An indirect method to compare the reference centres for corneal measurements

An indirect method to compare the reference centres forcorneal measurementsJingjing Xu1, Jinhua Bao1, Fan Lu1 and Ji C He1,2

1Wenzhou Medical College, Wenzhou, China, and 2New England College of Optometry, Boston, Massachusetts, USA

Citation information: Xu J, Bao J, Lu F & He JC. An indirect method to compare the reference centres for corneal measurements. Ophthalmic

Physiol Opt 2012, 32, 125–132. doi: 10.1111/j.1475-1313.2011.00880.x

Keywords: corneal topography, corneal

vertex, corneal apex, pupil centre

Correspondence: Fan Lu

E-mail address: [email protected]

Received: 6 January 2011; Accepted: 4

October 2011

Abstract

Purpose: Corneal measurements are commonly presented with respect to a spe-

cific reference centre, but the location of the reference centre on the corneal

surface could vary from one diagnostic modality to another. This study aimed

to develop a method for comparing reference centres used by corneal measure-

ment systems.

Methods: An indirect method was developed to compare reference centres by

making use of the pupil centre and its offset from the reference centre. Refer-

ence centres in a Scheimpflug imaging system, the Pentacam HR, and a Placi-

do-ring corneal topography system, the ATLAS Corneal Topography System,

were compared for the right and left eyes of 30 subjects. The subjects all had

similar pupil sizes when measured by the two systems. Differences and correla-

tions of the pupil centre offsets between the two systems were statistically

tested and compared by Bland–Altman analyses.

Results: There were no significant differences in mean pupil offsets between the

two systems for either the right or left eyes (p > 0.05). There were strong cor-

relations of the pupil centre offsets between the two systems for each eye (right

eye x-axis: r = 0.95, p < 0.0001; right eye y-axis: r = 0.98, p < 0.0001; left eye

x-axis: r = 0.96, p < 0.0001, left eye y-axis: r = 0.93, p < 0.0001). Bland–

Altman analyses revealed no significant differences in pupil centre offsets

between the two systems.

Conclusions: The Pentacam HR system and the ATLAS system have very similar

reference centres. Thus it is possible to directly analyze data from the Pentacam

HR and other instruments using the corneal vertex or the pupil centre as the

reference centres due to the similarity in the reference centre settings between

the two systems.

Introduction

In addition to the traditional Placido-ring corneal topog-

raphy, a variety of other techniques, including slit-scan-

ning and Scheimpflug imaging, have been developed

recently to directly or indirectly measure geometrical

properties of the cornea. While each technique has its

own unique functional feature, depending on its opera-

tional principle, all techniques could share some common

functions in their measurements. For example, the

Pentacam HR (http://www.pentacam.com/sites/hr.php) is

capable of measuring the posterior corneal surface and

corneal thickness due to its Scheimpflug principle, and it

is also capable of accessing the anterior corneal surface

with a function equivalent to that of the conventional

Placido-ring corneal topography. Because different tech-

niques accomplish the same function, it becomes impor-

tant to ensure that measurements of corneal properties

are compatible and exchangeable across different modali-

ties in clinical applications.1

However, different corneal measurements might be

presented with respect to different reference points (or

Ophthalmic & Physiological Optics ISSN 0275-5408

Ophthalmic & Physiological Optics 32 (2012) 125–132 ª 2011 The College of Optometrists 125

