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Preliminary tests and construction of a computerized quantitative surgical keratometer

Carvalho, Luis MSa,b,*; Tonissi, Silvio A. MSa; Castro, Jarbas C. PhDa

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Journal of Cataract & Refractive Surgery: June 1999 - Volume 25 - Issue 6 - p 821-826
doi: 10.1016/S0886-3350(99)00037-1
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The first commercial operative keratometer was introduced by Troutman and coauthors in 1977.1 The fundamental purpose was to give the surgeon greater control of the operative factors that contribute to induction of postoperative astigmatism. Since then, many other devices have been introduced and tested,2 most of which can be divided into 2 categories: qualitative and quantitative.

Qualitative keratometers are based on the principle of Placido disks3 or concentric light dots, such as the Troutman keratometer. They do not objectively measure the radius of curvature; therefore, a better description might be operative keratoscope. Quantitative keratometers are based on the principle of keratometry4 and measure corneal curvature at different meridians. Thus, the amount of astigmatism and its axis can be determined.

The general advantages and disadvantages of commercial devices using these methods have been reported.2 In summary, most qualitative keratometers are less expensive and easy to use and manipulate; however, they depend on the surgeon's experience and ability to make decisions based exclusively on the distortion patterns and apparent dimensions of the reflected images. In contrast, objective keratometers are more expensive, usually have many components, and are awkward to handle, especially during surgery. However, they depend little on surgeon ability during measurement, and data are usually displayed in analog scales or digital number displays that are easier to interpret.

One of the most popular corneal measurement devices available is the computer-aided topographer. Unfortunately, corneal topographers are not designed for intraoperative use. Some advantages of these devices over conventional keratometers are ease of manipulation, automation of the focusing process (only with some models), semiautomation of image grabbing and processing, and display of the results in a visually appealing manner (color-coded maps, originally suggested by Klyce5).

Our goal was to develop an instrument that would combine the positive characteristics of surgical qualitative keratometers with those of computer-aided topographers; that is, an easy-to-mount system that would grab and process disc images rapidly and semiautomatically, calculating several values for radius of curvature (or diopters) and astigmatism, and display results on a computer screen. Each measurement should take only a few seconds so the surgeon can analyze the output and adjust irregularity by tightening or loosening sutures. We believe the earlier work of Troutman and coauthors1,6 and Amoils,7 and more recently that of Igarashi et al.,8 are only a few examples of contributions that support the importance of more advanced surgical keratometers in diminishing postsurgical corneal irregularities and astigmatism.

Materials and Methods

Functioning Principle and Hardware

Most surgical environments have limited space for inclusion of new instruments. To overcome this, a compact illumination system that forms a ring of light pattern (a single Placido disk) was used (Edmund Scientific, Industrial Optics Division) (Figure 1). The system was originally designed as a light guide for industrial applications but works well as a “one-ring” Placido disk projecting system. It mounts directly to any conventional surgical microscope (e.g., Zeiss). It has a cold light source that travels on a cable made with 15 000 fiber optics. The end of each fiber is positioned to form the ring pattern. The pattern's light intensity can be adjusted so its reflection can be seen even when ambient light is present.

Figure 1.
Figure 1.:
(Carvalho) One-ring disc projecting system. The fiber optic cable has 1 end input in a light source (upper right) and at the other end, forms a perfect ring of light.

This device is easily mounted or removed from the microscope's objective pod and does not interfere with its functionality and maintenance. It also does not restrict the surgeon's hand movements or side view. We adapted a red light emitting diode (LED) at its center to serve as a fixation point (not shown in Figure 1).

The image reflected from the cornea, besides its normal path, hits the microscope's beam splitter and focuses on the charge-coupled device of an attached monochromatic camera. The patient's eye must be correctly aligned with the axis of the optical system. During image digitizing, the microscope's light must be turned off because the image-processing phase uses the LED reflection to start the border detection.

The camera's output signal goes to a frame grabber (Meteor, Matrox Electronic Systems Ltd.) installed on an IBM-compatible personal computer running Windows 95. This allows the cornea's image to be visualized in real time. After image digitizing, an algorithm for border detection is applied. The border information is then used to calculate curvature.

The algorithm performs the following steps: (1) detection of the central LED reflection and from this point, detection of the ring border in 360 different angles (semimeridians); (2) input of the 360 distance (central point to border) values in an algorithm containing a calibration curve for calculation of diopter values; (3) generation of a graphic output for ease of diagnosis and friendly visual display. The graph is a plot of diopter versus angle for each semimeridian. One can analyze the smoothness of the cornea by observing how close the graph is to a straight horizontal line.

Generating the Calibration Curve

The calibration curve was generated using the following algorithm: Given n spheres of radius (Rn) for each sphere, a sampling image from the reflection pattern is taken. For each sphere there will be a distance (dn) from the center to the border ring. The n sample points plotted on a graph of radius versus ring border distance may be fit by a straight line of parameters a and b and equation R = a + bd, where R = radius and d = border distance. Suppose an arbitrary surface is to be measured. Its border distance is input into this equation and the radius calculated.

Table 1 shows the radius and border distance values obtained for 4 calibrating surfaces. Equation 1 is the mean square fit for Table 1 data, where R = radius of curvature and d = distance (in pixels).

Table 1
Table 1:
Values of border distance measured on 4 calibrating spheres.

The diopter at each point was calculated using the formula

where nc = the index of refraction of the cornea and nair = the index of refraction of the air. For nc the Gullstrand reduced schematic eye index of refraction 1.3375, normally used for keratometers,9 was used. For nair, the value 1.000 was used. The denominator is the local radius of curvature in meters.

