It is known that the front surface of the cornea contributes to more than two-third of the refractive power of the eye. Consequently, measuring corneal power is useful in ophthalmic practice for diagnostic purposes. Corneal power as well as corneal aberrations is easily derivable from the corneal shape. To measure corneal shape, corneal topography techniques are used where information is gathered from reflected and scattered light from the cornea. There are various corneal topographic techniques based on different principles, i.e., specular reflections, slit-imaging based, or anterior segment optical coherence tomography. Among these techniques, specular reflection topography gives more precise measurement of corneal shape and aberrations1–3 because it is a technique that does not require scanning and therefore is less prone to movement artifacts. The most common specular reflection topographers use the Placido technique where a pattern of concentric rings produces corneal reflections. However, it is known that skew ray error remains a problem in this technique.4–7 This error occurs because in the reconstruction of the corneal shape, it is assumed that the corneal reflection of a single point of the Placido ring pattern happens within a meridian plane of the eye. This meridional assumption about the light path is valid only if the shape of the anterior corneal surface is rotationally symmetric, which is not necessarily true. Consequently, errors will arise in reconstructing the three-dimensional shape of the cornea. Similar problems are reported for aberrometry.8
In Placido-based corneal topography, numerical solutions were developed to solve the skew-ray error problem.9,10 However, recently, it was demonstrated that these algorithms do not completely resolve the problem mainly because of its sensitivity to measurement noise.11 The VU topographer (Fig. 1) was developed as an alternative solution to the skew-ray error problem in corneal topography.
Using a color-coded pattern to establish one-to-one correspondence between reflection source and image points,12 this topographer is able to use corneal reconstruction algorithms that are free from skew ray errors.13 Furthermore, this color-coded point-source corneal topographer (PCT) was found to be superior in reconstructing the non-rotationally symmetric features of the anterior corneal surface.14 However, the clinical validation of these findings and their clinical implications has yet to be shown.
There are several corneal types where there are substantial non-rotationally symmetric aberrations. Examples of these are keratoconic corneas, postlaser-assisted in situ keratomileusis corneas and postcorneal transplanted corneas. In this study, the focus will be on postcorneal transplants, particularly, those that were treated with conventional penetrating keratoplasty (PKP). In PKP, a full thickness of the central 8.0 to 9.0 mm recipient cornea is removed and replaced with donor tissue. PKP provides good visual results in most cases. However, large amounts of postkeratoplasty astigmatism may remain even after all sutures are removed.15,16 Recently, it was demonstrated that corneal topography-guided penetrating keratoplasty and suture adjustment provided stable astigmatism 24-month postsurgery.17 In this technique, it is important to monitor corneal aberrations. Accurate information of higher order aberrations helps in assisting the visual recovery process in PKP patients by providing a progress metric in healing, a metric to optimize the suture geometry and suture removal or an indicator for possible extra treatment.18–20
In this study, the accuracy of PCT is compared with Placido-based topography in clinical measurements of post-PKP eyes. Typical corneal topography photographs of these eyes derived from both techniques are shown in Fig. 2. The central corneal zone reflects a relatively uniform pattern whereas the deformations in the pattern are usually seen in the peripheral corneal zone which coincides to the region near the boundary of the trephination. Both techniques are able to qualitatively display typical geometric features of post-PKP eyes. The effect of skew ray error in Placido-based topography is not easily observed from visual inspection of the images and therefore a quantitative comparison of corneal aberration measurements from both techniques is important.
Artificial surfaces are used in the validation of these corneal topographers because it is difficult to have a gold standard measurement on real eyes. Recently, it has been theoretically shown that surface reconstruction algorithms used in PCT are more accurate compared with Placido-based algorithms in determining non-rotationally symmetric corneal aberrations, particularly the quadrafoil aberration.11 Therefore, an artificial quadrafoil surface was used as an accuracy reference for both types of topographers.
