The Orbscan II corneal topographer (Technolas GmbH Ophthalmologische Systeme, Feldkirchen, Germany) has been shown to perform well in terms of validity and repeatability when measuring spherical test surfaces.^{1} The original Orbscan instrument derived anterior and posterior corneal surface data from slit-scanning alone. The Orbscan II instrument utilizes a combination of a slit scanning technique and Placido disc image acquisition to determine a three-dimensional topographical plot for the anterior and posterior corneal surfaces. Acquisition of corneal data with Orbscan II comprises an image capture of the Placido disc reflection from the anterior cornea followed by capture of 40 corneal slit images. These narrow (0.3 mm) slit beams are incident upon the cornea at 45Â° from the instrument axis. The series of two-dimensional corneal section images are then processed automatically by the Orbscan II software, which, in combination with the Placido disc image data, is used to produce a range of topographic representations of the cornea, e.g., curvature maps, elevation maps, pachymetry maps.^{2}

A number of validation studies of the Orbscan II instrument have been conducted on test surfaces and human corneas. Many of the studies carried out on human corneas have reported the validity and repeatability of pachymetry data, rather than surface curvature.^{3,4} Cairns et al.^{5} conducted a validation of Orbscan II measurements against Form Talysurf analysis of spherical and aspheric test surfaces, finding a statistically significant difference between these two methods of surface profile assessment. They concluded that the difference, if also evident in the human cornea, would be small enough to be considered clinically insignificant. Cho et al.^{6} examined intra-examiner repeatability and inter-examiner reproducibility of four corneal topographers, including Orbscan II, on normal corneas of young adult subjects. The upper and lower 95% limits of agreement for the Orbscan II were large: 2.26 D and âˆ’2.49 D for apical radius repeatability, and 3.72 D and âˆ’3.39 D for reproducibility of apical radius.

The EyeSys videokeratoscope is based on image analysis of a Placido disc, and therefore can only provide curvature data on the anterior corneal surface. The instrument is valid and repeatable when compared with conventional keratometric methods of measurement on both test surfaces and human corneas.^{7â€“9} This instrument may be regarded as one of the first successful clinical instruments used to measure corneal topography.

The aim of this work was to compare the Orbscan II and EyeSys topographers' performance on a set of test buttons with known ellipsoidal surface profile characteristics, and on normal human corneas. The human cornea is tilted in relation to the instrument optical axis when a topographical measurement is made. This tilt produces apparent asymmetry in the semimeridians being examined and could be up to 8 deg.^{10} With this in mind, it was decided to examine the ellipsoidal buttons with a 4-deg tilt in order to simulate conditions that exist when a corneal measurement is made.

#### METHODS

##### Aspheric Buttons

Twelve conicoidal surface convex polymethylmethacrylate buttons were manufactured to produce surfaces similar to the normal healthy human cornea with apical radii ranging from 7.19 to 8.20 mm and p-values ranging from 0.41 to 0.80. These buttons were sent to the Rank Taylor Hobson Calibration and Measurement Laboratory for Form Talysurf Analysis, which is calibrated with reference to traceable standards. The instrument uses a stylus that traverses any requested meridian of the surface. A laser interferometric transducer transmits the signals to a computer for detailed processing. Relative to the best fit arc, the accuracy is claimed to be within two parallel planes having a separation of 0.1 Î¼m over a 20-mm traverse after removal of the best fit reference line. The measurement was made along the meridian parallel to an engraved line on the underside of the button. Measurements were made over the central 10 mm of each button. The apical radius (*r*_{o}) and the surface asphericity (p-value) were calculated for each meridian from the results of the measurements, which confirmed the ellipsoidal nature of the surfaces. These two parameters fully describe the surface characteristics of a conic section just as radius of curvature mathematically describes a circular arc. The apical radius indicates how steep or flat is the curvature of the section and the p-value quantifies the asphericity.

The buttons were then subjected to a single measurement using the EyeSys (version 3.2) and a single measurement using the Orbscan II topographer (version 3.12). In both cases measurements were made by one examiner following the manufacturers' guidelines on procedure, being particularly careful to ensure accurate centration of the image with focus being as precise as possible. The buttons were mounted on a matt black holder and adjusted to give a 4-deg tilt in the horizontal meridian. The black holder produced a surface reflection from the button of the same order (3.9% calculated) as that of the cornea (2.5% calculated) with no extra reflected light from the holder itself. Measurements were recorded for the meridian marked by the engraved line, which was horizontal.

