AMERICAN
OF
OPHTHALMOLOGY®
NUMBER 4
APRIL, 1990
JOURNAL
VOLUME 109
A Computer Model for the Evaluation of the Effect of Corneal Topography on Optical Performance Jon J. Camp, B.S.E.E., Leo J. Maguire, M.D., Bruce M. Cameron, M.S., and Richard A. Robb, Ph.D.
We developed a method that models the effect of irregular corneal surface topography on corneal optical performance. A computer program mimics the function of an optical bench. The method generates a variety of objects (single point, standard Snellen letters, low contrast Snellen letters, arbitrarily complex objects) in object space. The lens is the corneal surface evaluated by a corneal topography analysis system. The objects are refracted by the cornea by using raytracing analysis to produce an image, which is displayed on a video monitor. Optically degraded images are generated by raytracing analysis of selected irregular corneal surfaces, such as those from patients with keratoconus and those from patients having undergone epikeratophakia for aphakia.
Some investigators believe that Snellen visual acuity testing is an insensitive measurement of the types of visual degradation observed in patients with irregular topography. Contrast sensitivity testing is a more sensitive method of evaluating optical performance, but the clinical relevance of abnormal contrast sensitivity test results is not clear to most ophthalmologists. To address the need to correlate corneal topography with corneal optical performance, we developed computer software that acts as an electronic optical bench. An object and object vergence are defined by the software. The lens is the corneal surface as described by a topography analysis system. An image is generated by ray tracing analysis of the object through the corneal surface.
CORNEAL TOPOGRAPHY studies show that good visual acuity as measured by Snellen tests is often found in patients who have surprising degrees of corneal irregularity.':" These patients may describe image degradation, but such complaints are difficult to quantitate.
Material and Methods
Accepted for publication Jan. 24, 1990. From the Departments of Physiology (Mr. Camp, Mr. Cameron, and Dr. Robb) and Ophthalmology (Dr. Maguire), Mayo Clinic and Foundation, Rochester, Minnesota. This study was supported in part by Research to Prevent Blindness, Inc., New York, New York, National Institutes of Health grant RR 02540, and the Mayo Foundation, Rochester, Minnesota. This study was presented at the 16th Cornea Research Conference, Massachusetts Eye and Ear Infirmary, Boston, Massachusetts, Sept. 23,1989. Reprint requests to Leo J. Maguire, M.D., Department of Ophthalmology, Mayo Foundation, 200 First St. S.W., Rochester, MN 55905.
©AMEtuCAN JOURNAL OF OPHTHALMOLOGY
109:379-386,
The objects are modeled to appear within an area 0.45 x 0.45 m located 6.0 m from the lens surface. The 6.0-m vergence was chosen because it approximates optical infinity. The 0.45 x 0.45-m field allows a 20/10 letter to be 5 x 5 pixels on the video monitor. The object can be a point source or a complex figure, such as a Snellen visual acuity chart, a chart of letters of variable contrast (Fig. 1), or any 512 x 512 pixel monochromatic scene. The refractive surface used in the ray tracing program is the cornea as represented by the Corneal Modeling System, a keratoscope-based topography analysis system." The Corneal Modeling System provides a power measurement and polar coordinates for each corneal surface point it measures (Fig. 2). APRIL,
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Fig, 1 (Camp and associates). Computer-generated objects. Left, Snellen letters. Right, Variable contrast letters. The images generated by ray tracing analysis of these objects by three corneas with varying degrees of irregularity are shown in Figure 6.
These measurements are found in the processed data file of the Corneal Modeling System analysis. This information is used in the ray tracing program, and we assume its accuracy. The Corneal Modeling System is known to provide accurate and reproducible readings when steel calibration spheres are measured.Vbut its accuracy and reproducibility in evaluating more complex surfaces is unknown. An image is always a degraded version of the original object. Optical engineers commonly display optical degradation by a point-spread function." This function shows the degree and location of blur caused by the refraction of a single point on the optical axis through the lens under investigation. The electronic optical bench calculates a point-spread function by performing ray tracing analysis through 2,560 corneal surface points (all measured points on the central ten keratoscope mires of the Corneal Modeling System). A simple raycasting technique based on lensmakers equations is used as follows:
ri
= rs -
no ' [rs . [(Os' so) - 1] + ro] [ [(z s " no) . [(D. ' so) - 1]) - (n.> so)
[Zs - no [(Or:i ,':'> - I]J
J.
