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Abstract
There is an increasing interest in applying optical coherence tomography (OCT) to quantify the topography of ocular structures. However, in its most usual configuration, OCT data is acquired sequentially while a beam is scanned through the region of interest, and the presence of fixational eye movements can affect the accuracy of the technique. Several scan patterns and motion correction algorithms have been proposed to minimize this effect, but there is no consensus on the ideal parameters to obtain a correct topography. We have acquired corneal OCT images with raster and radial patterns, and modeled the data acquisition in the presence of eye movements. The simulations replicate the experimental variability in shape (radius of curvature and Zernike polynomials), corneal power, astigmatism, and calculated wavefront aberrations. The variability of the Zernike modes is highly dependent on the scan pattern, with higher variability in the direction of the slow scan axis. The model can be a useful tool to design motion correction algorithms and to determine the variability with different scan patterns.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical Coherence Tomography (OCT) is a noninvasive imaging technique developed in the 1990s [1] which has experienced an increase in its sensitivity, axial range, and acquisition speed in the last decades to become a standard of care in ophthalmology [2]. In particular, A-line acquisition speed increased from the 0.41 Hz of the first OCT image of the anterior segment [3], to the KHz using spectral domain OCT [4], or to MHz regime using swept sources [5,6]. With the increase in the acquisition speed, volumes of data can be acquired rapidly and the images can be quantified to study the 3D shape of the cornea and the crystalline lens [7–11].
An accurate measurement of the corneal power and astigmatism is important for a correct prescription of some ophthalmic corrections such as specialty contact lenses, and for precise planning of refractive or cataract surgery. While Placido ring-based corneal topography can accurately measure the shape of the anterior surface, the posterior surface is not accessible with this technique. The limitation is particularly important in the calculation of the corneal power, which, has traditionally involved assumptions regarding the posterior corneal shape, such as a constant ratio between the radius of curvature of the anterior and posterior surface. Currently, there are several commercially available OCT-based topographers, such as CASIA2 (Tomey Corporation, Nagoya, Japan), Optopol (Zawiercie, Poland) or Anterion (Heidelberg Engineering) and biometers that combine keratometry and OCT such as IOLMaster 700 (Carl Zeiss Meditec, Jena, Germany). Scheimpflug photography has also the ability to image both the anterior and posterior corneal surfaces, but acquisition times are usually larger because of the mechanical movements needed to image the different meridians of the eye.
Though multiplexing schemes using several beams simultaneously [12–14] and non-scanning techniques, such as line or full field OCT [15,16] have been described, in its most usual configuration, OCT uses a single beam that is scanned through the region of interest and the data is acquired sequentially. The two most common scan patterns employed to study the shape of the anterior segment 3D OCT are raster (where cross-sectional images, or B-scans, are stacked laterally) and radial scanning (where images are obtained from line radial scans, typically around a central corneal location). The advantage of raster scan is that it allows a uniform spacing in the x and y directions. However, due to the lower SNR for points far from the corneal apex, the information in the first and last B-scans of a volume is generally limited. With radial scan, the B-scans are images of the different meridians and aside from being relatively similar, which facilitates image processing, they share a common point that can be used to register all B-scans. However, sample density is usually not constant through the region of interest.
Aside from the scan pattern used to obtain the OCT data, its accuracy can be affected by movements present during the acquisition. While many OCT retinal imaging systems use raster scans and compensate the eye movements registering the images with respect to specific retinal features, most commercial anterior segment OCTs use a radial scan pattern, probably due to the relative symmetry of the cornea and the crystalline lens. There are different methodologies described in the literature to avoid the influence of eye movements on anterior segment OCT. A common approach is to assume that the data from each B-scan (i.e. each image of the eye meridian) is free from eye movements because it was acquired in a short amount of time. To register the different B-scans, the data in each of them can be translated axially to register at the central point [17–19]. With this method, residual axial movements present in each B-scan and lateral eye movements that could occur during the acquisition would not be corrected. Translating the data in each B-scan axially and laterally to register all meridians at a point has also been suggested [20]. While this methodology aims to compensate axial and lateral movements, intra B-scan movements can still affect the results. Also, the method could have challenges to segregate tilted, decentered corneas, and data obtained with non-axial incidence.
In this work, we develop a model of the sequential data acquisition with eye movements and compare the variability in corneal topography obtained experimentally in healthy subjects with raster and radial scan patterns with the variability found in the simulated data. Characterizing the variability is essential to estimate the variability of the measurements. The development of acquisition models can help to design strategies to increase the accuracy of the measurements.
2. Methods
2.1 OCT system
Images of the cornea were acquired with a custom spectral domain Optical Coherence Tomography system based on a fiber/optics Michelson interferometer that has been described in detail before [21]. Essentially, a superluminescent diode (λ0 = 840 nm, Δλ = 50 nm; Superlum, Ireland) was used as a light source and a spectrometer consisting of a volume diffraction grating and a 12-bit line-scan camera (Basler sprint spL4096-140 k; Basler AG, Germany) detected the interference signal. The axial range of the instrument was 7 mm in depth and its axial resolution 6.9 microns. Two galvanometer optical scanners (Cambridge Technology Inc., USA) driven by an analog input/output card (National Instruments, USA) and a 75-mm focal length collimating lens were used to scan the beam across the sample. The acquisition speed was 20000 A-scans per second. The measurements were obtained while subjects fixated on a Maltese cross projected on a screen by a DLP (PicoPix, 854 × 480 pixels, Phillips, Amsterdam, Netherlands). A Badal optometer with a motorized stage was used to allow the subject to correct stimulus defocus.