For both instruments, the sagittal radii with the perpendicular distances from the instrument optical axis were recorded for eight points on each semimeridian. This is the raw data from the instrument measurement. Figure 1 considers measurement at point P on a given meridian of the surface. The sagittal radius is distance PCs and the tangential radius is PCt. The location of point P is specified by distance *y*, which is the perpendicular distance from the instrument optical axis. The EyeSys measurements were recorded for eight points, which were the image borders of rings 5 to 12. These ring images cover perpendicular distances from 1.3 to 3.2 mm in an average cornea. For the Orbscan, the eight perpendicular distances ranged from 1.26 to 3.5 mm in the same cornea. In both cases the eight points on each semimeridian were used to calculate *r*_{o} and the p-value. Thus for both instruments, the results were derived from a surface region of internal diameter around 2.5 mm and external diameter around 6.5 mm. The surface region covered by rings 5 to 12 was chosen because any keratometer or keratoscope produces less precise radius values when the target diameter (the mire diameter) is small. The larger rings are often incomplete when measuring the human cornea due to the upper eyelid and the nose imposing limits on the peripheral measurements. The 6.5-mm diameter image was always present and so the region examined was the same for all subjects. The use of data from this limited surface region produced very similar results for the EyeSys instrument to those acquired by using all the data points available.^{11}

The curvature and asphericity of the meridian were calculated using the conic section equation:

The surface characteristics, *r*_{o} and the p-value (*p*) are both constants of the section and so this equation generates a straight line graph. A scatterplot of sagittal radius squared (*r*_{s}^{2}) against perpendicular distance squared (*y*^{2}) should theoretically produce a straight line function when a conic section is measured. The intercept on the ordinate indicates *r*_{o}^{2} and the slope of the line has a value 1 âˆ’ *p* for the meridian examined. A circular section has a p-value of unity and a parabolic section has a p-value of zero. Corneal asphericities are likely to lie between these limits.

Mathematical modeling can be used to simulate the instrument readings from a conicoidal surface, where it is found that a surface tilt produces apparent semimeridian asymmetry. If the semimeridian pairs are averaged for both perpendicular distance and sagittal radius then the single point values collapse onto the regression line.^{10} Figure 2 illustrates the scatterplots derived from the measurement of one of the ellipsoidal buttons by the Orbscan where the apical radius is âˆš51.05 = 7.14 mm and the p-value is 1 minus 0.23 = 0.77.

##### Human Corneas

Single measurements were made on the right eye of 18 subjects (12 females) with ages ranging from 18 to 25 years. Subjects were selected from an initial group of 100 subjects to give a range of corneal asphericities and apical radii spread across the normal range. In all cases the flat principal corneal meridian derived from keratometry was the meridian selected for analysis. The apical radius of this meridian ranged from 7.41 to 8.37 mm. The p-value ranged from 0.54 to 0.86. Informed consent was obtained from the participating subjects after the nature of the procedure had been explained. The experiment followed the tenets of the Declaration of Helsinki. None of the subjects were contact lens wearers. All measurements were taken by one examiner. No image editing was performed. The resulting data were analyzed as for the buttons to give *r*_{o} and the p-value for the flat corneal meridian, using both the EyeSys and the Orbscan instruments. All the corneas were found to be tilted in relation to the instrument optical axis. Figure 3 illustrates an Orbscan measurement on the flat meridian of a human cornea. The surface tilt was around 4 deg and this produced apparent asymmetry as shown in (a). Averaging of the semimeridians produced data points close to the regression line as shown in (b). The high coefficient of determination (*R*^{2} = 0.984) indicates that this surface is producing results like that of a tilted surface with a conic section.

Therefore, for the corneas in this investigation, the scatterplots were derived using semimeridian averages as in Figure 2(b) to derive the apical radius and the p-value for the flat corneal meridian.

Two sets of independent measurements were taken for both the aspheric buttons and a new group of 20 human corneas by the same observer in order to assess the repeatability of a single measurement.

#### RESULTS

All parameters appeared to display normal distribution, which was supported by a Kolmogorovâ€“Smirnov d-test. Parametric statistics were therefore used for all analyses.

##### Aspheric Buttons

The Talysurf results may be regarded as the best estimate of the apical radius and the p-value for the engraved meridian. Table 1 illustrates the means and standard deviation of the differences between the two instruments and the Talysurf result for the 12 buttons.

A repeated measures ANOVA, with *post hoc* comparisons using the ScheffÃ© test, for the apical radius (*F*_{2, 22} = 84.982, p = 0.000) indicates that the differences between the Talysurf and both clinical instruments are significant. The ANOVA results for the p-value (*F*_{2, 22} = 84.757, p = 0.000) show no significant difference between the Talysurf and EyeSys (p = 0.954) with the Orbscan showing a significant difference from the other two methods of measurement (p = 0.000).