where: r, = r coordinate of image point r, = r coordinate of surface point z, = z coordinate of surface point O. = diopter power at surface point no = index of refraction outside eye (1.00) r, = r coordinate of object point (0 for point-spread function calculation) So = object distance Orer = reference diopter power (mean of 2,560 corneal surface points) n, = index of refraction of the cornea (1.3375) The program calculates an in-focus image plane and magnification for each of the 2,560 corneal surface points through which the object point is refracted. The surface point and its corresponding in-focus image point are used to construct a ray, which intersects with a reference plane (that is, the plane in the image space of interest to the computer operator) (Fig. 3). Unless the operator directs otherwise, the program automatically displays the reference plane of best focus. In our method, the vergence of this plane is determined by calculating the mean power of the 2,560 corneal points through which the object point is refracted. The method is best understood by viewing the point-spread function produced when a single object point is refracted through the
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Computer Model for Evaluating Corneal Topography
Fig. 2 (Camp and associates). The Corneal Modeling System represents the processed keratoscopic data in polar coordinates. Three variables locate each corneal point in space. Theta (TH) shows its hemimeridian location. Its distance from the calculated center point is r Its sagittal location, Z, not shown, is determined by a proprietary algorithm. The raytracing program uses these data and the corneal power calculation of each point to make the point-spread function. l •
topography analysis representation of corneal surface power. The topographic maps of a normal cornea (Fig. 4) and a cornea with early keratoconus (Fig. 4) are used to demonstrate the ray tracing method. The three eyes have excellent visual acuity and minimal refractive error. A cursor marks the position of keratoscope ring 10 in each display in Figure 4. The point-spread functions derived by raytracing analysis of each of the corneal surfaces are shown in Figure 5. The data may be displayed on a linear or logarithmic scale. These figures show a linear scale. They are oriented in the same fashion as visual field displays. Point-spread functions may interest optical engineers, but most clinicians prefer to view image degradation of familiar objects such as Snellen letters. Our method generates these images by convolving the Snellen object with
~EFERENCE
- ~- - -=-_: -----=--:...------------ --- --- ---
---
::::===== :;:~ -
381
the point-spread function of the cornea under investigation. This technique is commonly used in the field of optical computing." Figure 6 shows the images obtained by refracting the 20/80 and 20/20 variable contrast Snellen targets shown in Figure 1 through the corneal surfaces shown in Figure 4. An image obtained by raytracing analysis of a patient from an earlier study" on epikeratophakia for aphakia is included as well. The raytracing computations were performed on a MASSCOMP 5700 vector accelerator at the Mayo Biotechnology Computer Resource. The computational speed of this hardware allows calculation of a point-spread function for 2,560 corneal surface points in 0.167 second. An arbitrary 512 x 512 pixel object can be processed in under three seconds. Computer workstations such as the Sun 3 require an order of magnitude greater processing time. Images are reviewed, displayed, and evaluated with the aid of ANALYZE, a comprehensive interactive image analysis system developed by the Mayo Biotechnology Computer Resource.lv" The availability of this preexisting code precluded the need to develop original software for image display.
Results A graphical representation of the pointspread function for three corneas shown is shown in Figure 5. A perfect lens system would focus all light on a single point in the image plane of best focus. The point-spread function of the normal cornea closely approximates such an output, but a small amount of signal spread is seen. The point-spread function of the cornea from the patient who underwent epikeratophakia shows a central peak but more central spread of signal than observed in the normal cornea. The point-spread function from the cornea with keratoconus shows a high-ampli-
PLANE
Fig. 3 (Camp and associates), Schematic representation of refraction through two hemimeridians of an irregular cornea. The reference plane is the plane shown by the raytracing analysis. Our method determines the point-spread function at the image plane of interest to the operator.
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Fig. 4 (Camp and associates). Color contour maps of two corneal surfaces with different amounts of corneal irregularity. Top, Map of a normal patient with no keratometric astigmatism and uncorrected visual acuity of 20/10. Bottom, Map of a patient with keratoconus. Best-corrected visual acuity is 20/20 with a - 2.50 sphere.
tude central peak and a low-amplitude asymmetric spread of signal. Figure 6 shows the images from refraction of the variable contrast 20/20 and 20/80 letters through the two corneas shown in Figure 4 and the cornea of a patient who underwent epikeratophakia." The image from the normal cornea shows excellent resolution of the 20/80 and 20/20 letters at all contrast levels. The output for the eye that underwent epikeratophakia for aphakia shows more image degradation, but
the 20/80 letter is well visualized to 6.25% contrast. The 100% and 50% contrast 20/20 letters are degraded but recognizable. The lower contrast 20/20 letters are not discernable. The images from the patient with keratoconus have sharper borders than the images from the patient who underwent epikeratophakia, but they show a relative reduction in contrast. The higher contrast 20/80 letter shows an obvious ghost image that is not as apparent at lower contrast levels.
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Fig. 5 (Camp and associates). Point-spread function display for three corneal surfaces. Top left, Patient with the normal corneal surface in Figure 4 shows most of the signal centered around signal peak. Top right, Patient who underwent epikeratophakia for aphakia. More spread of the central signal peak is observed. Bottom left, Patient with early keratoconus shown in Figure 4. A high-amplitude central peak with a low-amplitude asymmetric peripheral spread of signal is observed.