2.2 Sample and OCT experimental measurements
The right eye of 7 normal subjects (age range 22 to 34 years old, spherical error between −6.75 and 0 D) was imaged with the system. Subjects signed a consent form approved by CSIC Institutional Review Boards, that followed the tenets of the Declaration of Helsinki after they had been informed on the nature and possible consequences of the study.
Subjects head was stabilized with a dental impression and the eye pupil was aligned with the OCT axis while the subjects fixated on the Maltese cross.
Axial and lateral motion was studied by imaging consecutively the horizontal meridian of the eye (150 images composed of 300 A-lines each, 2.25 s acquisition time) resulting in videos with a frame rate of 33 Hz.
Three-dimensional (3D) topography data were collected with two different scan patterns: a raster scan pattern (50 B-scans with 300 A-scans each, total acquisition time 0.75 s), and a radial scan pattern with the same number of A-scans (50 meridians with equal angular separation and 300 A-scans per meridian), in an 8 × 8 mm region around the corneal reflex. Figure 1 shows a schematic representation of the patterns and the algorithms for data processing that are detailed in the next section. All measurements were repeated 5 times and the complete imaging session lasted less than 30 minutes.
Fig. 1. Schematic representation of the motion correction strategies studied with raster (left) and radial (right) scans. After segmentation, the corneal elevation obtained was studied without motion correction algorithms, using raster (a) and radial (d) scans, and after two correction strategies. In the first one, Raster Cz (b) and Radial Cz (e), the data of each B-scan was shifted axially to register with a vertical B-scan for raster and with the central point of the scan in the radial scan pattern. In the second one, Raster Cxz (c) and Radial Crz (f), the data was fitted to a conic section and shifted axially and laterally in the plane of the B-scan or the meridian to register its apex with the vertical B-scan for raster or the center of the scans for radial.
2.3 OCT experimental data processing
The custom algorithm used to segment the anterior and posterior surfaces of the cornea has been described in previous publications [10]. Essentially, a mask containing the regions with signal was created by thresholding the image and using morphological operators and the common areas with the result of a Canny edge detector were selected. The two surfaces of the cornea are labeled using a-priori knowledge based on its relative position and outliers were removed by recursive fitting to a low order polynomial.
Lateral shifts between consecutive B-scans that occur due to the delay caused by galvanometer mirror inertia were characterized imaging a glass sphere with both raster, and radial scan patterns and the shift (6 pixels) was corrected.
For the axial and lateral motion study, the anterior surface in each of the images was fitted with a conic, and the movement of the conic apex was studied as a function of time.
To study the 3D elevation measurements, we implemented two different motion correction strategies that emulate previously published procedures [17,20] that shift the data in each B-scan axially, and axially and laterally in the plane of the B-scan. While the methods were conceived to be used with radial scan pattern acquisitions only, we elaborated a similar procedure to correct eye movements using a raster scan and an additional B-scan in the vertical direction. In all cases, motion was estimated for each B-scan, i.e. assuming that intra-B-scan movements were negligible, and axial or axial and lateral movements were allowed depending on the method but no out-of-plane motion was considered. In Raster Cz and Radial Cz, Fig. 1(b) and (e), the data of each B-scan was shifted axially to register with the additional B-scan in the y direction in the raster scan acquisitions, and with the center of the scan, i.e. the common point to all meridians, in the radial scan acquisitions. In Raster Cxz and Radial Crz, Fig. 1(c) and (f), the data of each B-scan was fitted with a conic section and shifted axially and laterally along the B-scan plane so that the apex was coincident with the vertical B-scan at that point for raster, or with the center of the scan for radial scan pattern acquisitions. The raw and corrected corneal elevation data were fitted with a sphere and the residuals with Zernike polynomials up to the 6th order expansion using least mean squares in a 6-mm pupil diameter.
2.4 Simulation of the OCT acquisition with eye movements
Lateral (horizontal and vertical) eye movements were simulated with the Image System Engineering Toolbox for Biology (ISETBIO) [22,23] every 1 ms using the code object fixationalEM for a duration of 2.25 s. Since the spatial characteristics of the eye movements can be subject dependent and influenced by the task [24], the amplitude of the generated eye movements was compared to the amplitude of the lateral movements obtained experimentally and an amplitude factor, AFxy, was calculated as the ratio between the average amplitude of the eye movements measured with the OCT and the average amplitude of the simulated movements. To simulate axial eye movements, we used the same generator, but with the implemented option to remove microsaccades. As in the simulation of lateral eye movements, an amplitude factor in the axial direction, AFz, was calculated as the ratio between the average amplitude of the axial movements measured with the OCT and the amplitude of the generated axial eye movements. The outputs of the lateral and axial eye movement generator were multiplied by the amplitude factors, and their frequency content was compared with the one found in the experimental data.
