Automated keratometry at low cost

© Digital Vision & Digital Stock 1996 An Automatic Optical System that Uses Slit-Lamp Technology for Cornea Analysis Laboratório de Física Oftálmica - FMRP-USP 2 Departamento de Física e Matemática da FFCLRP-USP, São Paulo ture. The cornea behaves as a convex mirror and reflects about 10% of incident light (as do eyeglasses). We have developed a system attached to a slit lamp that uses the fixed target size principle (image of object used to calculate astigmatism). ciation of the change in the size of the reflected image of the target (or the change in size of the target) on the patient’s eye leads to information regarding the radius of curvature of the cornea [3]. Figure 1 schematically shows these two principles. As a fixed target is projected onto the eye [Fig. 1(a)], the image size changes according to the radius of curvature of the surface (cornea). For systems that use the Javal-Schiötz principle, the target should change size [Fig. 1(b)] in order to keep the image size fixed for surfaces (cornea) having different radii of curva- The Structure of the Cornea The anterior transparent part of the human eye is known as the cornea [4] (Fig. 2). It consists of three main layers: the epithelium, the stroma, and the endothelium. The epithelium is the external cover of the cornea. It works as a mechanical protection for the cornea, just like the skin, which protects all the other parts of the human body. The stroma is the cornea itself, corresponding to 95% of its total thickness. It consists of fiber tissue disposed in regular layers with low hydration and no blood vessels. These his article discusses an automatic opti- Tcal system that is attached to a slit lamp in order to provide automatic keratometry at low cost. The system consists of projecting a light ring as a target onto the patient’s cornea as well as analysis of the deformation of the target in order to obtain the radius of curvature and the axis of the associated astigmatism. The reflected image of the target is displayed on a PC monitor, while dedicated software performs the analysis of the image, which provides the corneal keratometry. Overview There are basically two types of keratometers available on the market: the automat i c and t he manual . The keratometers use either the Helmholtz principle (fixed size of the target) or the Javal-Schiötz principle (fixed size of the reflected image) [1, 2]. Geometrical assoSeptember/ October 2000 1 1 Liliane Ventura , André M. Vieira Messias , Sidney J.F. Sousa1 , Renato Coelho1,2 1 The Human Cornea IEEE ENGINEERING IN MEDICINE AND BIOLOGY 0 7 3 9 -5 1 7 5 / 0 0 / $ 1 0 .0 0 © 2 0 0 0 IEEE 97 emmetropic eye); the internal radius of curvature varies from 6.2-6.8 mm. Hence, the cornea is equivalent to a negative lens. However it is very thin, and for calculations relating to the central part of the cornea, this region can be considered as having parallel faces [6, 7]. The cornea is not perfectly spherical; actually it is ellipsoidal. Therefore, the vertical and horizontal axes have different lengths. Only the central part of the cornea, the so called central optical zone of approximately 4.0 mm (see Fig. 3), may be considered spherical. The light rays that strike the cornea refract mainly because of the difference of refractive indexes between the air and the corneal surface, rather than because of the cornea’s corresponding refractive powers (45 and 95 diopters). The small central portion of the cornea has a refractive power of 41-45 D and may be flattened to 37 D or curved to 60 D under unusual conditions. Our specially developed software analyzes the results, providing the radius of curvature of the corneal surface and the axis of the associated astigmatism. The Slit Lamp The slit lamp [1] is an ocular biomicroscope that has several functions for eye measurement and diagnosis. It has a peculiar slit-shaped illumination system and provides for visualization of all parts of the eye. There are basically two kinds of slit lamps [8]: those that uses a Galilean telescope as the magnifying system and the ones that do not (the slit lamp system allows observations with magnification up to 40X). Also, there are two kinds of illumination systems available: upper and lower illuminations, but this is not important for our purposes. We will focus on the magnifying system. Figure 4 shows the optical schematic of a typical slit lamp that has a Galilean telescope [8] as the magnifying system. In features are responsible for its high transparency. Finally, the endothelium covers the internal side of the cornea with a unique polygonal cells layer. Optical Properties of the Cornea The endothelium is particularly important for being the layer responsible for active preservation of corneal stroma dehydration and transparency. The cornea has a curved surface, with a refractive index of 1.376 and a thickness of 0.480 mm [5, 6]. The external radius of curvature is approximately 7.8 mm (7.00-8.00 mm for Target Cornea Cornea Target Image Image Target Target System Development In developing our system, we use a slit lamp with the Galilean telescope. A light ring, composed of approximately 15,000 carefully aligned optical fibers (see Fig. 5), is attached to the objective