reference centres) due to the unique operational princi-

ples of each instrument. For example, a conventional

Placido-ring system directly measures reflected ring loca-

tions from which corneal power and elevation are indi-

rectly derived. For this system, the corneal measurements

are typically described in two-dimensional maps originat-

ing at the corneal vertex (or the vertex normal), defined

as the point at which the optical axis of the instrument

intercepts the cornea.2–4 However according to the user

manual from the company, the Pentacam HR system cor-

neal maps are referenced or centred at the corneal apex,

defined as the point of greatest corneal curvature or

shortest radius. Previous studies3–6 suggested that the cor-

neal vertex is located differently from the corneal apex in

most eyes. If there is a true difference in the corneal loca-

tions of reference points between the two systems, it

would first be necessary to determine the magnitude of

the difference. Then it would be necessary to correct it

through data translation and/or data rotation before a

comparison or exchange of the data between the two sys-

tems could be performed. This is important for current

wavefront applications for diagnosing and correcting

aberrations in the human eye. In clinical practices such as

the wavefront guided laser refractive surgery and aberra-

tion correcting contact lenses, the wavefront pattern and

the relevant distribution of Zernike coefficients depend

on the location of the reference centre.7

To find the exact corneal location of the reference

point for a system or to compare the reference points

between different systems is not straightforward. There is

no special point in the corneal measurement (or corneal

map) that could be used as a local marker to determine

its location. Fortunately, some systems directly provide

the location of the pupil centre, in addition to corneal

measurements. The pupil centre is a relatively stable local

marker if the pupil size is fixed.8–10 Thus, the location of

the corneal reference point from the pupil centre gives

rise to an indirect estimate of the corneal location of the

reference centre. In this article, we use this indirect

method to compare corneal locations of the reference

points in a Scheimpflug imaging system, the Pentacam

HR and a Placido-ring corneal topography system,

the ATLAS Corneal Topography System (http://www.

meditec.zeiss.com/atlas).

Methods

Subject

Thirty nine healthy volunteers participated in this study.

Of these, nine had pupil sizes that differed by over

0.5 mm between the ATLAS measurement and the Penta-

cam HR measurement. Since the pupil centre may shift

with pupil size,8–10 we excluded the data from the nine

subjects for analysis. Thus, data analysis was performed

for 30 subjects, including eight emmetropes and 22 myo-

pes, with a mean ± standard deviation age of 25.4 ±

3.2 years old. The mean spherical equivalent refractive

errors were )2.02 ± 2.03 dioptres (D, range +0.50 to

)6.25D) for the right eye and )1.70 ± 1.93D (range

+0.63 to )5.75D) for the left eye. Astigmatism was

<2.00D for all subjects. The best corrected visual acuity

for all subjects was 0.0 logMAR (Snellen 6/6) or better.

The mean curvature for the front surface of the corneas

were 44.19 ± 1.03D (range 46.37–41.94D) for right eyes

and 44.11 ± 0.87D (range 45.92–41.98D) for left eyes. No

history of eye injury or surgery was reported, and no ocu-

lar pathology was found in routine eye examination. The

research project followed the tenets of the declaration of

Helsinki and was approved by the Committee of Ethics of

Wenzhou Medical College. Informed consent was signed

by each subject before the study.

Apparatus

Data collected with a Pentacam HR system (http://www.

oculus.de) utilizing the Scheimpflug imaging principle and

a Humphrey ATLAS Corneal Topography System with the

Placido-rings were used to compare corneal locations of

the reference points. Since the pupil sizes tended to be

smaller in Pentacam HR measurements than in ATLAS

measurements, even when illumination conditions in the

test room were the same,11 the room light was switched

off in the Pentacam HR tests and switched on in the

ATLAS tests. Both systems had an internal fixation target.

For the Pentacam HR tests, a mode of 25 single captures

in 1-s was chosen, and the instrument automatically

acquired Scheimpflug images once the system was adjusted

by the examiner to the correct position in front of the sub-

ject’s eye. For each subject, right and left eyes were both

tested with the Pentacam HR and ATLAS systems, but

with a randomized order for the eye and the system. Three

measurements were performed at each condition.

Data analysis

The pupil centre was used as the local marker in this

study, and the offset of pupil centre from the reference

centre was the measure of the corneal reference point

location. In the Pentacam HR system, offsets of the pupil

centre in both x- and y-axes were directly provided in the

result panel (Figure 1).

The ATLAS system also provided pupil centre offsets,

but in some cases the pupil edge was wrongly processed

by the software provided in the instrument. This error

could result in an incorrect estimate of the pupil margin.

Errors of this type were easily recognized by the examiner

Comparing reference centres for corneal measurements J Xu et al.