OCT topography measurements with eye movements were simulated on spherical surfaces
where R represents the radius of the sphere. For each A-scan acquisition time, ${t_{A - scan}}$, the lateral OCT beam position, $[{{x_{beam}}({{t_{A - scan}}} ),\; {y_{beam}}({{t_{A - scan}}} )} ]$, was calculated for each scan pattern using the OCT repetition time. Lateral and axial eye movements were generated for the duration of the scan to calculate the eye position $[{{x_{eye}}({{t_{A - scan}}} ),\; {y_{eye}}({{t_{A - scan}}} ),{z_{eye}}({{t_{A - scan}}} )} ]$, and the sphere was moved following the generated eye movements to calculate the sag at the position of the OCT beam:The points $[{{x_{beam}}({{t_{A - scan}}} ),\; {y_{beam}}({{t_{A - scan}}} ),{z_{beam}}({{t_{A - scan}}} )} ]$ represent the OCT measurement of the anterior surface of the cornea. When simulating the measurements of the two surfaces of the cornea, the optical path between anterior and posterior surface was calculated at the beam location $[x^{\prime}({{t_{A - scan}}} ),\; y^{\prime}({{t_{A - scan}}} )]$ and added to ${z_{beam}}$ to simulate the signal from the posterior surface of the cornea in a measurement.
Simulated OCT data were generated for raster and radial scan patterns with the same number of A-scans, and OCT repetition rate that was used experimentally. A Gaussian noise was added in the axial direction to represent other sources of error such as noise in the detector or edge detection algorithm variability. The amplitude of the axial noise, 23 µm, was estimated from the residuals to the experimental data with Zernike polynomials up to the 6th order.
2.5 Corneal power, astigmatism and high order aberrations
The experimental data and model-generated data were fitted to spheres and the residuals fitted with Zernike polynomials up to the 6th order using least mean squares within a 6-mm circular pupil.
Optical distortion due to the refraction by the anterior surface of the cornea was corrected, and the posterior corneal power, astigmatism and surface high order terms were calculated. Essentially, the elevation fitting parameters of the anterior surface of the cornea were exported to the ray tracing software OpticStudio using a ZernikeSag surface type. To obtain the elevation of the posterior surface of the cornea, ray tracing was performed to refract the rays at the surface using a cornea phase refractive index of np = 1.376, and traced a distance equal to the experimental optical path difference divided by the corneal group refractive index at the OCT wavelength, ng = 1.385 [25]. The reconstructed posterior corneal elevation was fitted to a sphere and the residuals fitted with Zernike polynomials, and the fitting parameters were exported into OpticStudio. The phase refractive index, and an aqueous refractive index of 1.336, were used to calculate the power, astigmatism and wave aberrations of the full cornea.
2.5 Data analysis
The variability of five repeated topography corneal measurements in subjects was characterized by the standard deviation (STD) of each of the fitting parameters. The experimental STD was compared with the STD of the parameters fitting the simulated data, for each scan pattern with and without applying the motion correction algorithms described above. The STD of the optical prediction (power, astigmatism and wavefront aberrations) from the experimental and simulated data were also compared.
The accuracy in the calculation of optical power, cylinder and spherical aberration was evaluated simulating the acquisition of the cornea of the Gullstrand eye model [26]. The deviation from the nominal parameters (43.05 D power, 0 D cylinder, and 0.33 µm spherical aberration) was calculated and one-sample t-tests were performed to determine if the differences were statistically different from zero.
3. Results
3.1 Measured and simulated fixational eye movements
Figure 2(a) shows one of the central B-scan images obtained for one of the subjects, and Fig. 2(b) the lateral and axial movements of the apex of the conic fitting the anterior corneal surface as a function of time. The mean and STD amplitude of the experimental movements observed in all the measurements performed was 128 ± 57 and 158 ± 53 µm in the lateral and axial directions respectively. The mean amplitude of the simulated movements was 87 ± 19 and 68 ± 22 µm, which resulted in amplitude factors of AFxy = 1.47 and AFz = 2.32. Figure 2 shows five eye movements generated with the amplitude factors obtained.
Fig. 2. (a) OCT image of the central meridian of the eye, (b) experimental lateral eye movements measured on repeated images of the central meridian for one of the subjects and five simulated lateral eye movements, and (c) experimental axial eye movements and simulated axial eye movements.
Figure 3 shows the frequency content of the 5 lateral and axial movements measured in the 7 subjects (in red) and the frequency content of 35 simulated lateral and axial movement (in blue) and their average (in black). The frequency content of the simulated and measured distributions was compared though unpaired t-test every 5 Hz. The differences were statistically significant for 30 Hz in the lateral motion amplitude, and above 10 Hz in the axial motion amplitude. The difference between curves in terms of RMS was 0.81 and 0.61 µm, and peak difference was 3.8 and 2.0 µm for lateral and axial motion frequency content respectively.
Fig. 3. (a) lateral and (b) axial frequency content of the measured and simulated fixational eye movements.
