Computer-assisted videokeratography has emerged as a useful clinical and research tool.1-3 All of the currently available commercial units utilize a modified placido disk image and require a smooth reflective corneal surface.4-6 These systems produce a color-coded contour map that depicts the curvature or power of the cornea. We describe our initiai work with the PAR Technology Corneal Topography System (PAR CTS). This system is a prototype of a new corneal imaging device that produces a true topographical map by calculating corneal elevation as opposed to angle of reflection. The system is unique in that it utilizes raster photogrammetry to determine the corneal topography.
The CTS uses a form of stereophotogrammetry, a standard method of extracting object information using two or more overlapping photographs or views of that object. This technique, used extensively in terrain mapping, lends itself well to extracting positional information about discrete features of an object or field of view, but lacks in its ability to measure overall shape, In the case of the cornea, it is more important to measure the shape of the cornea rather than positions of specific points. In order to properly measure shape, the position of a great number of points uniformly distributed over the entire cornea surface must be measured. Another problem encountered when standard stereophotogrammetry is used is the fact that the cornea is rather uniform and structureless in appearance, which makes it difficult if not impossible to find conjugate points in a stereoscopic image pair. These problems can be overcome by a special illumination technique called structured lighting.
Figure 1: A block diagram of the PAR CTS Illustrating the components of the system. The PAR CTS utilizes a modified Topcon silt lamp. The two optical paths are separated by 13.8° to permit raster photogrammetry analysis. The central processing unit synchronizes the two systems and allows for manipulation of the data.
Structured lighting involves projecting a regular pattern of Unes or a grid of known geometry onto the object of interest. This light pattern is then viewed and imaged from an offset angle. Using the image of the projected pattern and the defined information about the geometry of the grid or line pattern used to create the projected pattern, elevation values can be computed for each discrete point in the projected pattern. This technique is commonly referred to as raster photogrammetry, and has been used in a variety of medical and nonmedical applications (eg, optic nerve analysis). This technique was initially adapted for corneal topography by Warnicki et al.7 Their original prototype utilized vertical lines as the structured lighting. The current system utilizes a grid pattern which enhances system accuracy.
Figure 2: A grid pattern projected onto a fluorescein-stained cornea. The two vertically oriented rectangles are used in centering the grid. At the current magnification, × 16, the grid provides for a maximum of 1700 analyzable points.
Because the cornea is a transparent, nondiffusing surface, additional means must be used in order for the projected pattern to appear on the surface of the cornea. This is accomplished by using topical fluorescein to stain the tear film, and using a cobalt blue light to produce the structured light pattern.
MATERIALS AND METHODS
The PAR CTS utilizes a modified Topcon slit-lamp microscope. The system views the cornea through two identical optical paths which are oriented at a fixed angle of 13.8° relative to each other (defined by the slit-lamp optics) (Fig 1). A second configuration utilizes a custom optical bench with an angle of separation of 29°. The PAR CTS projects a two-dimensional grid pattern through a cobalt blue filter onto the eye through one of the optical paths (Fig 2). This pattern provides discrete analysis points at each grid intersection. The current point density spacing at × 16 magnification is 0.22 mm on the surface of the cornea for a total of approximately 1700 points. The tear film is stained with fluorescein so that the projected grid pattern produces a fluorescent image that can be recorded. A video camera views the image through the second optical path. The grid pattern is captured and analyzed by the computer imaging system.
The CTS utilizes a photogrammetric method of aerotriangulation to compute elevation values from image point positions. The following simple equation defines elevation from the position of the grid intersections in the image:
Elevation = deviation of grid (sine alphaXcos beta)/magnification ratio
where alpha = the angle between the projected grid and the viewing optics, beta = V2 the angle of alpha, and the magnification is the number of pixels per millimeter of the image.8 This equation does not accurately depict the total processing that is currently performed by the system. It does however, denote an elementary relationship between image point displacement and elevation.
The current algorithm uses a ray intersection method to compute a grid point's position on the surface of the cornea. For each grid intersection that is projected onto the surface of the cornea, the image processing algorithm determines the position of the actual grid intersection in the projection device that was used to create that grid intersection and the position of the image of the projected grid intersection in the image plane. This information, together with calibration information which denotes the orientation of the projection and camera devices, is used to compute a mathematical model of both the ray which projected the grid intersection onto the cornea and the ray which formed the image of the projected grid intersection. Once these two rays are defined mathematically, they can be intersected mathematically thus producing a position in space. This process is performed for each projected grid intersection which is imaged successfully. These data are utilized to produce an elevation map of the cornea. Utilizing the elevation data, the PAR CTS computes corneal curvature.
The ability of the PAR CTS to accurately measure corneal topography is a function of the following parameters:
* Elevation detection accuracy;
* System's optical angle of separation;
* Number of points defined (grid intersections); and
* True object curvature.