Twenty post-PKP eyes from 17 subjects were included in this study: average age of 61 years, ranging from 34 to 85 years, 8 males and 9 females, and 8 OD and 12 OS. Eyes with stitches still present, dry eyes and extensive scar tissue were excluded. Measurements are done at least more than 6-month postsurgery. To maintain the stability of the tear film, all subjects were asked to blink before every individual measurement which makes the duration of one complete measurement less than a second. The research followed the tenets of the Declaration of Helsinki. Informed consent was obtained from the subjects after explanation of the nature and possible consequences of the study. The research was evaluated and approved by the medical ethics committee of the VU University Medical Center.
Corneal elevation data were obtained from PCT (VU topographer, prototype; VU University Medical Center, Amsterdam, The Netherlands) and Placido-based topography (Keratron, Optikon 2000, Rome, Italy). A basic conic fit is used to derive radius and asphericity values from corneal elevation data.21 It is known that a basic conic fit is not sufficient to model the corneal shape,22 therefore in addition to radius and asphericity, corneal aberrations in Zernike convention are calculated to show the effects of fine corneal shape features. The corneal aberrations were derived from the corneal elevation data using a numerical wavefront ray-tracing procedure for which the details are described in an earlier publication.1 The rms values (up to Zernike radial order 8 and corneal zone of 6 mm) of the non-rotationally symmetric aberrations (astigmatism, coma, trefoil, and quadrafoil) were recorded in micrometers (in some cases converted to equivalent diopters).23 A paired student t-test was used to compare medians1 from measurements of PCT and Placido-based topography because the data were characterized by normal distributions as confirmed by Shapiro-Wilk tests. The mean value and SD of parameters, including difference between instruments, measured from all subjects were tabulated. Precision was quantified using the SD of values on the three trials performed when obtaining the elevation data. The mean and the SD of the precision over all subjects were reported.
An artificial surface was used as a reference for the eye measurements. For precision measurements, six trials were used. The surface used has a quadrafoil feature and is constructed in the same class of an octafoil surface type first described by Rand et al.5 These surfaces can be described in cylindrical coordinates (ρ,θ,z) where the corneal sag, z, is:
ε is the amplitude of the peripheral corrugation on the surface, r is the surface base radius of curvature, and n defines the rotational frequency of the surface. The artificial surface used in this study has an amplitude ε = 0.01 mm (10 μm), a surface base radius of r = 8 mm, and a rotational frequency n = 4 corresponding to a quadrafoil shape. The artificial surface was manufactured by SUMIPRO BV, Almelo, The Netherlands. The surface specifications were verified by talysurf measurements and the tolerance in the sagitta was found to be 0.2 μm, which is a tolerance of 0.07 μm in terms of corneal aberrations. The manufacturer's specifications (2.05 ± 0.07 μm for quadrafoil aberration) were considered as the gold standard. The error (mean ± SD) from each instrument compared with the gold standard is reported.
A summary of the results obtained from the anterior corneal measurements of post-PKP eyes is presented in Table 1. Paired student t-tests indicate that only the quadrafoil aberration measurements are significantly different (p < 0.02) between the two instruments with a difference of 0.15 ± 0.28 μm (0.12 ± 0.22 eq. Dpt.).
Table 2 shows the precision of the measurements of the post-PKP eyes that are quite similar for both instruments. Table 3 shows the performance of the instruments in measuring the quadrafoil aberration of the artificial surface. Compared with the gold standard, the PCT has an absolute error of 0.16 μm (0.12 eq. Dpt.) whereas the Placido-based topographer has an absolute error of 1.50 μm (1.15 eq. Dpt.).