Discussion Our electronic optical bench method is an initial attempt to bridge a gap that exists between technologies that describe irregular corneal surfaces (such as corneal topography analysis) and measurement methods that describe what the patient sees after the image encountered at the neurosensory retina is processed through to the occipital cortex (such as standard visual acuity testing and contrast sensitivity testing). We believe such a system is needed because methods currently used to evaluate
keratorefractive procedures measure corneal optical performance indirectly or not at all. This status quo is not acceptable given the growth in the field of refractive corneal surgery. Standard visual acuity measurements are adequate for evaluating corneal optical performance in comparative studies only when the physical optical system is assumed to be similar between groups. When the optical system degrades in an unknown fashion, as after keratorefractive corneal surgery, visual acuity charts with 100% contrast target letters are not as sensitive a measure of optical performance as they are when used for refraction of the normal
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Fig. 6 (Camp and associates). Images generated by ray tracing analysis of three corneas. Top left, Normal cornea. Minimal degradation of image is seen in both the 20/80 and 20/20 letters at all contrast levels. Top right, Image from the patient who underwent epikeratophakia for aphakia. The 20/80 E is discernible at all contrast intervals but shows degradation and indistinct borders when compared with the normal. The 20/20 letter is discernible but degraded at the 100%,50%, and 25% contrast level. No E is identifiable at the lower contrast levels. Bottom left, Image from patient with keratoconus. The 20/80 letters are resolved to 6.25% contrast, but an obvious ghost image is seen, which is most obvious at the 100% level. The 20/20 E is recognizable to 25% contrast. Note the well-defined borders of the letters and the relative loss of contrast compared to the output from the patient who underwent epikeratophakia.
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eye." Such charts detect only gross abnormalities of visual performance. The insensitivity of high-contrast visual acuity charts is well documented in many contrast sensitivity studies.P'" Topography analysis studies document that relatively severe degrees of corneal irregularity are compatible with visual acuities of 20/20 to 20/40. 3,7-10 Vision scientists know that contrast sensitivity testing is a more sensitive method of testing optical performance than standard visual acuity testing when studying patients who have irregular optical surfaces. Unfortunately, problems limit the implementation of contrast sensitivity testing in clinical practice. Contrast sensitivity cannot gauge the optical performance of the cornea in isolation, because results are affected by confounding variables in the visual system, such as spectacle blur,24,25 lenticular opacity." retinal disease,27-29 and optic nerve abnormalities, such as glaucoma and optic neuritis.P Controversy exists about the most appropriate method of testing. The reproducibility of some of these tests has been questioned." Finally, and most importantly, the clinical ophthalmologist has difficulty interpreting the clinical significance of contrast sensitivity results and extrapolating abnormal findings to a patient's visual performance outside the laboratory. Problems exist with the use of corneal topography analysis to evaluate surgical success after refractive surgery. The recently introduced topography analysis systems'v':" have improved our understanding of the patterns of power distribution found in patients after refractive corneal surgery.2,4-6,8-10 Unfortunately, the results of these topographic studies are descriptive and not easily adapted to statistical analysis. Inspection of the power maps provides no information on the optical performance of the cornea. Our electronic optical bench method allows an approximation of corneal optical performance to be made by using the information provided by corneal topography analysis as a component of a larger software program. We emphasize that the method does not allow us to see through the eyes of the patient, which would require that we know how the visual system processes the degraded image. Rather, our method isolates and measures the optical performance of the corneal surface as directly as present technology permits. By modeling refraction of familiar objects used in clinical practice, we believe this method
385
shows the clinician that fairly severe degrees of image degradation from irregular surface topography can exist and still allow a small 100% contrast visual acuity test object to be visualized. The Snellen figures of the three corneas show that not all 20/20 visual acuity is the same. We believe this concept must be well understood by the public, eye care policy analysts, and eye care providers given the current and impending flood of refractive corneal surgical techniques and the recently popularized concept of pseudophakic correction of presbyopia. Possibilities for the future include userfriendly interactive software that can alter object vergence and add spectacle correction and intraocular lens design to the ray tracing analysis. Other improvements include analysis of a larger portion of the corneal surface area, analysis of surface points relative to the pupil position and pupil size." and programs to evaluate glare. As these developments occur and improvements are made in topography analysis technology, electronic optical bench software should allow an increasingly accurate understanding of the contribution of corneal surface topography to visual performance. If future testing finds that the output of the electronic optical bench correlates with conventional measures of visual performance, systems similar to the one described herein may provide a method of performing statistical analysis on the optical quality of the corneal surface after refractive surgical procedures. Our understanding of unusual visual phenomena often noted by patients after refractive corneal procedures may improve. 5,6,8,10,33 In an age when radial keratotomy, epikeratophakia, intralamellar implants, keratomileusis, excimer laser corneal ablation, and multifocal intraocular lens implants are under investigation, we believe that ray tracing systems are needed to allow differentiation between irregular corneas with good optical performance and those with bad optical performance.