In order for curvature to be calculated from an elevation map, it is important that the amount of elevation error or noise be significantly smaller than the true relative elevations on the surface being measured. This desired high signal/noise ratio can be accomplished in several ways. The most obvious way is to reduce the elevation error or noise. Another way is to increase the signal amplitude (ie, relative elevations being measured). This second solution is accomplished by the last two parameters listed previously. The larger the area of measurement or the smaller the grid spacing, the more grid intersections are detected, and thus a larger signal is generated. The effect of the object curvature can be understood when considering the difference between measuring a flat surface as opposed to a curved surface. A relatively flat surface has little change in elevation from one point to another, such that the elevation noise can be larger than the actual change in elevation across the surface. A surface with a high curvature will have significant changes in elevation from one point to another which will be larger than the background noise. Elevation detection accuracy can also be significantly improved by increasing the system's optical angle of separation.
In the current software configuration, the PAR CTS can display its information in any one of three primary modes:
1. An elevation map. This assigns an elevation value relative to a fixed calibration plane. The data are displayed in a 10-color relative value scale.
2. A reconstructive spherical subtraction map. This program displays the amount of deviation from the best fit sphere for the entire cornea or any selected portion of the cornea. The information is displayed in a 10-color map in either a relative scale or a number of predetermined absolute value scales.
3. A meridional display. This mode images the cornea in 18 preselected meridians at 10-degree intervals. The display shows the actual points relative to the best fit curve. This program can also display the actual points and best fit curve relative to any selected curve. The data are presented where the fixed X-axis represents the specified curve and the Y-axis represents the deviation from that specified curve. The X and Y intercept represents the high point (greatest elevation) on the cornea, though any point may be operated selected, and distance along the X-axis its meridian length. A further option allows the actual points and best fit curve to be shifted along the Y-axis by l-µ increments relative to the specified curve (X-axis). This last feature allows for the theoretical computation of ablation depths within specified optical zones for both myopic and hyperopic corrections by selecting a specified curve (flatter or steeper than computed best fit curve respectively) and an optical zone diameter.
A normal cornea shows concentric rings of elevation (Fig 3). This display is the least useful clinically in that major changes in corneal curvature (eg, keratoconus, radial keratotomy, and postpenetrating keratoplasty) show a similar picture. These elevation data, however, are the basis for all subsequent displays. The spherical subtraction map is a sensitive indicator for variations in topography. Figure 4 represents the subtraction data for a normal eye with a small degree of with-the-rule astigmatism. The resulting color map shows minimal deviation from sphericity. Figure 5 is of an eye with 5.00 diopters of with-the-rule astigmatism. The resulting subtraction map shows negative deviation or steepening from the best fit sphere at the 90-degree meridian and positive deviation or flattening at 180°. The utility and uniqueness of the subtraction mode can easily be demonstrated comparing an eye after radial keratotomy (Fig 6) with an eye that has moderate keratoconus (Fig 7). A preselected absolute value scale can also be utilized in the spherical subtraction map, allowing for both intersubject and intrasubject comparisons (Figs 5B, 6B, 7B).
Figure 8 shows a normal cornea in the meridian mode. In this instance, the X-axis represents the best fit curve relative to the actual points displayed. The Y-axis represents the deviation from the best fit or any preselected curve. The scale of the Y-axis is operated selected, with the machine default assigning a scale that maximizes deviation from the best fit or selected curve. One potential application of the PAR CTS is its theoretical use in predicting results for refractive ablative surgery. The meridian display allows the data to be easily manipulated to compute theoretical ablation areas necessary for either corneal flattening or steepening. Figure 9 represents the meridian display by specifying a curve approximately 2.00 D flatter than the best fit curve. By moving the data points along the Y-axis, one can select varying optical zones. The upper display shows the theoretical depth of an ablation necessary to accomplish 2.00 D of flattening for a 6-millimeter optical zone. The lower display shows the reduction in depth and total tissue loss needed to obtain the same degree of flattening with an smaller optical zone. Figure 10 displays the actual and best-fit points relative to a curve specified 2.00 D steeper. By elevating the data points until they are just tangent to the specified curve, one can directly show the tissue to be removed for a hyperopic correction of varying optical zones.
Except for the initial elevation map, all the displays have recently been incorporated into the system and represent work done by the authors in conjunction with PAR Technology Corporation Vision Systems Group.