Bland's one sample *t* method^{12} for comparing two methods of measurement from a small sample was used to determine the extent to which the two clinical instruments differed from the Talysurf result. The results of this analysis derived from the mean and standard error of the differences are shown in Table 2 which indicates, with a 95% confidence interval, the degree to which the clinical instruments under- or over-read in relation to the Talysurf result.

The measurements made on corneas can only be made with the EyeSys and the Orbscan and so it was thought appropriate to compare these two with each other for the buttons. The results are illustrated in Figure 4, which is a Bland and Altman plot,^{13} where the Orbscan underestimates the mean apical radius by 0.118 mm with limits of agreement from 0.040 to 0.196 mm. The limits of agreement are simply twice the standard deviation of the differences. The Orbscan also underestimates the p-value by a mean of 0.062 with limits of agreement from 0.022 to 0.102.

Bland's method^{12} for comparing measurements from a small sample was applied to compare the two clinical instruments. The Orbscan apical radius reading was found to under-read from 0.094 to 0.142 mm and the Orbscan p-value result was under reading from 0.049 to 0.075 compared to the EyeSys VK result on the buttons.

##### Human Corneas

The group mean apical radii were 7.80 mm for the EyeSys and 7.76 mm for the Orbscan. A t-test for dependant samples indicated that this small difference was statistically significant (*t* = 3.857, p = 0.001). The group means for the p-value were 0.69 EyeSys and 0.64 Orbscan. Again, this difference was statistically significant (*t* = 2.731, p = 0.014).

Bland's analysis^{12} was applied to compare the two instruments on the corneas. The Orbscan apical radius reading was found to under-read from 0.020 to 0.070 mm and the Orbscan p-value result was under-reading from 0.010 to 0.086 compared to the EyeSys VK result on normal human corneas.

The Orbscan software provides an asphericity for the surface. This is an asphericity averaged for all meridians. This is unfortunate because it has been shown^{11,14} that both curvature and asphericity change between the flat and the steep principal meridians of the cornea. The Orbscan display describes the asphericity as a shape factor, which is the p-value. Comparison of the p-value derived as described in this investigation with the asphericity provided by the Orbscan display (via the *View/Aconic* route) shows a reasonable agreement for the aspheric surfaces, which deteriorates for the corneas. Figure 5 shows a Bland and Altman plot^{13} of the mean against the difference for both the aspheric surfaces and the corneas.

##### Repeatability of the Orbscan

##### Aspheric Buttons.

Two sets of independent Orbscan measurements on the aspheric buttons were taken by the same observer. These measurements represent repeatability assessed under optimum conditions because the test surfaces remain perfectly still during measurement. The British Standards Institution^{15} recommended that repeatability can be represented as the value below which the difference between the two measurements will lie with a probability of 0.95. Provided the measurement errors are from a normal distribution, this is estimated by 1.96 Ã— âˆš(2*s*^{2}) where *s* is the standard deviation of the differences for the group. Following this recommendation, the apical radius is likely to change by <0.101 mm on repeated measurement and the p-value is likely to change by <0.091 for these buttons.

##### Human Corneas.

Two sets of independent measurements on a set of 20 corneas were taken by the same observer. These measurements represent repeatability assessed on surfaces that are not going to remain perfectly still during the measurement procedure. Following the British Standards Institution recommendation, it was found that the apical radius is likely to change by <0.096 mm on repeated measurement and the p-value is likely to change by <0.125 for this group of subjects.

#### DISCUSSION

The perpendicular distance and sagittal radius data extracted from the two topographers represent the raw data before unknown algorithms are applied. The Orbscan measurement for both the buttons and the corneas involved the Placido disc image and slit scanning analysis. The EyeSys result was derived from the Placido disc image only. The apical radius indicates surface curvature and the p-value quantifies the asphericity.

##### Aspheric Buttons

The aspheric buttons possessed conicoidal surfaces. The Talysurf measurements may be considered to be the most accurate assessment of the surfaces. If this is accepted then a comparison of the results of the two clinical instruments with those of the Talysurf will indicate the likely error in the measurement of the EyeSys and the Orbscan instruments. Table 2 indicates that the Orbscan under-read and the EyeSys over-read by a similar amount for the apical radius. The EyeSys p-value was not significantly different to that of the Talysurf, but the Orbscan under-read compared with the Talysurf result. Bland's analysis^{12} of the differences established that the Orbscan under-read by up to 0.077 mm for apical radius and 0.047 for the p-value compared to that of the Talysurf. Comparing the two clinical instrument results on the buttons, the Orbscan was seen to under-read by up to 0.142 mm for apical radius and by 0.075 for the p-value compared to the EyeSys. The increase in disagreement for apical radius between the two clinical instruments may arise from the EyeSys reading high and the Orbscan reading low compared with the Talysurf.