126 Ophthalmic & Physiological Optics 32 (2012) 125–132 ª 2011 The College of Optometrists

because the derived pupil circle did not match the real

pupil. Therefore, the derived pupil centres from the

incorrect pupil circles in these cases were not true pupil

centres. To avoid false estimate of the pupil centre from

the ATLAS system, original images of the tested eyes cap-

tured by the CCD camera of the ATLAS system were

exported from the ATLAS system in a photokeratoscopic

mode. The exported images were processed with a self-

developed MatLab (MathWorks, http://www.mathworks.

com) program to derive the pupil centre. On the original

image, a small white cross indicated the corneal vertex

(Figure 2a). The Matlab program was used to fit the pupil

margin on the figure with a circle. We could change the

size and location of the circle to best fit the pupil margin.

With the best-fit circle and its centre location, the centre

and the offsets of the pupil centre from the corneal vertex

were determined after a calibration of the pupil distance

for each pixel size of the image. A solid white circle was

used to mark the pupil margin (Figure 2b).

To examine the performance of the MatLab program, a

comparison was made between the pupil sizes estimated

directly from the ATLAS system and those derived from

the MatLab program for a group of 19 subjects, whose

pupil margins were obviously correctly measured by the

ATLAS system. We found no significant difference in

the mean pupil sizes between the two methods in either the

right (3.27 ± 0.39 vs 3.27 ± 0.39 mm) or the left eyes

(3.24 ± 0.41 vs 3.21 ± 0.39 mm). The correlation between

the two methods was also very high (r = 0.98, p < 0.0001

for OD; r = 0.99, p < 0.0001 for OS). The widths (the dif-

ference between the upper and lower limits) of 95% limit

of agreement (LOA) between the two methods were 0.74

and 0.73 mm for right and left eyes respectively. Bland–Alt-

man analysis12,13 of pupil sizes determined by the ATLAS

system and the Matlab program for the right (Figure 3a)

and left eyes (Figure 3b) indicated that the MatLab pro-

gram provided pupil estimates that were comparable to the

correct pupil measurements from the ATLAS system.

Figure 1. Result panel of the Pentacam HR system for a measurement of the left eye of a subject. Offsets of the pupil centre from the reference

centre were directly provided in the result panel (left portion of figure encircled with red line). Pupil size was also displayed (lower red line).

J Xu et al. Comparing reference centres for corneal measurements


The mean of three measurements was used as the

final estimate of the pupil centre offsets for each eye.

SPSS 13.0 software (IBM, http://www.ibm.com) was used

to determine means and standard deviations and to sta-

tistically analyze differences and correlations between the

two systems. Comparisons with p £ 0.05 were considered

statistically significant.

Results

There were no significant differences in mean pupil sizes

between the Pentacam HR and ATLAS systems for either

the right or left eyes (p > 0.05 respectively). Bland–Alt-

man analyses showed that the LOA ranges of pupil size

measurements between the two systems in both the right

(Figure 4a) and left eyes (Figure 4b) were very narrow.

There was no significant bias for the mean differences.

For both the Pentacam HR and ATLAS systems, the

mean pupil centre offset in the x-axis was always signifi-

cantly different from zero, but the y-axis offset was not

(Table 1). Surprisingly, there was no significant difference

in the mean pupil offsets between the two systems for

either the right or left eye in any axis (p > 0.05 for all

comparisons). When distances of the pupil centres from

the reference centres were considered, there was no signif-

icant difference between the Pentacam HR and the

ATLAS systems in either the right or left eyes (p > 0.05).

We then analyzed the correlation of the pupil centre

offsets between the two systems. There were strong corre-

lations in both eyes and at both axes between the Penta-

cam HR and ATLAS systems (Table 2, r > 0.90 and

p < 0.0001 for all correlations).

Bland–Altman analyses of the pupil offset distances in

the right (Figure 5a) and left eyes (Figure 5b) had narrow

LOAs with no substantial biases between the Pentacam

HR and ATLAS systems. Similarly, pupil offsets in both

the x- and y-axes in the right eyes (Figure 6a,b respec-

tively) and in the left eyes (Figure 6c,d respectively) had

narrow LOAs with no substantial biases between the two

systems. It confirms that the difference in the pupil centre

offsets between the two methods is not significantly

different from zero as shown by Figures 5 and 6.