lens of the slit lamp. The light ring (a 50W lamp illuminates the fibers) is projected onto the cornea as the fixed-size measuring target with dimensions of: n inner diameter: φin = 54 mm n outer diameter: φou = 56 mm. It is important for the external diameter to be of high precision regarding the position (alignment) of the optical fibers, as this affects the precision of our results (the software description below provides more details about this topic). The fibers are all aligned parallel to the optical axis that passes through the center of the ring and the center of the patient’s eye. Figure 6(a) shows the setup of the system, and Figure 6(b) shows a picture of the optical system attached to the slit lamp. A commercial beam splitter is placed in the optical path of the parallel rays and diverts 40% of the reflected light (the light ring reflected by the patient’s cornea) to an optical system (two lenses, a prism, and an iris). The image is captured by a charge-coupled detector (CCD), the features of which are given in Table 1. The image is displayed on a PC monitor via a frame grabber (a real-time display feature is required). Our specially developed software analyzes the results, providing the radius of curvature of the corneal surface and the axis of the associated astigmatism. The remaining 60% of the reflected light is observed at the eyepiece, so the clinician may observe the image simultaneously with the monitor. Epithelium Cornea Cornea Image Image (a) Stroma (b) 1. Schematic of (a) the Helmholtz principle (fixed size of the target) or (b) the Javal-Schiötz principle (fixed size of the reflected image). 98 this section of the optical path, parallel rays travel through the system, which is a required feature for development of our system. Then it is possible to introduce a beam-splitter and then attach some extra optical components to the slit lamp. IEEE ENGINEERING IN MEDICINE AND BIOLOGY Endothelium 2. Representation of the layers of the human cornea. September/ October 2000 The clinician is able to determine how far the astigmatism in that corneal region is from the astigmatism as measured in the onto which the target is projected. Calculations to determine the cornea’s radius of curvature lead us to consider it as a spherical convex mirror. This is a well-established condition, known as the “keratometry principle” [9, 10]. Figure 9 illustrates the model to be used for calculation of the radius of curvature of the cornea. A target h is placed at distance d from form the cornea. The reflected target results in a virtual image y at distance s from the cornea. Distance d is much greater than the focal length of the corneal surface f. Considering that the light fibers from y R− s R− s ≅ , d >> R . = h R+ d d (1) For targets that are far away from the cornea ( d >> R), we have s ≅ R 2. Thus, we have: Zone Peripheral Zone Zone Mid Central standard region. The slit lamp is set for 40X magnification, where the focal depth displacement is minimal and does not significantly interfere with our results. Figure 7 shows the ring projected onto the patient’s cornea. An infrared filter is used to avoid patient discomfort (the CCD detector has appropriate sensitivity for detection of infrared wavelengths). A lens adapter was also constructed and attached to the slit lamp, after the beam-splitter and before the optical system. This adapter provides the analysis of two other regions of the cornea by simply placing, one at a time, two different lenses (+5.0 D and +2.25 D lenses from the retinoscopy system) and trying to focus the system only with the monitor (the eyepieces will be out of focus). As the system moves toward or away from the patient as it tries to focus, the projected ring is larger or smaller than the standard one (with no lens in the adapter), respectively. Hence, when the system is in focus on the monitor, a frame of the projected ring is captured and analyzed by our software. Figure 8 shows a picture of the adapter. As the image is captured, our software determines the radius of curvature of the cornea, as described below. the target reach the cornea at small angles relative to the optical axis, we consider the radius of curvature of the cornea R to be twice the focal length of the cornea. The geometric relation between the size of the reflected image of the target from the corneal surface and its radius of curvature is given as follows: Optical Zones and Pupil Dilation 3. Schematic of the optical zones of the cornea. Galilean Telescope Objective Lens Patient’s Eye Eyepiece Biomicroscope Softw are Development Illumination System Determining the Radius of Curvature of the Cornea The cornea can be considered to have a spherical shape in the central optical zone, and it behaves there as a convex mirror, September/ October 2000 4. Optical schematic of a typical slit lamp that has a Galilean telescope as the magnifying system. IEEE ENGINEERING IN MEDICINE AND BIOLOGY 99 R= 2d y. h (2) The radius of curvature given in Eq. (2) is linearly proportional to the image size (d, e, h are fixed parameters). Usually, the results presented on a conventional keratometer are the inverse of the radius of curvature of the cornea, known as the refraction power F as expressed in diopters (D): n −1 F= c R (3) where n c is the refractive index of the cornea. Considering triangles AQP and OPF, OF ≅ Ox + xF and that for a spherical mirror, 2 f = R, we have: R= 2 dh 2 + 2 yh d 2 + h 2 − y 2 (h 2 − y 2 ) (4) which is a well-known expression for building a keratometer. Calibrating the System In order to calibrate the system, we use several high-precision-diameter steel spheres. We tested 20 spheres, varying from 5 to 20 mm D, for each magnification of the slit lamp (6X, 10X, 16X, 25X, 40X). Each sphere was tested ten times for each magnification, and an average value of the image size as a function of the radius of curvature of the sphere was obtained. In this manner, a conversion factor for the number of pixels to millimeters was obtained. especially useful for communities that are Basic Routines of the Software The software basically executes the following routine: 1. As the image is captured, the ring is fully filled with white pixels to become a circle, so that just the outer ring is analyzed. The outer ring is used because it is very precise with regard to the alignment of the optical fibers, as described above. 2. The border of the circle is determined. 3. The center of mass of the circle is determined. 4. The longest and the shortest distances between two points of the circle that also includes the center of mass of the circle are determined. 5. Equation (4) is used to determine the curvature radii of the cornea for the two distances obtained. 6. The conversion factor of pixels to millimeters is used to display the largest and the shortest curvature radii of the cornea. Target CCD Camera Patient’s Eye Slit Lamp Light Source 5. Schematic of the developed system. Table 1. CCD Features CCD Sensitivity 3.0 lux Detection Area 6.4 (H) x 4.8 (V) mm Signal/Noise 40 dB Lines 430 TV lines 100 This system is IEEE ENGINEERING IN MEDICINE AND BIOLOGY not able to afford expensive keratometers. M anipulating The System The Optical System The system is easy to operate. The slit lamp magnification is set to 40 (imprecision in the results, due to focal depth uncertainty, is significant for other magnifications) and the ring is projected onto the patient’s cornea. The real-time image is available as the “camera sign” button is selected and the image is captured as the “stop sign” button is selected (refer to Fig. 10). For the standard measurement, the clinician chooses the “sem lente” option, which means that no lens is required in the optical system. Then the clinician focuses the ring on the patient’s cornea, captures a frame of the image, and selects the option to determine the radii of curvature of the surface (“calcula” button should be activated). For measurements on other regions of the cornea, lenses from the retinoscopy system corresponding to the region of interest are inserted into the optical system, and the corresponding option should be selected (“lente –5 D” or “lente –2.25 D”). The results for the three analyzed regions are displayed on a screen that is printed later (see Fig. 11). As the measurements on the other two regions, besides the standard region, are not available with commercial systems, a screen for the analysis of the results is provided as a reference for the clinician. A sin2 function is plotted as reference (the astigmatism of the cornea is proportional to a sin2 function [11]) within the signature that describes the radii of curSeptember/ October 2000 vature of the surface for the 360º. Thus, the clinician is able to determine how far the astigmatism in that corneal region is from the astigmatism as measured in the standard region. Figure 12 illustrates the graphical interface. Results Measurements were made on 40 volunteer patients. All patients were examined with three systems of measurement: our system (OS), a manual commercial keratometer (MC), and an automatic commercial keratometer (AC). The correlation coefficient of OS and the MC was 0.996, and the correlation coefficient of OS and the AC was 0.983, with respect to the radius of curvature of the cornea. The correlation coefficient of OS and the MC was 0.949, and the correlation coefficient of OS and the AC was 0.989, with respect to the axis of astigmatism. The inherent (nominal) precision of our system is 0.005 mm for the radius of curvature and 2º for the axis of astigmatism; i.e., these values refer to the precision of the equipment itself, as the focal depth precision of the slit lamp, calculations, tolerance, etc. These values are quite suitable for the precision expected for these measurements in clinical practice. Conclusions Commercial keratometers may be classified into two groups: manual and automatic. Manual instruments require special care by the user to project the target onto the patient’s eye as well as some patience by the user in trying to find the axis of astigmatism. The measurements become even more difficult if the patient (a) 7. The light ring projected onto the patient’s cornea. (b) 6. (a) Schematic of the system setup; (b) picture of the optical system attached to the slit lamp. September/ October 2000 IEEE ENGINEERING IN MEDICINE AND BIOLOGY 8. Picture of the lens adapter for the projection of the two extra light rings. 