References 1. Maguire, L. j.. Singer, D. E., and Klyce, S. D.: Graphic presentation of computer analyzed keratoscope photographs. Arch. Ophthalmol. 105:223, 1987. 2. Maguire, L. r.. Klyce, S. D., Singer, D. E., McDonald, M. B., and Kaufman, H. E.: Corneal to-
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pography in myopic patients undergoing epikeratophakia. Am. J. Ophthalmol. 103:404, 1987. 3. Maguire, L. J., and Bourne, W. M.: Corneal topography of transverse keratotomies for astigmatism after penetrating keratoplasty. Am. J. Ophthalmol. 107:323,1989. 4. Rowsey, J. J., Balyeat, H. D., Monlux, R., Holladay, J., Waring, G. 0., III, Lynn, M. J., and The Perk Study Group: Prospective evaluation of radial keratotomy. Photokeratoscope corneal topography. Ophthalmology 95:322, 1988. 5. McDonnell, P. J., McClusky, D. J., and Garbus, J. J.: Corneal topography and fluctuating visual acuity after radial keratotomy. Ophthalmology 96:665, 1989. 6. McDonnell, P. J., Garbus, J., and Lopez, P. F.: Topographic analysis and visual acuity after radial keratotomy. Am. J. Ophthalmol. 106:692, 1988. 7. Maguire, L. J., and Bourne, W. M.: Corneal topography of early keratoconus. Am. J. Ophthalmol. 108:107,1989. 8. - - : A multifocal lens effect as a complication of radial keratotomy. Refract. Corneal Surg. 5:394,1989. 9. Maguire, L. J.: Corneal topography of patients with excellent Snellen visual acuity after epikeratophakia for aphakia. Am. J. Ophthalmol. 109:162, 1990. 10. Wyzinski, P., and O'Dell, L.: Subjective and objective findings after radial keratotomy. Ophthalmology 96:1608,1989. 11. Gormley, D. J., Gersten, M., Koplin, R. S., and Lubkin, V.: Corneal modeling. Cornea 7:30,1988. 12. Hannush, S. B., Crawford, S. L., Waring, G. 0., Ill, Gemmill, M. c.. Lynn, M. J., and Nizam, A.: Accuracy and precision of keratome try, photokeratoscopy, and corneal modeling on calibrated steel balls. Arch. Ophthalmol. 107:1235, 1989. 13. Feitelson. D. G.: Optical Computing. A Survey for Computer Scientists, ed. 1. Cambridge, Massachusetts, MIT Press, 1988, pp. 83-84. 14. Robb, R. A.: Multidimensional biomedical image display and analysis in the Biotechnology Computer Resource at the Mayo Clinic. Machine Vision and Applications 1:75, 1988. 15. Robb, R. A., and Barillot, c. Interactive display and analysis of 3-D medical images. IEEE Trans. Med. Imaging 8:217,1989. 16. Ginsburg, A. P.: Spatial filtering and vision. Implications for normal and abnormal vision. In Proenza, L. M., Enoch, J. M., and [arnpolsky, A. (eds.): Clinical Applications of Visual Psychophysics. Cambridge, Cambridge University Press, 1981, pp. 70-106. 17. Carney, L. G.: Visual loss in keratoconus.
April, 1990
Arch. Ophthalmol. 100:1282, 1982. 18. Zadnik, K., Mannis, M. J., and Johnson, C. A.: An analysis of contrast sensitivity in identical twins with keratoconus. Cornea 3:99, 1984. 19. Mannis, M. J., Zadnik, K., and Johnson, C. A.: The effect of penetrating keratoplasty on contrast sensitivity in keratoconus. Arch. Ophthalmol. 102:1513,1984. 20. Lin, S., Reiter, K., Dreher, A. W., Frucht-Pery, J., and Feldman, S. T.: The effect of pterygia on contrast sensitivity and glare disability. Am. J. Ophthalmol. 107:407, 1989. 21. Krasnov, M. M., Avetisov, S. E., Makashova, N. V., and Mamikonian, V. R.: The effect of radial keratotomy on contrast sensitivity. Am. J. Ophthalmol. 105:651, 1988. 22. Mannis, M. J., Zadnik, K., Johnson, C. A., and Adams, c.: Contrast sensitivity after epikeratophakia. Cornea 7:280, 1988. 23. - - : Contrast sensitivity after penetrating keratoplasty. Arch. Ophthalmol. 105:1220, 1987. 24. Marmor, M. F., and Gawande, A.: Effect of visual blur on contrast sensitivity. Clinical implications. Ophthalmology 95:139,1988. 25. Campbell, F. W., and Green, D. G.: Optical and retinal factors affecting visual resolution. J. Physiol. 181:576, 1965. 26. Hess, R., and Woo, G.: Vision through cataracts. Invest. Ophthalmol. Vis. Sci. 17:428, 1977. 27. Skalka, H. W.: Comparison of Snellen acuity, VER acuity and Arden grating scores in macular and optic nerve diseases. Br. J. Ophthalmol. 64:24, 1980. 28. Marmor, M. F.: Contrast sensitivity versus visual acuity in retinal disease. Br. J. Ophthalmol. 70:553, 1986. 29. Wolkstein, M., Atkin, A., and Bodis-Wollner, I.: Contrast sensitivity in retinal disease. Ophthalmology 87:1140,1980. 30. Rubin, G. S.: Reliability and sensitivity of clinical contrast sensitivity tests. Clin. Vision Sci. 2:169, 1988. 31. Klyce, S. D.: Computer-assisted corneal topography. High resolution graphic presentation and analysis ofkeratoscopy. Invest. Ophthalmol. Vis. Sci. 12:1426,1984. 32. Uozato, H., and Guyton, D. L.: Centering corneal surgical procedures. Am. J. Ophthalmol. 103(1 ):264, 1987. 33. Santos, V. R., Waring, G. 0., III, Lynn, M. J., Holladay, J. T., Sperduto, R. D., and The Perk Study Group: Relationship between refractive error and visual acuity in the prospective evaluation of radial keratotomy (PERK) study. Arch. Ophthalmol. 105:86, 1987.