(a) (b)

Figure 2. Determination of the pupil margin in ATLAS system photokeratoscopes. (a) Original photokeratoscope image of a right eye pupil with

the reflected Placido-ring was exported from the ATLAS system. The white + marked the corneal vertex. (b) After image processing with a MatLab

program, the white solid circle marked the pupil margin and the dotted big white cross aligned with the Placido ring centre.

(a) (b)

Figure 3. Bland–Altman analysis of pupil sizes determined by the ATLAS system and the Matlab program. The ordinate represents the difference

of pupil sizes determined directly from the ATLAS images and derived from the Matlab program for (a) right eyes and (b) left eyes. The abscissa

represents average pupil size from these two readings.



Discussion

For the 30 subjects tested in this study, there was no sig-

nificant difference in the mean pupil size as measured by

the Pentacam HR and the ATLAS systems for either the

right or the left eye. The pupil size wasn’t significantly

different between the Pentacam and Atlas measurements,

so the potential pupil shift with pupil size8–10 was avoided

thereby making it reasonable to use pupil centre as a

common reference point for the comparison.

The reference point in conventional Placido-ring sys-

tems is located at the corneal vertex. In a previous study

by Mandell et al.,3 the mean distance of the corneal sight

centre, which is the intersect of the line of sight on the

corneal surface and corresponding to the pupil centre

measured by the ATLAS in this study, from the corneal

vertex was about 0.38 mm. This value was about a half of

the mean distance of the corneal sight centre from the

corneal apex, about 0.82 mm. According to their study,

offsets of the pupil centre from the reference centre

(a) (b)

Figure 4. Bland–Altman analysis of pupil sizes determined by the Pentacam HR and ATLAS systems. The ordinates represent the difference of

pupil sizes for (a) right eyes and (b) left eyes for the two systems. The abscissas represent average pupil size for the two systems.

Table 1. Mean pupil size, distance, and offsets of the pupil centre from the reference centre in the x- and y- axes measured by the Pentacam HR

and ATLAS systems

Eye Pupil size (mm) Distance (mm) Pupil offsets ± S.D. (mm) p

Pentacam HR RE 3.27 ± 0.48 0.17 ± 0.09 x-axis )0.07 ± 0.13 <0.0001

y-axis +0.002 ± 0.13 0.99

LE 3.10 ± 0.42 0.15 ± 0.09 x-axis +0.07 ± 0.12 <0.0001

y-axis +0.02 ± 0.12 0.64

ATLAS RE 3.24 ± 0.41 0.16 ± 0.09 x-axis )0.08 ± 0.12 <0.0001

y-axis +0.02 ± 0.12 0.81

LE 3.18 ± 0.37 0.14 ± 0.10 x-axis +0.06 ± 0.11 0.001

y-axis )0.004 ± 0.11 0.81

For pupil offsets, a negative sign for the x-axis represents a temporal shift of the pupil centre compared to the corneal vertex or apex in the right

eye. A temporal side shift in the left eye is indicated by positive sign. For either eye, a negative sign for the y-axis represents a downward shift of

the pupil center. An upward shift is indicated by positive sign. n = 30 eyes.

Table 2. Correlation between Pentacam HR and ATLAS systems of distances and offsets of pupil centre from reference centre for right and left

eyes

Eye Pupil offset Mean difference ± S.D. (mm) Correlation (r) p Value

Right Distance 0.01 ± 0.039 0.90 <0.0001

x-axis 0.01 ± 0.043 0.95 <0.0001

y-axis )0.01 ± 0.027 0.98 <0.0001

Left Distance 0.02 ± 0.038 0.92 <0.0001

x-axis 0.02 ± 0.031 0.96 <0.0001

y-axis 0.02 ± 0.043 0.93 <0.0001

n = 30 eyes.



between the Pentacam HR and ATLAS systems were

expected to be very different from each other because the

two systems were assumed to have different originating

points, the corneal apex vs the corneal vertex. This

assumes that the Pentacam HR system truly utilizes the

corneal apex as the reference point as claimed by the

company. However, we found that the width of the 95%

LOA of pupil centre offsets (the upper–the lower)

between the two systems was <0.18 mm, which was much

smaller than we expected, that is 0.82 mm. Bland–Altman

analyses also showed high agreement between the two sys-

tems in measuring the pupil centre offsets. A previous

study also found that there was only a small difference in

the pupil offset estimates between the Pentacam and

another Placido disk–based videokeratoscope.11 Here, our

study showed there was no significant difference in pupil

(a) (b)

Figure 5. Bland–Altman analysis of the total pupil centre offset (the distance from pupil centres to corneal vertexes), determined by the Penta-

cam HR and ATLAS systems. The ordinate represents the difference of the distance from the pupil centre to the reference centre in right eyes (a)

and left eyes (b) in the two systems. The abscissa represents average distance from the pupil centre to the reference centre.