##### Human Corneas

Talysurf measurement cannot be applied to the cornea and so we are left with a comparison between the two clinical instruments. In these circumstances, a mean vs. difference plot is useful because the mean of the two clinical instruments provides the best estimate of the parameter for the cornea. The corneal group means of the two instruments combined were 7.78 mm for apical radius and 0.66 for the p-value. The limits of agreement will only become representative with more subjects examined than has occurred here. With only 18 subjects examined the limits of agreement predict what may be an unrealistically wide spread; therefore, the differences in readings were estimated using Bland's one-sample *t* method.^{12} The limits of agreement were applied to the graphs in order to provide a sensitive illustration of spread for comparison purposes.

A general comparison of the instruments could be made from the mean difference, which suggests that the Orbscan apical radius reading is likely to be an under-reading around 0.045 mm and the p-value reading is likely to be an under-reading around 0.048 on human corneas. The Orbscan and the EyeSys data for a cornea could be used to calculate the sagittal radius of the surface at any given semidiameter using Eq. (1). The disagreement in the apical radius and the p-value will produce different sagittal radii at any given semidiameter. The disagreement will be larger for larger semidiameters. The outer region of the cornea examined here is around diameter 7 mm. Assuming corneal apical radii of 7.20, 7.70, and 8.40 mm with p-values 0.4, 0.6, and 0.8 (EyeSys), then the differences in sagittal radii for a semidiameter of 3.5 mm would be between 0.03 and 0.05 mm. The 0.05 mm radius difference makes an approximate corneal power difference of 0.25 D. These errors may help to gauge the clinical significance of the differences between the instruments. The differences appear to be relatively small from a clinical point of view.

The analysis described in this investigation is only valid for surfaces with conic sections. The cornea has been described as a surface with sections that approximate to conic sections.^{16} The extent to which the corneal sections examined in this study approximate to that of a conic section was quantified by noting the coefficient of determination (*R*^{2}) of the distance squared vs. radius squared semimeridian averaged scatterplots, where the *R*^{2} for all 18 subjects never fell below 0.95 for both instruments. These high values support the notion that the corneal section of the region examined can be considered to approximate well to a conic section and thus this approach to analysis is appropriate.

Figure 5 illustrates the amount of agreement between the p-value derived in this investigation for a specified meridian and the shape factor of all meridians provided by the Orbscan software. The mean and double standard deviation of the differences represent the bias and the limits of agreement respectively. The bias was similar for the buttons compared to the corneas. The increase in the limits of agreement in the measurement of the corneas casts doubt on the value of providing a single mean asphericity for all meridians of the cornea. The better agreement between the p-value and shape factor on the buttons could have arisen due to the p-value being constant for all meridians. The human cornea will display change in the p-value moving from the flat to the steep corneal meridian, which would lead to a deterioration in the agreement. Asphericity should be referred to a specific meridian. For contact lens fitting purposes, practitioners will be particularly interested in the curvature and the asphericity of the flat meridian.

##### Repeatability of the Orbscan

The repeatability of the measurements is of some concern in the Orbscan because of the time taken to complete the measurement. The 40 slit images are processed in two 0.7-s periods. The manufacturer claims that eye movement monitoring minimizes errors arising from eye movements during this period. The buttons will obviously remain absolutely still and movement during measurement will only be a problem with the corneas.

Bland and Altmann^{13} make the point that comparison between any two methods will inevitably be poor when either one of them shows poor repeatability. The repeatability analysis for the buttons indicated that a repeat measurement is likely to be within 0.101 mm for apical radius and 0.091 for the p-value. The Orbscan repeatability on human corneas was 0.096 mm for apical radius and 0.125 for the p-value. There is little evidence for a deterioration associated with the time taken to acquire the measurement, which is of little consequence for the stationary aspheric buttons but may be a problem for measurements made on a human eye. It must be noted that the repeatability is no worse than that of the EyeSys on human corneas^{17} where the repeatability was found to be 0.12 mm for apical radius and 0.16 for the p-value comparing two single measurements. In the clinical situation, repeatability may be improved by taking more than one measurement and analyzing averaged data.

In summary, the Orbscan instrument appears to underestimate the apical radius and the p-value by a small amount, which may not be clinically significant. Its repeatability appears to be at least as good as that of the EyeSys.

#### ACKNOWLEDGEMENTS

The authors have no commercial or proprietary interests in the instruments discussed.

William A. Douthwaite

Department of Optometry

University of Bradford

Richmond Road, Bradford

West Yorkshire BD7 1DP

United Kingdom

e-mail: W.A.Douthwaite@Bradford.ac.uk