OF
OPHTHALMOLOGY®
NUMBER 4
APRIL, 1990
JOURNAL
VOLUME 109
A Computer Model for the Evaluation of the Effect of Corneal Topography on Optical Performance Jon J. Camp, B.S.E.E., Leo J. Maguire, M.D., Bruce M. Cameron, M.S., and Richard A. Robb, Ph.D.
We developed a method that models the effect of irregular corneal surface topography on corneal optical performance. A computer program mimics the function of an optical bench. The method generates a variety of objects (single point, standard Snellen letters, low contrast Snellen letters, arbitrarily complex objects) in object space. The lens is the corneal surface evaluated by a corneal topography analysis system. The objects are refracted by the cornea by using raytracing analysis to produce an image, which is displayed on a video monitor. Optically degraded images are generated by raytracing analysis of selected irregular corneal surfaces, such as those from patients with keratoconus and those from patients having undergone epikeratophakia for aphakia.
Some investigators believe that Snellen visual acuity testing is an insensitive measurement of the types of visual degradation observed in patients with irregular topography. Contrast sensitivity testing is a more sensitive method of evaluating optical performance, but the clinical relevance of abnormal contrast sensitivity test results is not clear to most ophthalmologists. To address the need to correlate corneal topography with corneal optical performance, we developed computer software that acts as an electronic optical bench. An object and object vergence are defined by the software. The lens is the corneal surface as described by a topography analysis system. An image is generated by ray tracing analysis of the object through the corneal surface.
CORNEAL TOPOGRAPHY studies show that good visual acuity as measured by Snellen tests is often found in patients who have surprising degrees of corneal irregularity.':" These patients may describe image degradation, but such complaints are difficult to quantitate.
Material and Methods
Accepted for publication Jan. 24, 1990. From the Departments of Physiology (Mr. Camp, Mr. Cameron, and Dr. Robb) and Ophthalmology (Dr. Maguire), Mayo Clinic and Foundation, Rochester, Minnesota. This study was supported in part by Research to Prevent Blindness, Inc., New York, New York, National Institutes of Health grant RR 02540, and the Mayo Foundation, Rochester, Minnesota. This study was presented at the 16th Cornea Research Conference, Massachusetts Eye and Ear Infirmary, Boston, Massachusetts, Sept. 23,1989. Reprint requests to Leo J. Maguire, M.D., Department of Ophthalmology, Mayo Foundation, 200 First St. S.W., Rochester, MN 55905.
©AMEtuCAN JOURNAL OF OPHTHALMOLOGY
109:379-386,
The objects are modeled to appear within an area 0.45 x 0.45 m located 6.0 m from the lens surface. The 6.0-m vergence was chosen because it approximates optical infinity. The 0.45 x 0.45-m field allows a 20/10 letter to be 5 x 5 pixels on the video monitor. The object can be a point source or a complex figure, such as a Snellen visual acuity chart, a chart of letters of variable contrast (Fig. 1), or any 512 x 512 pixel monochromatic scene. The refractive surface used in the ray tracing program is the cornea as represented by the Corneal Modeling System, a keratoscope-based topography analysis system." The Corneal Modeling System provides a power measurement and polar coordinates for each corneal surface point it measures (Fig. 2). APRIL,
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Fig, 1 (Camp and associates). Computer-generated objects. Left, Snellen letters. Right, Variable contrast letters. The images generated by ray tracing analysis of these objects by three corneas with varying degrees of irregularity are shown in Figure 6.