3.2 Variability of the OCT experimental data with the different scan pattern
Figure 4 shows the five repeated measurements performed in one of the subjects with raster and radial scan patterns using either the OCT data without attempting to correct eye movements (a) and (b), registering the data by moving axially the information in each B-scan, (c) and (d) or shifting the data laterally and axially, (e) and (f). The figure shows the anterior corneal topography and the wavefront aberrations obtained by ray tracing through the two surfaces of the cornea. When no attempt to correct eye movement was implemented, the variability in both topographical measurements and wavefront maps was apparent in the direction of the slow scan axis in raster scan (horizontal bands in Fig. 4(a)) and in the angular direction in radial scan (angular features in Fig. 4(b)). When the data was registered by moving the information in each B-scan axially, variability was reduced, but residual variability could be visually identified in both raster and radial scan results (Fig. 4(c) and (d)). The variability was further reduced when the data from each B-scan was moved axially and laterally in the plane of the B-scan (Fig. 4(e) and (f)).
Fig. 4. Experimental anterior surface topography and corneal wavefront aberrations obtained in one subject with (a) raster and (b) radial scan pattern without attempt to correct eye movements; when correcting data by registering the information in each B-scan axially (c) and (d); and when correcting the eye movements by registering the information with axial and lateral movements (e) and (f).
3.3 Variability of the surface topography measurements
Figure 5 shows the variability of the fitting parameters (radius of curvature and Zernike coefficients up to the 6th order) of the experimental topography of the anterior surface of the cornea for each subject (in grey) and the average variability (in black). It also shows the variability of the simulated measurements on the Gullstrand model anterior corneal surface (in red). Without motion correction algorithm, Fig. 5(a) and (b), the STD for the radius of curvature was, on average, 0.19 and 0.08 mm for the experimental data, and 0.18 and 0.01 mm for simulated data, in raster and radial scans respectively. The variability in the Zernike terms was clearly dependent on the scan pattern and was above 2 µm in some Zernike coefficients (Zernike coefficients 5 to 7, 12 to 17 and 25 and 26 in raster and 3, 5, 9 to 11, 13, 14 and 21 to 24 in radial scan). The difference between experimental and simulated Zernike coefficients variability was always below 3 µm (RMS 0.9 for raster and 1.4 µm for radial scan). When axial registration was implemented, Fig. 5(c) and (d), the data of the radius of curvature STD was reduced to values below 0.1 mm and all Zernike coefficients STD was below 2 µm except for trefoil terms in radial scan, and the difference in Zernike coefficient variability between experimental and simulated data was below 2 µm (RMS 0.5 for raster and 0.6 µm for radial scan). When registering the data axially and laterally, Fig. 5(e) and (f), the variability of the Zernike coefficients further decreased and only peaked in both experimental and simulated data for vertical astigmatism in raster scan pattern, and the simulated Zernike coefficient variability agreed well with the experimental values (RMS of the difference was 0.4 for raster and 0.5 µm for radial scan).
Fig. 5. Standard deviation of the fitting parameters to the experimental (black) and simulated (red) anterior corneal elevation: best fitting sphere radius and Zernike polynomials, obtained with raster (a), (c) and (e), and radial (b), (d) and (f), without correcting motion, and with two different eye movement correction algorithms. In general, the variability in the simulated data agrees well with the variability found experimentally.
3.4 Variability of the optical power, cylinder and high order wave aberrations
Corneal power and cylinder variability was also dependent on the scan pattern. Figure 6 shows that the estimated power and cylinder variability was high when no algorithm to remove the effect of eye movements was implemented (experimental power STD was, on average, 1.2 for raster and 2.1 D for radial scan pattern, and experimental cylinder STD was, on average, 1.9 for raster and 7.6 D for radial scan pattern). When the data was registered by axially shifting the information in each B-scan, the experimental variability was lower (0.26 and 0.32 D in power, and 0.49 and 0.33 D in cylinder for raster and radial scans, respectively). Registering the data allowing axial and lateral motion in each B-scan the experimental variability was similar in raster and slightly lower in cylinder (in power 0.25 and 0.28 D, and in cylinder 0.24 and 0.22 D with raster and radial scans, respectively). In general, there was a good agreement between the experimentally obtained STD and the one found using the data generated with the model.
Fig. 6. Standard deviation of the experimental (black) and simulated (red) power, cylinder and wavefront aberrations calculated from the OCT data when using raster (a), (c) and (e), and radial (b), (d) and (f) scan patterns.
3.5 Accuracy of the results vs eye decentration
Figure 7 shows the resulting power, cylinder and first order spherical aberration calculated with the data simulated when decentering the cornea between 0 and 2 mm. As expected because of the constant spacing between A-lines, the average values are not affected by decentration when a raster scan pattern is used and no eye movements are corrected, Fig. 7(a). However, if a vertical B-scan at the center of the pattern is used to register the data, since the method assumes that it represents the vertical B-scan passing through the corneal apex, the cylinder and power deviate from their nominal values, Fig. 7(b) and (c). When a radial scan pattern is used, the difference with the nominal power and cylinder was statistically significant only when lateral and axial registration was used, Fig. 7(f).
Fig. 7. Mean and standard deviation of the error in power, cylinder and spherical aberration (Z40) calculated tracing rays through the cornea obtained from simulated OCT data using different scan patterns and motion correction algorithms. When motion between different B-scans is not corrected, (a) and (d), the differences with the nominal data are not statistically significant but the standard deviations are high. When correcting eye movements, (b), (c), (e) and (f), the standard deviations are lower but some strategies are affected by corneal decentration. The only pattern and motion correction strategy that is not affected by decentration is the radial scan with axial registration between B-scans at the center of the pattern.