The accuracy of this device has been verified against a series of calibrated tests spheres (55.76, 42.21, and 33.55 D). The test spheres were steel balls coated with a thin white silicon polyester coating that was necessary for grid projection, because standard steel balls are too highly reflective. The test spheres were measured by a Taylor-Hobson contact profilometer possessing submicron accuracy. Utilizing the CTS custom optics with an optical angle of separation of 29°, test areas 3 to 8 mm in diameter, and the above test spheres, we determined system accuracy by eight repeated analyses with refocusing. System accuracy at the 8-millimeter test area was 0.03 (SD 0.03), 0.00 (SD 0.02), and 0.07 (SD 0.01) D respectively.9 Smaller diameter test areas resulted in a predicted loss of accuracy (Table 1). The slitlamp optics with its reduced angle of separation also resulted in a predicted loss of accuracy (Table 2).
Figure 8: A normal eye in the meridian display mode. The top tracing represents the 50-degree meridian and the lower the 140-degree meridian. The blue line on the X-axis represents the best fit circular curve. The distance between each large marker on the X-axis represents 1 mm of chord length. The green line depicts the actual points on the cornea. The variation of the green line from the blue line along the Y-axis represents deviation from sphericity. The Y-axls is shown in an operator selected scale ±0.025 mm. A small Y-axls scale was purposely selected to visually separate the actual corneal points (green line) from the best fit sphere (blue line).
Figure 9: The meridian display demonstrating a 2-diopter myopic photoablattve area of varying optical zone size. The X-axis represents the specified curve; in this case, a curve 2.00 D flatter than the best fit curve. The green represents the actual corneal points, and the blue the best fit circular curve to those points. The optical zone size can be varied by moving the actual and best fit curves along the Y-axis and reading the optical zone size from where the curves intersect the X-axis. The top display represents the total ablation zone necessary for a 2-diopter myopic correction with a central optical zone of 6.0 mm. The lower display shows the same 2.00 dioptric flattening, but with a smaller optical zone of 3.5 mm. The Y-axSs scale is operator selected at ±0.035 mm.
To determine the reproducibility, three investigators measured three non-calibrated spheres (20 mm, 18 mm, and 12 mm prior to coating). The slit-lamp microscope was purposely decentered and refocused after each analysis. Maximum intraobserver variability was 0.09, 0.06, and 0.11 D respectively. Maximum interobserver variability measured 0.18, 0.12, and 0.16 D (Table 3).9
Comparison With Videokeratoscopes
The PAR CTS has certain theoretical advantages over other commercially available corneal imaging systems:
1. The PAR CTS can measure the surface topography of the cornea regardless of the cornea's orientation relative to the instrument. Proper use of placidobased systems requires that the rings be coaxial to the cornea. Improper positioning of placido-based systems will yield erroneous results.
2. Measuring the topography of the cornea via reflected light techniques can yield errors and incomplete results when the cornea has sudden topographic changes such as those resulting from severe scarring, ulcerations, or sutures. Under these circumstances, the image mires or reflected rings of a placido disk system will tend to merge into one another and become undiscernible. The PAR CTS measures the surface elevation instead of the surface normal. This allows the system to measure much larger surface deviations than traditional placido-disk-based systems. This departure UOm using reflected light also enables the CTS to be used on corneas which do not reflect well due to scarring, epithelial defects, or irregular shape. The system has successfully imaged deepithelialized and freshly keratectomized corneas.
Figure 10: A hyperopic ablation can be illustrated by specifying a curve steeper than the best fit curve. This example shows a 2-dlopter hyperopic correction (upper tracing 40-degree meridian, lower tracing 130-degree meridian). The actual and best fit curves are raised along the Y-axls until the corneal apex just touches the X-axis. The ablation area is that area under the corneal (green) curve and above the X-axis (specified curve). Optical zone size can be chosen along the X-axis. The Y-axis was operator selected at ±0.045 mm.
Accuracy of CTS-PAR Custom Optics on Calibrated Test Spheres (Diopters)
3. Because the PAR CTS initially determines elevation and not its second derivative curvature, the data are more amenable to the mathematical computations necessary to determine ablation depths and optical zones for future photorefractive surgery and/or reconstructive modeling.
4.One of the current systems utilizes the optical delivery system of an ophthalmic slit-lamp without affecting the working distance. This large working distance enables the use of the system in an operating room environment. The large working distance, the ability to integrate the CTS as a subsystem into other existing optical devices, and the capability to image keratectomized corneas suggest that the CTS may have a role as a measurement subsystem for refractive surgical laser systems.
The Par Technology Corneal Topography System is a prototype of a new unique corneal imaging device. With continued development, the PAR CTS may become a useful tool for predictive modeling and as a monitoring system for photoablative surgery.
Accuracy of PAR - CTS Slit-Lamp Optics on Calibrated Test Spheres (Diopters)
Reproducibility of PAR - CTS Calibrated on Test Spheres (Diopters)*
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Accuracy of PAR - CTS Slit-Lamp Optics on Calibrated Test Spheres (Diopters)
Reproducibility of PAR - CTS Calibrated on Test Spheres (Diopters)*