These measurements are found in the processed data file of the Corneal Modeling System analysis. This information is used in the ray tracing program, and we assume its accuracy. The Corneal Modeling System is known to provide accurate and reproducible readings when steel calibration spheres are measured.Vbut its accuracy and reproducibility in evaluating more complex surfaces is unknown. An image is always a degraded version of the original object. Optical engineers commonly display optical degradation by a point-spread function." This function shows the degree and location of blur caused by the refraction of a single point on the optical axis through the lens under investigation. The electronic optical bench calculates a point-spread function by performing ray tracing analysis through 2,560 corneal surface points (all measured points on the central ten keratoscope mires of the Corneal Modeling System). A simple raycasting technique based on lensmakers equations is used as follows:
ri
= rs -
no ' [rs . [(Os' so) - 1] + ro] [ [(z s " no) . [(D. ' so) - 1]) - (n.> so)
[Zs - no [(Or:i ,':'> - I]J
J.
where: r, = r coordinate of image point r, = r coordinate of surface point z, = z coordinate of surface point O. = diopter power at surface point no = index of refraction outside eye (1.00) r, = r coordinate of object point (0 for point-spread function calculation) So = object distance Orer = reference diopter power (mean of 2,560 corneal surface points) n, = index of refraction of the cornea (1.3375) The program calculates an in-focus image plane and magnification for each of the 2,560 corneal surface points through which the object point is refracted. The surface point and its corresponding in-focus image point are used to construct a ray, which intersects with a reference plane (that is, the plane in the image space of interest to the computer operator) (Fig. 3). Unless the operator directs otherwise, the program automatically displays the reference plane of best focus. In our method, the vergence of this plane is determined by calculating the mean power of the 2,560 corneal points through which the object point is refracted. The method is best understood by viewing the point-spread function produced when a single object point is refracted through the
Vol. 109, No.4
Computer Model for Evaluating Corneal Topography
Fig. 2 (Camp and associates). The Corneal Modeling System represents the processed keratoscopic data in polar coordinates. Three variables locate each corneal point in space. Theta (TH) shows its hemimeridian location. Its distance from the calculated center point is r Its sagittal location, Z, not shown, is determined by a proprietary algorithm. The raytracing program uses these data and the corneal power calculation of each point to make the point-spread function. l •
topography analysis representation of corneal surface power. The topographic maps of a normal cornea (Fig. 4) and a cornea with early keratoconus (Fig. 4) are used to demonstrate the ray tracing method. The three eyes have excellent visual acuity and minimal refractive error. A cursor marks the position of keratoscope ring 10 in each display in Figure 4. The point-spread functions derived by raytracing analysis of each of the corneal surfaces are shown in Figure 5. The data may be displayed on a linear or logarithmic scale. These figures show a linear scale. They are oriented in the same fashion as visual field displays. Point-spread functions may interest optical engineers, but most clinicians prefer to view image degradation of familiar objects such as Snellen letters. Our method generates these images by convolving the Snellen object with
~EFERENCE
- ~- - -=-_: -----=--:...------------ --- --- ---
---
::::===== :;:~ -
381
the point-spread function of the cornea under investigation. This technique is commonly used in the field of optical computing." Figure 6 shows the images obtained by refracting the 20/80 and 20/20 variable contrast Snellen targets shown in Figure 1 through the corneal surfaces shown in Figure 4. An image obtained by raytracing analysis of a patient from an earlier study" on epikeratophakia for aphakia is included as well. The raytracing computations were performed on a MASSCOMP 5700 vector accelerator at the Mayo Biotechnology Computer Resource. The computational speed of this hardware allows calculation of a point-spread function for 2,560 corneal surface points in 0.167 second. An arbitrary 512 x 512 pixel object can be processed in under three seconds. Computer workstations such as the Sun 3 require an order of magnitude greater processing time. Images are reviewed, displayed, and evaluated with the aid of ANALYZE, a comprehensive interactive image analysis system developed by the Mayo Biotechnology Computer Resource.lv" The availability of this preexisting code precluded the need to develop original software for image display.
Results A graphical representation of the pointspread function for three corneas shown is shown in Figure 5. A perfect lens system would focus all light on a single point in the image plane of best focus. The point-spread function of the normal cornea closely approximates such an output, but a small amount of signal spread is seen. The point-spread function of the cornea from the patient who underwent epikeratophakia shows a central peak but more central spread of signal than observed in the normal cornea. The point-spread function from the cornea with keratoconus shows a high-ampli-
PLANE
Fig. 3 (Camp and associates), Schematic representation of refraction through two hemimeridians of an irregular cornea. The reference plane is the plane shown by the raytracing analysis. Our method determines the point-spread function at the image plane of interest to the operator.