4. Discussion
We have developed a model to simulate elevation measurements with OCT in presence of eye movements that can be used to study the quality of the data obtained with different scan patterns and motion correction algorithms. The variability found experimentally using raster and radial scan patterns when imaging the cornea of 7 healthy subjects was compared to the variability of the simulated data when no motion correction algorithm was used, and when two different motion correction strategies that were designed to be used with radial scan patterns were applied. The model was also used to study the accuracy of the results obtained when the cornea was decentered from the pattern center.
Lateral and axial subject motion during OCT acquisition was characterized imaging repeatedly the horizontal meridian of the eye and tracking the apex of the best fitting conic to the anterior surface of the cornea. Since we imaged only the horizontal meridian, vertical movements of the cornea could be confounded with axial movements. However, as the horizontal line imaged was close to the corneal apex, the resulting axial motion due to a vertical movement would be small. For example, a corneal radius of curvature of 7.7 mm and a vertical movement of 0.1 mm which is close to the maximum lateral movements measured, would result in an apparent axial movement of 6.5 µm, which is about 3% of the range of axial movements measured. The frequency content of the measured movements in the direction of the OCT beam, agrees well with the axial movements reported using an M-mode scan approach [19]. However, since we imaged the full horizontal meridian the bandwidth of the measurement was reduced and we characterized the eye movements only between 0 and 33 Hz. The frequency content of the simulated eye movements in that range was similar to the one measured experimentally. The largest differences were found for the lateral movements in high frequencies, which we attribute to imprecisions in the scan repeatability that were observed imaging a glass sphere, and in axial movement, which could be explained because of the different physiological origin of lateral and axial movements, and the use of a simplified lateral eye movement model to simulate axial movements.
The standard deviation of the anterior corneal elevation fitting parameters (radius of curvature and Zernike coefficients) and of the corneal power, cylinder and spherical aberration found experimentally agree well with the standard deviation found in the simulated data. With raster scan without motion correction, the maximum variability was in the direction of the slow scan axis and peaked for the Zernike coefficient number 5, i.e. vertical astigmatism. The standard deviation in the vertical astigmatism was 2.3 D and decreased to 0.5 and 0.4 D with the two motion correction algorithms studied but remained as the most variable Zernike coefficient. However, when a radial scan pattern was used the variability was highest in the angular Zernike terms such as vertical and oblique astigmatism and trefoil. When motion correction algorithms were implemented the variability in all terms decreased being highest for angular order terms.
The influence of eye movements in the reproducibility of corneal power measured with OCT had been addressed before. Table 1 shows the literature studies where corneal power or curvature variability was reported, along with the variability obtained with the model developed here. A study by Tang et al. [27] using a radial scan pattern with 8 evenly spaced meridians, formed with 128 A-lines and a repetition rate of 2 KHz, reported a variability of 0.71 D, and suggested that the variability in the measurements should be the result of motion error. In 2011, Zhao et al. [17] suggested to register axially all meridians and found that with 50 radial B-scans, 1000 A-lines per B-scan and a 20 KHz repetition rate, the variability could be reduced to 0.18 D. Pavlatos et al. [20] proposed to register the data with axial and lateral movements of the data in each B-scan, and using 8 meridians, 1024 A-lines per B-scan and a 70 KHz repetition rate reported a variability of 0.14 D. With the acquisition model that we have developed here, the variabilities found in the corneal power when using the OCT repetition rate, scan pattern and motion correction method reported were 0.50, 0.11 and 0.13 D, which are relatively close to the 0.71, 0.18 and 0.14 D reported by those studies despite differences in head stabilization and data processing. In this study, we used 50 radial B-scans and 300 A-lines per B-scan and found an experimental variability of 2.5 D without motion correction algorithms, 0.4 when axial registration was implemented, and 0.35 with axial and lateral registration.
Table 1. Literature reports of corneal power or radius of curvature variability using different scan patterns. The last column represents the variability expected using the model developed in the current study for radial and raster scan patterns.
Raster scan pattern topography measurements were reported by Ortiz et al. [28] in 2010 using 100 B-scans, with 450 A-lines per B-scan resulting in an acquisition time of 2.25 s, in one subject, and by Karnowski et al. [7] using 50 B-scans with 500 A-lines per B-scan and a total acquisition time of 230 ms in three clinical patients, but neither study reported the variability of the measurements. In a subsequent study we used 50 B-scans and 360 A-lines per B-scan [8] and found that the variability in the measured corneal radius of curvature was between 20 and 100 µm, which is in the order but below the 170 µm predicted by our model.