In this study, PCT was compared with only one Placido-based topographer: the Keratron. Nevertheless, previous studies show that the Keratron measures comparable elevation data with that of other Placido-based topographers in measuring artificial surfaces.24 It was also demonstrated that the Keratron measures corneal curvature of keratoconus corneas with similar precision compared with other Placido-based topographers.25 Furthermore, it was shown that at least for normal eyes, the elevation data of the Keratron is interchangeable with that of Scheimpflug-based topographers.1 For these reasons, it is sufficient to use only the Keratron for comparison with PCT because it can be considered as a typical Placido-based topographer. It is important to note that Placido devices do not align to the line of sight,26 which the PCT instrument does. However, the Keratron has software to realign its measurements to the line of sight, which makes the alignment equivalent to the PCT alignment. Typical differences in coma aberration because of an alternate alignment27 are therefore not observed anymore.1
In PKP, we often see strange corneal distortions around the trephination (Fig. 2). For PCT, the square pattern gets stretched and pinched. In these cases, filter functions can still detect most corners.12,14 In some cases, there will be corners that cannot be detected but this will not disrupt one to one assignment between source and image points because of color-coded pattern recognition. Therefore, a reasonable surface reconstruction can still be made. However, for Placido-based topography systems, corneal distortions can cause merging of the rings in the reflection image. This creates problems especially in edge detection algorithms, but it is difficult to assess how these difficulties are treated because these algorithms are proprietary. Failure in image processing is likely to occur near the area of trephination. This is located mostly at the edges of the 8 to 9 mm corneal zone. In this study, the evaluation of corneal aberrations is done at a corneal zone diameter of 6 mm where image processing is still manageable. The difference in image processing techniques between PCT and Placido-based topography is therefore unlikely to have a significant effect on the measured corneal aberrations.
A significant difference (p = 0.02) was observed for quadrafoil aberration in PKP eyes as measured by PCT and Placido-based topography (Table 1). Results on the artificial surface (Table 3) show that the measured value of the quadrafoil aberration is more accurate for PCT. The mean error measured by PCT (0.12 eq. Dpt) is within clinically tolerable limits (0.125 eq. Dpt)1,28 whereas the mean error measured by the Placido-based topographer (1.15 eq. Dpt.) is not. Because the precision of both instruments is not statistically different as can be seen from Table 2, this implies that the measured difference in post-PKP eyes is a result of the inaccuracy of Placido-based corneal topography. It is noticeable that the quadrafoil aberration of the artificial surface is more than 2 times the mean corneal quadrafoil aberration of the measured PKP eyes. This could be a reason why the error in the artificial surface measurements is larger than the error observed for the actual eye measurements. It should also be noted that the quadrafoil surface is designed based on the Rand surface,5 which is designed to maximize the skew ray ambiguity in Placido-based topography. This ambiguity is expected to be less in actual eye measurements. Also, when the corneal aberrations in the eye are not substantial, as in the case of normal eyes, the effect of skew ray error is not observed as reported in previous studies where PCT and Placido-based topography corneal aberration measurements were interchangeable.1
A recent study that numerically evaluated the performance of algorithms used in PCT in comparison with that of Placido-based topography shows that the effect of skew ray error and measurement noise affects the accuracy of Placido-based topography corneal aberration measurements particularly the non-rotationally symmetric aberrations such as astigmatism, trefoil, and quadrafoil aberration.11 The effect is greatest on the quadrafoil aberration. This is consistent with the observed statistically significant difference in the quadrafoil measurements done in this study. It could be that the effect on trefoil and astigmatism is lower and therefore shows no statistically significant differences.
The inaccuracy of the Placido topographer for measuring quadrafoil aberration of PKP eyes is 0.15 ± 0.28 μm (0.11 ± 0.21 eq. Dpt.). Statistics show that this is significant but the mean value is lower than the coefficient of repeatability of PCT quadrafoil measurements which is 2.77 × 0.07 = 0.19 μm. This means that the accuracy advantage of PCT can only be relevant in clinical practice if the precision of PCT is improved. In general, the precision is about 8% of the actual value of the corneal aberrations. Nevertheless, the potential relevance of the accuracy advantage in quadrafoil measurements can be important.