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Fig. 4 (Camp and associates). Color contour maps of two corneal surfaces with different amounts of corneal irregularity. Top, Map of a normal patient with no keratometric astigmatism and uncorrected visual acuity of 20/10. Bottom, Map of a patient with keratoconus. Best-corrected visual acuity is 20/20 with a - 2.50 sphere.
tude central peak and a low-amplitude asymmetric spread of signal. Figure 6 shows the images from refraction of the variable contrast 20/20 and 20/80 letters through the two corneas shown in Figure 4 and the cornea of a patient who underwent epikeratophakia." The image from the normal cornea shows excellent resolution of the 20/80 and 20/20 letters at all contrast levels. The output for the eye that underwent epikeratophakia for aphakia shows more image degradation, but
the 20/80 letter is well visualized to 6.25% contrast. The 100% and 50% contrast 20/20 letters are degraded but recognizable. The lower contrast 20/20 letters are not discernable. The images from the patient with keratoconus have sharper borders than the images from the patient who underwent epikeratophakia, but they show a relative reduction in contrast. The higher contrast 20/80 letter shows an obvious ghost image that is not as apparent at lower contrast levels.
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Fig. 5 (Camp and associates). Point-spread function display for three corneal surfaces. Top left, Patient with the normal corneal surface in Figure 4 shows most of the signal centered around signal peak. Top right, Patient who underwent epikeratophakia for aphakia. More spread of the central signal peak is observed. Bottom left, Patient with early keratoconus shown in Figure 4. A high-amplitude central peak with a low-amplitude asymmetric peripheral spread of signal is observed.
Discussion Our electronic optical bench method is an initial attempt to bridge a gap that exists between technologies that describe irregular corneal surfaces (such as corneal topography analysis) and measurement methods that describe what the patient sees after the image encountered at the neurosensory retina is processed through to the occipital cortex (such as standard visual acuity testing and contrast sensitivity testing). We believe such a system is needed because methods currently used to evaluate
keratorefractive procedures measure corneal optical performance indirectly or not at all. This status quo is not acceptable given the growth in the field of refractive corneal surgery. Standard visual acuity measurements are adequate for evaluating corneal optical performance in comparative studies only when the physical optical system is assumed to be similar between groups. When the optical system degrades in an unknown fashion, as after keratorefractive corneal surgery, visual acuity charts with 100% contrast target letters are not as sensitive a measure of optical performance as they are when used for refraction of the normal
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Fig. 6 (Camp and associates). Images generated by ray tracing analysis of three corneas. Top left, Normal cornea. Minimal degradation of image is seen in both the 20/80 and 20/20 letters at all contrast levels. Top right, Image from the patient who underwent epikeratophakia for aphakia. The 20/80 E is discernible at all contrast intervals but shows degradation and indistinct borders when compared with the normal. The 20/20 letter is discernible but degraded at the 100%,50%, and 25% contrast level. No E is identifiable at the lower contrast levels. Bottom left, Image from patient with keratoconus. The 20/80 letters are resolved to 6.25% contrast, but an obvious ghost image is seen, which is most obvious at the 100% level. The 20/20 E is recognizable to 25% contrast. Note the well-defined borders of the letters and the relative loss of contrast compared to the output from the patient who underwent epikeratophakia.
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eye." Such charts detect only gross abnormalities of visual performance. The insensitivity of high-contrast visual acuity charts is well documented in many contrast sensitivity studies.P'" Topography analysis studies document that relatively severe degrees of corneal irregularity are compatible with visual acuities of 20/20 to 20/40. 3,7-10 Vision scientists know that contrast sensitivity testing is a more sensitive method of testing optical performance than standard visual acuity testing when studying patients who have irregular optical surfaces. Unfortunately, problems limit the implementation of contrast sensitivity testing in clinical practice. Contrast sensitivity cannot gauge the optical performance of the cornea in isolation, because results are affected by confounding variables in the visual system, such as spectacle blur,24,25 lenticular opacity." retinal disease,27-29 and optic nerve abnormalities, such as glaucoma and optic neuritis.P Controversy exists about the most appropriate method of testing. The reproducibility of some of these tests has been questioned." Finally, and most importantly, the clinical ophthalmologist has difficulty interpreting the clinical significance of contrast sensitivity results and extrapolating abnormal findings to a patient's visual performance outside the laboratory. Problems exist with the use of corneal topography analysis to evaluate surgical success after refractive surgery. The recently introduced topography analysis systems'v':" have improved our understanding of the patterns of power distribution found in patients after