Several alternative scan patterns have been proposed to increase the accuracy of the estimated topography. In 2012, McNabb et al. [19] suggested to use a distributed radial scan with 20 meridian B-scans and 500 A-scans per B-scan, where the data was obtained in 5 passes and each B-scan was reconstructed after the acquisition using masks to find the relative axial and lateral movement between passes. The average repeatability found experimentally in a group of young subjects was 0.09 D. In a posterior study [29], the authors demonstrated the ability of the method to estimate not only power but also astigmatism in clinical patients with variabilities of 0.17 and 0.26 D for sphere and cylinder, respectively. Wagner et al. [30] proposed a scan pattern based on Fermat’s spiral in which the data is obtained in a distributed way allowing distorted parts of the scan to be excluded to reconstruct the full shape of the cornea even in the presence of severe eye movements, however the repeatability was not studied. Anderson et al. [14] obtained data from different points of the cornea simultaneously using a multichannel acquisition OCT and reported a repeatability on the order of 0.1 D. Other scan types such as a spiral with isotropic transverse sampling [31], Lissajous curves [32] and orthogonal raster scan patterns [33] have been proposed for retinal imaging OCT, where features in the images can help to register the data with each other. Also, using a classical raster scan pattern there are methods to correct intra-volume motion correction algorithms [34], but to our knowledge, the applicability of these methods to calculate the topography of the cornea and the crystalline lens remains unexplored. The development of models to accurately simulate data acquisition, such as the one presented here, could clarify the improvement in the quality of the data obtained with each of them and the variability dependence with scan parameters.
Carrasco-Zevallos et al. [35] showed that the image quality of the anterior segment obtained with OCT improved when an eye tracker was used to measure eye movements and the beam position was compensated, however to our knowledge the elevation of the ocular surfaces has not been studied. While with any scan pattern, the use of eye trackers should improve the fidelity of the elevation measurements, the cost and complexity of the system would increase, and the final accuracy of the results would depend on the bandwidth and accuracy of the eye tracker. Also, increasing the OCT acquisition rate expectedly reduces the influence of eye movements in the data. We simulated a 200 KHz acquisition rate using the same number of A-lines, 50 B-scan and 300 A-scans per B-scan, to study the decrease in variability when no motion correction algorithm was applied and observed an expected reduction of 40% in the variability for this 10-fold increase in acquisition speed. Corneal radius of curvature variability decreased from 0.18 to 0.07 and from 0.012 to 0.008 mm, and Zernike coefficients variability, that was reduced approximately by the same percentage for all terms, decreased from 1.79 to 0.65 µm and from 3.28 to 1.26 µm on average, for raster and radial scans respectively. These results are in good agreement with the experimental variability that we reported earlier [36] with our custom-developed swept source OCT [37].
When the cornea is decentered, we have found that only raster and radial scans without motion correction algorithm, which result in high STD values, and radial scan with axial registration of the B-scans result in reliable results. With the rest of the methods studied, the simulated measurements on a decentered cornea resulted in a significant deviation from the nominal power and cylinder. While corneal decentration could be detected to discard invalid scans, the ideal method should keep precision independent from the centration and tilt of the eye. The results obtained when imaging the anterior segment off-axis, i.e. when the OCT beam is not collinear with the pupillary axis, could also be affected by motion correction algorithms. Off-axis imaging has been suggested to visualize peripheral regions of the crystalline lens, not visible on axis due to the iris, [38] and in combination with wavefront measurements, would clarify the contribution of the different ocular structures to the off axis optical quality [39].
Several features of the model could be further refined. One of the main limitations of our approach is the relative simplicity of the eye movement model. In particular, we assumed that the axial eye movements of the eye could be simulated using a lateral eye movement model without microsaccades. While the frequency content of the experimental measurements is similar to the one of the axial movements generated, a better axial movements model could improve the theoretical validity of the model. Also, due to the relatively small eye movements expected with fixation eye rotation was not specifically considered, and solely accounted for by surface translations. The cornea movements that we have measured, ± 100 µm, would correspond to a rotation of about 0.5 degrees, and the maximum sag difference between translation and rotation, 30 µm, would probably not influence the results. However, larger eye movements should be controlled to either remove the data or to rotate instead of translate the B-scans. Finally, the simulations presented here used as nominal surface, the cornea of the Gullstrand model eye, that is a spherical surface. We have explored the results with more complex corneal shapes [40] and found similar variability. To our knowledge, the influence of the scan pattern in the measurement in more complex corneal topographies, such as the ones found in Keratoconus patients or after post radial keratotomy, remain unexplored.
The model developed can help to optimize the scan pattern and the number of A-lines to obtain accurate information of the topography of the ocular elements. Intuitively, while a lower number of A-lines would reduce the influence of eye movements, the available information of the corneal surface would also be reduced, and any small eye movement would affect the results considerably. As more OCT devices are introduced commercially, acquisition models such as the one developed here, could clarify the origin of the variance of the results.
4. Conclusion
The variability of simulated OCT corneal elevation incorporating eye movements match the experimental variability found in corneal shape (radius and Zernike polynomials elevation maps) and corneal power, cylinder and wavefront aberrations using raster and radial scan patterns and two different motion correction procedures. While eye rotations or scan position inaccuracies were not considered, the acquisition model developed in this study shows that eye movements are the major cause of variability in OCT topography measurements. The model can be used to determine the expected variability with different scan patterns and to design motion correction strategies.
Funding
Agencia Estatal de Investigación (FIS2017-84753-R, PID2020-115191RB-I00); European Research Council (H2020-ICT-2017 Ref.779960); National Institutes of Health (P30EY 001319,Unrestricted Funds to Research to Prevent Blindness).
Disclosures
E. Martinez and S. Marcos hold patents related with OCT quantification technology.
Data availability
Data underlying the results presented can be provided by the authors upon reasonable request.