(a) (b)

(c) (d)

Figure 6. Bland–Altman analysis of the pupil centre offsets differences determined by the Pentacam HR and ATLAS systems. The ordinates of the

left panels (a, c) represent the difference of x-axis pupil centre offsets in right and left eyes derived from the Pentacam HR and ATLAS systems.

The abscissae of the left panels represent average x-axis pupil centre offsets in right and left eyes from the two systems. For the right panels

(b, d), the ordinates represent the differences of y-axis pupil centre offsets, and the abscissae represent average y-axis pupil centre offsets in right

and left eyes.



centre offsets for this group of subjects in either the right

eye or the left eye when pupil size was carefully matched.

Moreover, the distance of the pupil centre from the refer-

ence point was almost identical between the two systems.

The results therefore indicate that the reference centre in

the Pentacam HR system was located on a similar point

as the ATLAS system, which was the corneal vertex.

Several studies have recently reported on the compati-

bility and exchangeability of corneal thickness measure-

ments between the Pentacam system and other

techniques.14–19 To perform the task correctly, finding a

common reference centre for different instruments is a

critical step before drawing any conclusion on the accu-

racy of the measurements for each system. This study

provides a useful example of how to perform such a task.

This is even more important for comparisons of corneal

topography produced by the Pentacam with other topo-

graphic systems.20–23 Having a common reference centre

is equally important to study the relationship between the

ocular and corneal wavefront aberrations of the normal

and diseased eyes. In fact, the pupil centroid was used as

the reference point to centralize the corneal maps mea-

sured by the Pentacam and a Placido disk-based corneal

topography system, the EyeSys, when keratometric values

were analyzed.1 For this type of study, knowledge about

the match of the pupil centres between the two systems is

obviously important.

While this study provides a good example of how to

compare reference points between systems so as to make

use of the measurements from different instruments, the

method, however, has its limits. We have used the pupil

centre as the reference point in this study. Application of

the method to any other system will require the system to

have pupil measurements available. If there are no pupil

measurements, an alternative method will be required.

Accurate estimate of the pupil centre is also critical to use

this method. During the experiment, we found that the

pupil estimate of the ATLAS system was not correct in

some cases. So we developed our own image analysis to

derive the pupil centre for the purpose of this study.

While the method we used was successful, it still includes

a limitation in the procedure of pupil fitting because a

circle was used in this study to fit the pupil margin while

the pupil shape was not perfectly circular for many of

our subjects. It is very likely that a different shape could

better describe the pupils. However, the problem for this

study was that the pupil was fitted with a circle shape in

the Pentacam system and it might cause a comparative

error if we used a different shape to fit the pupil from

the ATLAS image.

In both the Pentacam HR and ATLAS systems, a bright

point is available for the subjects to maintain fixation,

and the measurement can be performed very quickly.

Precise measurement of the pupil centre was achieved in

our study even though the pupil measurement could suf-

fer from a parallax error as in the case of eye tracking

during laser refractive surgery. Therefore we were able to

use this method in the current study. Nevertheless, the

limitation imposed by the accuracy of pupil estimate

should be always kept in mind before use.

Acknowledgements

This study was supported by research grants from Chi-

nese National Key Technologies R&D Program, Beijing,

China (2007BA118B09 to Lu), the National High-Tech-

nology Research and Development Program (‘863’Pro-

gram) of China (2006AA 02A 131), and the Zhejiang

Provincial Program for the Cultivation of High-level

Innovative Health Talents (to Lu).

Conflict of interest

The authors have no financial interests in this work.

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An indirect method to compare the reference centres for corneal measurements