The mean quadrafoil error of 0.11 eq. Dpt. is clinically acceptable, but the spread of the error covers a substantial amount of cases where the error is clinically relevant. Sixty percent, 25%, and 5% of the cases have absolute errors >0.125 eq. Dpt, 0.25 eq. Dpt, and 0.5 eq. Dpt, respectively. Although past studies have indicated that the impact of the individual quadrafoil aberration is relatively the lowest among the fourth order or lower aberrations,29 studies also reveal that the impact of quadrafoil aberration is quite substantial when it is combined with other aberrations of the eye (e.g., spherical aberration).30 Therefore, substantial amount of quadrafoil aberration in the eye will contribute to reduced visual acuity. It is therefore important to measure the actual aberration of the cornea precisely and accurately to avoid wrong diagnosis, e.g., cases where patients complain of reduced vision while Placido-based topography show minimal irregularity in the cornea.
Another important aspect of PKP is the management of suture removal. Postkeratoplasty astigmatism can be decreased by adjustment of a single running suture or selective removal of interrupted sutures.31 In these cases, the images obtained from Placido-based topography are quite handy because it gives a simple qualitative aid in suture removal management. PCT gives a more complex qualitative interpretation but, however, provides more accurate quantitative information of the corneal aberrations. For better management of suture removal in PKP patients, the combined information from both topographers is therefore recommended.
Furthermore, correctly measuring corneal aberrations is essential in customized applications of corneal refractive surgery. A recent study reveals that cornea wavefront-guided retreatment was effective in improving subjective night vision symptoms, reducing corneal spherical aberration, and decreasing asphericity in eyes that underwent myopic laser refractive surgery.17 In this study, a mean higher order aberration of 0.48 eq. Dpt was induced, but corneal wavefront-guided retreatment was able to reduce this to 0.37 eq. Dpt. However, this is still large enough to affect the quality of vision. With improved precision in the future, PCT as the more accurate corneal topography technique has therefore the potential to improve topography-guided laser-assisted in situ keratomileusis procedures.
Anne C. L. Vrijling
Royal Dutch Visio
Centre of Expertise for Blind and Partially Sighted People
1272 RR Huizen
1. Braaf B, Dubbelman M, van der Heijde RG, Sicam VA. Performance in specular reflection and slit-imaging corneal topography. Optom Vis Sci 2009;86:467–75.
2. Read SA, Collins MJ, Iskander DR, Davis BA. Corneal topography with Scheimpflug imaging and videokeratography: comparative study of normal eyes. J Cataract Refract Surg 2009;35:1072–81.
3. Tang M, Li Y, Avila M, Huang D. Measuring total corneal power before and after laser in situ keratomileusis with high-speed optical coherence tomography. J Cataract Refract Surg 2006;32:1843–50.
4. Tripoli NK, Cohen KL, Obla P, Coggins JM, Holmgren DE. Height measurement of astigmatic test surfaces by a keratoscope that uses plane geometry surface reconstruction. Am J Ophthalmol 1996;121:668–76.
5. Rand RH, Howland HC, Applegate RA. Mathematical model of a Placido disk keratometer and its implications for recovery of corneal topography. Optom Vis Sci 1997;74:926–30.
6. Klein SA. Axial curvature and the skew ray error in corneal topography. Optom Vis Sci 1997;74:931–44.
7. Iskander DR, Davis BA, Collins MJ. The skew ray ambiguity in the analysis of videokeratoscopic data. Optom Vis Sci 2007;84:435–42.
8. Atchison DA. The skew ray issue in ocular aberration measurement. Optom Vis Sci 2006;83:396–8.
9. Klein SA. Corneal topography reconstruction algorithm that avoids the skew ray ambiguity and the skew ray error. Optom Vis Sci 1997;74:945–62.
10. Turuwhenua J. An improved low order method for corneal reconstruction. Optom Vis Sci 2008;85:211–7.
11. Snellenburg JJ, Braaf B, Hermans EA, van der Heijde RG, Sicam VA. Forward ray tracing for image projection prediction and surface reconstruction in the evaluation of corneal topography systems. Opt Express 2010;18:19324–38.
12. Vos FM, van der Heijde RGL, Spoelder HJW, van Stokkum IHM, Groen FCA. A new instrument to measure the shape of the cornea based on pseudorandom color coding. IEEE Trans Instrum Meas 1997;46:794–97.