101 Cornea Q P h A y x O F R C d f s 9. Illustration of the model to be used for the calculation of the radius of curvature of the cornea. 10. The real-time window of the developed software. The real-time image is available as the “camera sign” button is selected, and the image is captured as the “stop sign” button is selected. has irregular astigmatism (irregular astigmatism cannot be determined with the manual keratometer). Automatic systems are easy to manipulate and are usually attached to autorefractors. However, they are not as precise as the manual units, since their focal depth interferes with measurement of the radius of curvature. (The main purpose of automatic systems is to measure refractive errors, and the keratometry measurements are just supplementary; however, the axis is precisely determined.) With our system, we have made an effort to combine the precision provided by the manual keratometer in the measurement of the radii of curvature, and the precision provided by the automatic keratometer in measurement of the axis, along with the ease in manipulating the system for these measurements. Hence, we developed an automatic system, attached to a slit lamp, which is extremely easy to manipulate. The developed 11. Screen showing the results for the three analyzed regions of the cornea. 102 IEEE ENGINEERING IN MEDICINE AND BIOLOGY software provided very good precision in our system. We have compared our system to both automatic and manual commercial systems. We have also compared the two types of commercial systems to obtain an idea of their relative accuracies. The manual commercial and the automatic commercial systems that we investigated have a 1.951% discrepancy for the measured radius of curvature and 8.9667% between their associated axes. The correlation coefficient of OS and the MC is 0.996, and the correlation coefficient of OS and the AC is 0.983, with respect to the radius of curvature of the cornea; the correlation coefficient of OS and the MC is 0.949, and the correlation coefficient of OS and the AC is 0.989, with respect to the axis of astigmatism. Based on these findings, our system is in good agreement with the discrepancies found in the commercial systems. Our system is quite easy to manipulate and has a user-friendly interface. It is of low cost, since any monochromatic CCD detector with a minimum resolution of 430 TV lines and a minimum sensitivity of 3 lux may be used. Any commercially available frame grabber may also be used, and they are also of low cost. This system is especially useful for communities that are not able to afford expensive keratometers. Acknow ledgments The authors would like to thank Fundação de Apoio à Pesquisa do Estado de São Paulo (FAPESP) for the financial support of this research and of some of our researchers as well as CNPq and CAPES, which have also supported our researchers. Liliane Ventura obtained her bachelor’s degree in physics in 1987. In 1990 she obtained her master’s degree in physics (solidstate physics). In 1995 she obtained her Ph.D. degree in applied physics in ophthalmology. In 1996, while doing post-doctoral work, Dr. Ventura set up an Ophthalmic Physics Lab (Laboratório de Física Oftálmica - FMRP) inside a public hospital, which has six main research projects running and several students under her responsibility. Her main field of interest is ophthalmic physics, especially September/ October 2000 Renato Coelho is a physicist and obtained his master’s degree at Laboratório de Física Oftálmica - FMRP in Ophthalmic Physics in 1998. His field of interest is developing systems for diagnostics in Table 2. Average Values of Corneal Radii of Curvature of Ten Volunteer Patients Measured in Three Different Systems for Comparison Major Radius (mm) Minor Radius (mm) Axis (Degrees) MC AC OS MC AC OS MC AC OS 8.2396 8.208 8.2124 8.0049 7.961 7.9901 144.5 152.6 153.0 MC = manual commercial system. AC = automatic commercial system. OS = our system. The major and minor radii refer to the radii of curvature of the main axis of the corneal astigmatism. The axis is the that of the associated astigmatism. ophthalmology. Address for Correspondence: Depto. de Oftalmologia FMRP/USP, Av. Bandeirantes 3900 (12 andar do HC), 14049-900 Ribeirão Preto - SP Brazil. E-mail: [email protected]. References 12. Screen presenting the results of the three analyzed regions of the cornea and the graphical interface for guiding the clinician to the irregularities of the analyzed regions in comparison to regular astigmatism. systems for corneal evaluation or correction. André M. Vieira Messias is an undergraduate student of the Medical School of Ribeirão Preto (Faculdade de Medicina de Ribeirão Preto - USP) and also a technician in software development. His field of interest is ophthalmology and developing software for diagnostics. September/ October 2000 Sidney J.F. Sousa graduated from medical school in 1972 and is a specialist in estrabism and in external ocular diseases. He is a professor in the Faculty of Medicine of Ribeirão Preto - USP, and he is responsible for all medical testing and control of the systems developed by the Laboratório de Física Oftálmica FMRP. He is also the director of the Eye Bank of the Hospital das Clínicas de Ribeirão Preto. 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