refractive corneal surgery.2,4-6,8-10 Unfortunately, the results of these topographic studies are descriptive and not easily adapted to statistical analysis. Inspection of the power maps provides no information on the optical performance of the cornea. Our electronic optical bench method allows an approximation of corneal optical performance to be made by using the information provided by corneal topography analysis as a component of a larger software program. We emphasize that the method does not allow us to see through the eyes of the patient, which would require that we know how the visual system processes the degraded image. Rather, our method isolates and measures the optical performance of the corneal surface as directly as present technology permits. By modeling refraction of familiar objects used in clinical practice, we believe this method
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shows the clinician that fairly severe degrees of image degradation from irregular surface topography can exist and still allow a small 100% contrast visual acuity test object to be visualized. The Snellen figures of the three corneas show that not all 20/20 visual acuity is the same. We believe this concept must be well understood by the public, eye care policy analysts, and eye care providers given the current and impending flood of refractive corneal surgical techniques and the recently popularized concept of pseudophakic correction of presbyopia. Possibilities for the future include userfriendly interactive software that can alter object vergence and add spectacle correction and intraocular lens design to the ray tracing analysis. Other improvements include analysis of a larger portion of the corneal surface area, analysis of surface points relative to the pupil position and pupil size." and programs to evaluate glare. As these developments occur and improvements are made in topography analysis technology, electronic optical bench software should allow an increasingly accurate understanding of the contribution of corneal surface topography to visual performance. If future testing finds that the output of the electronic optical bench correlates with conventional measures of visual performance, systems similar to the one described herein may provide a method of performing statistical analysis on the optical quality of the corneal surface after refractive surgical procedures. Our understanding of unusual visual phenomena often noted by patients after refractive corneal procedures may improve. 5,6,8,10,33 In an age when radial keratotomy, epikeratophakia, intralamellar implants, keratomileusis, excimer laser corneal ablation, and multifocal intraocular lens implants are under investigation, we believe that ray tracing systems are needed to allow differentiation between irregular corneas with good optical performance and those with bad optical performance.
References 1. Maguire, L. j.. Singer, D. E., and Klyce, S. D.: Graphic presentation of computer analyzed keratoscope photographs. Arch. Ophthalmol. 105:223, 1987. 2. Maguire, L. r.. Klyce, S. D., Singer, D. E., McDonald, M. B., and Kaufman, H. E.: Corneal to-
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pography in myopic patients undergoing epikeratophakia. Am. J. Ophthalmol. 103:404, 1987. 3. Maguire, L. J., and Bourne, W. M.: Corneal topography of transverse keratotomies for astigmatism after penetrating keratoplasty. Am. J. Ophthalmol. 107:323,1989. 4. Rowsey, J. J., Balyeat, H. D., Monlux, R., Holladay, J., Waring, G. 0., III, Lynn, M. J., and The Perk Study Group: Prospective evaluation of radial keratotomy. Photokeratoscope corneal topography. Ophthalmology 95:322, 1988. 5. McDonnell, P. J., McClusky, D. J., and Garbus, J. J.: Corneal topography and fluctuating visual acuity after radial keratotomy. Ophthalmology 96:665, 1989. 6. McDonnell, P. J., Garbus, J., and Lopez, P. F.: Topographic analysis and visual acuity after radial keratotomy. Am. J. Ophthalmol. 106:692, 1988. 7. Maguire, L. J., and Bourne, W. M.: Corneal topography of early keratoconus. Am. J. Ophthalmol. 108:107,1989. 8. - - : A multifocal lens effect as a complication of radial keratotomy. Refract. Corneal Surg. 5:394,1989. 9. Maguire, L. J.: Corneal topography of patients with excellent Snellen visual acuity after epikeratophakia for aphakia. Am. J. Ophthalmol. 109:162, 1990. 10. Wyzinski, P., and O'Dell, L.: Subjective and objective findings after radial keratotomy. Ophthalmology 96:1608,1989. 11. Gormley, D. J., Gersten, M., Koplin, R. S., and Lubkin, V.: Corneal modeling. Cornea 7:30,1988. 12. Hannush, S. B., Crawford, S. L., Waring, G. 0., Ill, Gemmill, M. c.. Lynn, M. J., and Nizam, A.: Accuracy and precision of keratome try, photokeratoscopy, and corneal modeling on calibrated steel balls. Arch. Ophthalmol. 107:1235, 1989. 13. Feitelson. D. G.: Optical Computing. A Survey for Computer Scientists, ed. 1. Cambridge, Massachusetts, MIT Press, 1988, pp. 83-84. 14. Robb, R. A.: Multidimensional biomedical image display and analysis in the Biotechnology Computer Resource at the Mayo Clinic. Machine Vision and Applications 1:75, 1988. 15. Robb, R. A., and Barillot, c. Interactive display and analysis of 3-D medical images. IEEE Trans. Med. Imaging 8:217,1989. 16. Ginsburg, A. P.: Spatial filtering and vision. Implications for normal and abnormal vision. In Proenza, L. M., Enoch, J. M., and [arnpolsky, A. (eds.): Clinical Applications of Visual Psychophysics. Cambridge, Cambridge University Press, 1981, pp. 70-106. 17. Carney, L. G.: Visual loss in keratoconus.
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