13. Sicam VA, Coppens J, van den Berg TJ, van der Heijde RG. Corneal surface reconstruction algorithm that uses Zernike polynomial representation. J Opt Soc Am (A) 2004;21:1300–6.
14. Sicam VA, van der Heijde RG. Topographer reconstruction of the nonrotation-symmetric anterior corneal surface features. Optom Vis Sci 2006;83:910–8.
15. Colin J, Velou S. Current surgical options for keratoconus. J Cataract Refract Surg 2003;29:379–86.
16. Vinciguerra P, Epstein D, Albe E, Spada F, Incarnato N, Orzalesi N, Rosetta P. Corneal topography-guided penetrating keratoplasty
and suture adjustment: new approach for astigmatism control. Cornea 2007;26:675–82.
17. Alió JL, Pinero D, Muftuoglu O. Corneal wavefront-guided retreatments for significant night vision symptoms after myopic laser refractive surgery. Am J Ophthalmol 2008;145:65–74.
18. Seitz B, Langenbucher A, Szentmary N, Naumann GO. Corneal curvature after penetrating keratoplasty
before and after suture removal: a comparison between keratoconus and Fuchs' dystrophy. Ophthalmologica 2006;220:302–6.
19. Kaiserman I, Bahar I, Rootman DS. Half-top-hat—a new wound configuration for penetrating keratoplasty
. Br J Ophthalmol 2008;92:143–6.
20. Langenbucher A, Seitz B. Changes in corneal power and refraction due to sequential suture removal following nonmechanical penetrating keratoplasty
in eyes with keratoconus. Am J Ophthalmol 2006;141:287–93.
21. Kiely PM, Smith J, Carney LG. The mean shape of the human cornea. Optica Acta 1982;29:1027–40.
22. Franklin RJ, Morelande MR, Iskander DR, Collins MJ, Davis BA. Combining central and peripheral videokeratoscope maps to investigate total corneal topography. Eye Contact Lens 2006;32:27–32.
23. Thibos LN, Hong X, Bradley A, Cheng X. Statistical variation of aberration structure and image quality in a normal population of healthy eyes. J Opt Soc Am (A) 2002;19:2329–48.
24. Tang W, Collins MJ, Carney L, Davis B. The accuracy and precision performance of four videokeratoscopes in measuring test surfaces. Optom Vis Sci 2000;77:483–91.
25. McMahon TT, Anderson RJ, Joslin CE, Rosas GA. Precision of three topography instruments in keratoconus subjects. Collaborative Longitudinal Evaluation of Keratoconus (CLEK) Study Topography Analysis Group. Optom Vis Sci 2001;78:599–604.
26. Mandell RB, Horner D. Alignment of videokeratographs. In: Gills JP, Sanders DR, Thornton SP, Martin RG, Gayton JL, Holladay JT, eds. Corneal Topography: the State of the Art. Thorofare, NJ: SLACK Inc.; 1995:17–23.
27. Salmon TO, Thibos LN. Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations. J Opt Soc Am (A) 2002;19:657–69.
28. Applegate RA, Marsack JD, Thibos LN. Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity. Optom Vis Sci 2006;83:635–40.
29. Cheng X, Bradley A, Ravikumar S, Thibos LN. Visual impact of Zernike and Seidel forms of monochromatic aberrations. Optom Vis Sci 2010;87:300–12.
30. Applegate RA, Marsack JD, Ramos R, Sarver EJ. Interaction between aberrations to improve or reduce visual performance. J Cataract Refract Surg 2003;29:1487–95.
31. Karabatsas CH, Cook SD, Figueiredo FC, Diamond JP, Easty DL. Combined interrupted and continuous versus single continuous adjustable suturing in penetrating keratoplasty
: a prospective, randomized study of induced astigmatism during the first postoperative year. Ophthalmology 1998;105:1991–8.
Keywords:© 2011 American Academy of Optometry
point-source corneal topography; Placido-based corneal topography; keratoplasty; corneal aberration; quadrafoil aberration