Image Grabbing and Processing

The surgical microscope and volunteer's head position were adjusted so that the optical axis of the microscope and the pupillary axis matched when the person fixated on the centered LED. When this condition was perfectly met and the image properly focused, the frame grabber was triggered by a foot pedal and the image digitized (bitmap file format).

The captured images are monochromatic (640 × 480), with 256 levels (intensities) of gray; 0 = totally black and 255 = totally white. In our border-detection algorithm, the image was defined as a Cartesian plane (point coordinates x, y) and 2-dimensional image-processing techniques10 were applied. The LED reflection point is the starting point for image processing and is detected by clicking the mouse at its interior (Figure 2). This reflected point is approximately centered inside the ring and from it the image is scanned radially for each angle, from center to border. By analyzing the slope of the intensity versus position (in pixels) for each angle, the border is determined as the medium point between maximum and minimum slopes (Figure 3). This method was applied instead of simply finding the highest point on the curve because of asymmetries caused by noise. This same process is repeated for each angle, and the Cartesian distance of each detected border to the center point is kept in a vector containing 360 distance values. The whole process took about 2 seconds because the good contrast of the image requires no filters. This finishes Step 1 of the algorithm.

Figure 2.
Figure 2.:
(Carvalho) Photograph of a disc reflected off a calibration sphere. The center blur is a reflection of the microscope's light, which must be turned off during corneal shape measurement. The LED reflection is not shown here.
Figure 3.
Figure 3.:
(Carvalho) The strong curve represents intensity along the ring. The medium point between the maximum and minimum slope is used as a border location. This avoids errors when noise causes the curve to be asymmetric, and results are better than when a maximum intensity point is used.

In Step 2, each distance is input as the d parameter in the fitted linear Equation 1, found from the calibrating spheres; 360 diopter values are calculated using Equation 2.

Step 3 displays the diopter values graphically so that analysis during surgery is straightforward and fast. A curve of diopter versus angle (from 1 to 360 degrees) is plotted. A typical graph for an astigmatic case is shown in Figure 4.

Figure 4.
Figure 4.:
(Carvalho) Output of the instrument on the computer screen showing a case of with-the-rule astigmatism.


Seven healthy volunteers (3 women, 4 men; aged 20 to 30 years) participated in the study. The procedure was fully explained to each volunteer, and formal consent was obtained in all cases. Fourteen corneas (left and right eye of each person) were measured by 3 experienced surgeons in a laboratory. As a control, the same corneas were measured on an EyeSys Topographer using the axial map display. Results were compared for the specific region of interest (3.0 to 4.0 mm central region). By using a small ruler (1 cm divided in 100 parts), the scale factors of the instrument (pixels/millimeter) and topographer were measured to precisely determine in which region the topography maps corresponded to the measurements. The results for each angle were then compared. A computer program was written to read the files from both instruments and calculate mean deviations. Results are shown in Table 2.

Table 2
Table 2:
Results of 14 healthy corneas using the new system and an EyeSys topographers.

The difference in radius of curvature between the 360 sets of values for all semimeridians was 0.05 mm or less in 78% of the cases. Corneal astigmatism values were 0.25 diopter (D) or less in 86%. The cylindrical axis was 5 degrees or less in 78% of cases.

The time for each examination was 4 seconds after image grabbing: 2 seconds for image processing and 2 seconds for calculation and display. This time can be reduced by using a more powerful computer (A Pentium 100 MHz was used here.) Time for image alignment, focusing, and grabbing varied by examiner. These times were not measured because they would only make sense under actual surgical conditions.


We constructed a new type of surgical keratometer. The system is based on a personal computer that rapidly processes grabbed images of a ring pattern reflected off the cornea. It is simple to mount and maintain and is based on relatively low-priced equipment.

Fourteen corneas of 7 healthy adults were measured by 3 experienced surgeons. Mean deviation was 0.05 mm for radius of curvature, 0.24 D for power, and 5 degrees for cylindrical axis. Therefore, we believe this method is sufficiently precise for measuring corneal astigmatism and may be effectively used as a quantitative means for diminishing astigmatism after surgery such as cataract and keratoplasty.1 More precision may be obtained by optimizing the focusing process and correctly aligning the patient's eye. These were subjectively determined during examination. The surgeons' opinion was that the instrument is easy to mount and use and the examination process fast. They were able to interpret the output but said that more types of data plots and colored user interfaces would improve the system.

The image-processing phase is fast and straightforward because it is based on the radially symmetric properties and good contrast of the reflected ring. It requires only 1 computer mouse click and takes only 2 seconds. Other systems require several mouse clicks.8 In most cases, it also requires no editing when the captured image is in proper focus and well aligned.

Another advantage of this system is that it calculates not only principle meridians and astigmatism for each examination as do most systems,1,2,7 but it also calculates 360 radius and power values for 360 semimeridians separated by equal angles of 1 degree. By plotting graphs of power versus angle on the computer screen, the instrument allows one to visually analyze the cornea's central shape. Straight and horizontal lines indicate a smooth and symmetric region, with little variation in radius and power, indicating a small amount of astigmatism. In addition, this system is easily mounted on a Zeiss-compatible slitlamp and, after proper calibration, works as a conventional keratometer.

The results obtained in preliminary tests indicate that the instrument is sufficiently precise to be used in ophthalmology clinics to monitor radius of curvature, power, and astigmatism. We are currently developing another projecting system with several discs based on the one discussed here. This will allow the surgeon to make topographical maps of a 7.0 mm region of the cornea instead of measurements along a single radial distance.


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© 1999 by Lippincott Williams & Wilkins, Inc.