References
1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef]
2. J. Fujimoto and E. Swanson, “The development, commercialization, and impact of optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 57(9), OCT1–OCT13 (2016). [CrossRef]
3. J. A. Izatt, M. R. Hee, E. A. Swanson, C. P. Lin, D. Huang, J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, “Micrometer-scale resolution imaging of the anterior eye in vivo with optical coherence tomography,” Arch. Ophthalmol. 112(12), 1584–1589 (1994). [CrossRef]
4. M. Wojtkowski, V. Srinivasan, T. Ko, J. Fujimoto, A. Kowalczyk, and J. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12(11), 2404–2422 (2004). [CrossRef]
5. T. Klein and R. Huber, “High-speed OCT light sources and systems [Invited],” Biomed. Opt. Express 8(2), 828–859 (2017). [CrossRef]
6. A. Martínez Jiménez, S. Grelet, V. Tsatourian, P. B. Montague, A. Bradu, and A. Podoleanu, “400 Hz volume rate swept-source optical coherence tomography at 1060 nm Using a KTN Deflector,” IEEE Photonics Technol. Lett. 34(23), 1277–1280 (2022). [CrossRef]
7. K. Karnowski, B. J. Kaluzny, M. Szkulmowski, M. Gora, and M. Wojtkowski, “Corneal topography with high-speed swept source OCT in clinical examination,” Biomed. Opt. Express 2(9), 2709–2720 (2011). [CrossRef]
8. S. Ortiz, D. Siedlecki, P. Perez-Merino, N. Chia, A. de Castro, M. Szkulmowski, M. Wojtkowski, and S. Marcos, “Corneal topography from spectral optical coherence tomography (sOCT),” Biomed. Opt. Express 2(12), 3232–3247 (2011). [CrossRef]
9. S. Ortiz, P. Perez-Merino, E. Gambra, A. de Castro, and S. Marcos, “In vivo human crystalline lens topography,” Biomed. Opt. Express 3(10), 2471–2488 (2012). [CrossRef]
10. E. Martinez-Enriquez, P. Perez-Merino, M. Velasco-Ocana, and S. Marcos, “OCT-based full crystalline lens shape change during accommodation in vivo,” Biomed. Opt. Express 8(2), 918–933 (2017). [CrossRef]
11. S. Marcos, E. Martinez-Enriquez, M. Vinas, A. de Castro, C. Dorronsoro, S. P. Bang, G. Yoon, and P. Artal, “Simulating outcomes of cataract surgery: important advances in ophthalmology,” Annu. Rev. Biomed. Eng. 23(1), 277–306 (2021). [CrossRef]
12. M. K. K. Leung, A. Mariampillai, B. A. Standish, K. K. C. Lee, N. R. Munce, I. A. Vitkin, and V. X. D. Yang, “High-power wavelength-swept laser in Littman telescope-less polygon filter and dual-amplifier configuration for multichannel optical coherence tomography,” Opt. Lett. 34(18), 2814–2816 (2009). [CrossRef]
13. T. Anderson, A. Segref, G. Frisken, and S. Frisken, “3D spectral imaging system for anterior chamber metrology,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XIX (SPIE, 2015), Vol. 9312, pp. 29–33.
14. T. B. Anderson, A. Segref, G. Frisken, D. Lorenser, H. Ferra, and S. Frisken, “Highly parallelized optical coherence tomography for ocular metrology and imaging,” in Biophotonics Australasia 2019 (SPIE, 2019), Vol. 11202, pp. 17–18.
15. D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016). [CrossRef]
16. P. Mece, J. Scholler, K. Groux, and C. Boccara, “High-resolution in-vivo human retinal imaging using full-field OCT with optical stabilization of axial motion,” Biomed. Opt. Express 11(1), 492–504 (2020). [CrossRef]
17. M. Zhao, A. N. Kuo, and J. A. Izatt, “3D refraction correction and extraction of clinical parameters from spectral domain optical coherence tomography of the cornea,” Opt. Express 18(9), 8923–8936 (2010). [CrossRef]
18. A. N. Kuo, R. P. McNabb, M. Zhao, F. Larocca, S. S. Stinnett, S. Farsiu, and J. A. Izatt, “Corneal biometry from volumetric SDOCT and comparison with existing clinical modalities,” Biomed. Opt. Express 3(6), 1279–1290 (2012). [CrossRef]
19. R. P. McNabb, F. Larocca, S. Farsiu, A. N. Kuo, and J. A. Izatt, “Distributed scanning volumetric SDOCT for motion corrected corneal biometry,” Biomed. Opt. Express 3(9), 2050–2065 (2012). [CrossRef]
20. E. Pavlatos, D. Huang, and Y. Li, “Eye motion correction algorithm for OCT-based corneal topography,” Biomed. Opt. Express 11(12), 7343–7356 (2020). [CrossRef]
21. I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842–4858 (2009). [CrossRef]
22. R. Engbert, K. Mergenthaler, P. Sinn, and A. Pikovsky, “An integrated model of fixational eye movements and microsaccades,” Proc. Natl. Acad. Sci. 108(39), E765–E770 (2011). [CrossRef]
23. N. P. Cottaris, H. Jiang, X. Ding, B. A. Wandell, and D. H. Brainard, “A computational-observer model of spatial contrast sensitivity: effects of wave-front-based optics, cone-mosaic structure, and inference engine,” J. Vis. 19(4), 8 (2019). [CrossRef]
24. N. R. Bowers, J. Gautier, S. Lin, and A. Roorda, “Fixational eye movements in passive versus active sustained fixation tasks,” J. Vis. 21(11), 16 (2021). [CrossRef]
25. W. Drexler, C. K. Hitzenberger, A. Baumgartner, O. Findl, H. Sattmann, and A. F. Fercher, “Investigation of dispersion effects in ocular media by multiple wavelength partial coherence interferometry,” Exp. Eye Res. 66(1), 25–33 (1998). [CrossRef]
