There were a couple of clinical limitations to this study. First, the topography measurements were evaluated only for normal corneas. As preliminary evidence of our ability to accurately measure pathologic corneas, we constructed topography maps for one keratoconus eye, which showed good agreement with Pentacam maps. However, analyses with a larger sample size are needed to quantify our algorithm's performance for diseased corneas. Second, the small levels of astigmatism for the eyes in this study were not ideal for the comparison of astigmatism measurements between OCT and Pentacam. As we acquire more scans of normal eyes, we will be able to test our method on eyes with more severe astigmatism.
The main technological limitations of this study were the relatively slow scan speed (70 kHz) and the low number of meridians provided by our current OCT device (8 vs. 50 for the Pentacam). As discussed previously, this may have a negative impact on repeatability, particularly for measurements of astigmatism. The 8-meridian radial scan pattern is also insufficient for reconstructing higher order Zernike surfaces. Although 4 th order Zernike polynomials are sufficient for characterizing the shape of normal corneas, higher order terms are needed to accurately capture the irregular surface profiles induced by conditions such as contact lens-related warpage and severe keratoconus [50]. We are currently evaluating a new OCT device which provides 16 meridians with the goal of improving measurement repeatability and allowing for more Zernike terms to capture the irregular surface profiles that are associated with corneal pathology. Another limitation of OCT imaging is the apical flare that appears in the image when the scan is centered on the corneal apex. We resolved this issue by obtaining pupil-centered scans and resampling the elevation data to be centered at the corneal apex during post-processing.
In summary, we have developed an OCT topography algorithm to measure the surface profiles of the anterior and posterior cornea. We devised a new and widely applicable strategy for detecting eye motion and constructing sets of meridional scans to build topography maps. OCT measurements of mean power and astigmatism were shown to have good repeatability and agreed well with the Pentacam. By combining anterior and posterior topography with measurements of pachymetry and epithelial thickness, OCT has the power to provide clinicians with comprehensive information to detect and classify a wide range of corneal diseases.

Disclosures
Oregon Health and Science University (OHSU) and Drs. Huang and Li have a significant financial interest in Optovue, Inc., a company that may have a commercial interest in the results of this research and technology. These potential conflicts of interest have been reviewed and managed by OHSU.