26. A. Gullstrand, in Handbuch Der Physiologischen Optik, 3rd ed. (Leopold Voss, 1909).
27. M. Tang, Y. Li, M. Avila, and D. Huang, “Measuring total corneal power before and after laser in situ keratomileusis with high-speed optical coherence tomography,” J. Cataract Refract. Surg. 32(11), 1843–1850 (2006). [CrossRef]
28. S. Ortiz, D. Siedlecki, I. Grulkowski, L. Remon, D. Pascual, M. Wojtkowski, and S. Marcos, “Optical distortion correction in optical coherence tomography for quantitative ocular anterior segment by three-dimensional imaging,” Opt. Express 18(3), 2782–2796 (2010). [CrossRef]
29. R. P. McNabb, S. Farsiu, S. S. Stinnett, J. A. Izatt, and A. N. Kuo, “Optical coherence tomography accurately measures corneal power change from laser refractive surgery,” Ophthalmology 122(4), 677–686 (2015). [CrossRef]
30. J. Wagner, D. Goldblum, and P. C. Cattin, “Golden angle based scanning for robust corneal topography with OCT,” Biomed. Opt. Express 8(2), 475–483 (2017). [CrossRef]
31. O. M. Carrasco-Zevallos, C. Viehland, B. Keller, R. P. McNabb, A. N. Kuo, and J. A. Izatt, “Constant linear velocity spiral scanning for near video rate 4D OCT ophthalmic and surgical imaging with isotropic transverse sampling,” Biomed. Opt. Express 9(10), 5052–5070 (2018). [CrossRef]
32. Y. Chen, Y. J. Hong, S. Makita, and Y. Yasuno, “Three-dimensional eye motion correction by Lissajous scan optical coherence tomography,” Biomed. Opt. Express 8(3), 1783–1802 (2017). [CrossRef]
33. M. F. Kraus, B. Potsaid, M. A. Mayer, R. Bock, B. Baumann, J. J. Liu, J. Hornegger, and J. G. Fujimoto, “Motion correction in optical coherence tomography volumes on a per A-scan basis using orthogonal scan patterns,” Biomed. Opt. Express 3(6), 1182–1199 (2012). [CrossRef]
34. Z. Li, V. P. Pandiyan, A. Maloney-Bertelli, X. Jiang, X. Li, and R. Sabesan, “Correcting intra-volume distortion for AO-OCT using 3D correlation based registration,” Opt. Express 28(25), 38390–38409 (2020). [CrossRef]
35. O. M. Carrasco-Zevallos, D. Nankivil, C. Viehland, B. Keller, and J. A. Izatt, “Pupil tracking for real-time motion corrected anterior segment optical coherence tomography,” PLoS One 11(8), e0162015 (2016). [CrossRef]
36. A. de Castro, E. Martinez-Enriquez, P. Urizar, A. Curatolo, and S. Marcos, “Effect of axial and lateral fixational eye movements in corneal topography measurement with OCT,” Invest. Ophthalmol. Visual Sci. 62, 2029 (2021).
37. A. Curatolo, J. S. Birkenfeld, E. Martinez-Enriquez, J. A. Germann, G. Muralidharan, J. Palací, D. Pascual, A. Eliasy, A. Abass, J. Solarski, K. Karnowski, M. Wojtkowski, A. Elsheikh, A. Elsheikh, and S. Marcos, “Multi-meridian corneal imaging of air-puff induced deformation for improved detection of biomechanical abnormalities,” Biomed. Opt. Express 11(11), 6337–6355 (2020). [CrossRef]
38. Y. Chen, S. Manzanera, J. Mompeán, D. Ruminski, I. Grulkowski, and P. Artal, “Increased crystalline lens coverage in optical coherence tomography with oblique scanning and volume stitching,” Biomed. Opt. Express 12(3), 1529–1542 (2021). [CrossRef]
39. M. Ruggeri, G. Belloni, Y.-C. Chang, H. Durkee, E. Masetti, F. Cabot, S. H. Yoo, A. Ho, J.-M. Parel, and F. Manns, “Combined anterior segment OCT and wavefront-based autorefractor using a shared beam,” Biomed. Opt. Express 12(11), 6746 (2021). [CrossRef]
40. J. J. Rozema, P. Rodriguez, I. Ruiz Hidalgo, R. Navarro, M.-J. Tassignon, and C. Koppen, “SyntEyes KTC: higher order statistical eye model for developing keratoconus,” Ophthalmic Physiol. Opt. 37(3), 358–365 (2017). [CrossRef]
