Contact Lens and Anterior Eye, Vol. 21, No. 4, pp. 109-114, 1998 © 1998 British Contact Lens Association Printed in Great Britain

A SIMPLE TECHNIQUE FOR MEASUREMENT OF CORNEAL THICKNESS

C Albarrdn *, R. Mont~s-Mic5 *, A.M. Pons'~, A. Gent* and A. Lorente$ (Received 2April 1998," in revised form 13July 1998)

Abstract -- Measurement of corneal thickness has potential benefit both in the fitting of contact lenses and in monitoring any pathology that could affect corneal thickness. Corneal thickness measurement is undertaken using an accessory to the biomicroscope, the optical pachometer, or by means of expensive apparatus such as the ultrasonic pachometer. There are other complex methods, such as

laser Doppler interferometry, or ultrasonic rasters of the cornea. In this study, an easier and low cost method, based on the measurement of the optical section formed of the cornea by the biomicroscope illumination system, is proposed. The advantages of this new method are the simplicity of its experimental set-up which consists of a calibrated graticule in an eyepiece of the biomicroscope, the speed of the measurement which increases with practice and the low cost, due to the fact that the biomicroscope is standard equipment

in the ophthalmic consulting room.

KEY WORDS: corneal thickness, biomicroscope, pachometry, optical section

Introduction

T he existence of a variety of conditions that affect normal corneal thickness such as keratoconus 1'2,

alteration of the corneal metabolism 2, and oedema caused by hypoxia in contact lens wearers 3,4, demon- strates the importance of having a method of measure- ment of corneal thickness. At present, there are several measurement methods: optical 5-7 and ultrasonic s 13 pachometry and laser Doppler inferferometry. 14,1~

In clinical practice, the most widely used method of corneal thickness measurement method is optical pachometryfi -7 The optical pachometer 16'~7 is an acces- sory for the biomicroscope, by means of which the image of an optical section of the cornea is doubled and the measurement of corneal thickness is obtained when both images are appropriately aligned.

Another method employed to measure corneal thickness is ultrasonic pachometry. 8-1° This technique is based on the measurement of the time elapsed between the emission of an ultrasonic beam from the anterior surface of the cornea and its detection at the same point after being reflected at the posterior surface of the cornea. The major drawback of this method is the necessity for corneal anaesthesia.

In the literature, it is possible to find more accurate, but more complex methods of measurement of corneal thickness. Using ultrasonic pachometry as a basis, Reinstein et al. 1~-~3 have developed a method with which the epithelial thickness can be measured but corneal anaesthesia is required. On the other hand, Hitzenberger et al. ~4,~5 have recently modified laser Doppler Interferometry (LDI), initially developed for axial eye length measurement ~8,~9, in order to allow corneal thickness measurement. The principal advan-

*OD. ~PhD. $OD, MSc.

tage of this method is the fact that it avoids the effect of ocular movements during measurements. 15

Although measurements of corneal thickness depend on the method employed, it is possible to state that the thickness at the centre of the normal cornea ranges from 0.51 to 0.58 ram. 2°

All the above methods require accessories which are not usually present in the consulting room, or involve high cost and technical knowledge, as in the two latest methods. In this work, we propose a simple, low cost method for corneal thickness measurement with an accuracy level sufficient to differentiate between normal and abnormal corneas. For this purpose, a modified biomicroscope is used as a measurement device using only a calibrated graticule in one eyepiece. The graticule, was computer-designed using Corel Draw 7.0 software, then photographed at several different distances. The resultant slides were calibrated with a microscope in order to obtain one with a precision of 0.05 mm.

The illumination system of the biomicroscopC 7 is basically composed of the following elements: a source of illumination (composed in turn of a bulb and a condenser lens), a diaphragm, and a projection lens. The projection lens makes the diaphragm conjugate with the structure under study, in this case the cornea. The image of the diaphragm formed on the cornea limits the width of the incident beam. In the Ktihler systemlL the filament of the bulb is imaged by the condenser system at the projection lens. The illumination system in our slit-lamp is a modification of the standard K6hler system, and the filament of the bulb is imaged between the slit image and the projection lens close to the mirror.

Corneal Thickness Calculation In order to measure the central corneal thickness, a narrow slit (of size H) is projected and imaged onto the cornea with a size h that depends on the light incident at angle, ~, and the size of H (Figure 1). If we consider the

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C ALBARRAN, R MONTt~S-MIC(), &M. PONS, A GENI~ AND A. LORENTE

cornea as a piano-parallel plate, we can evaluate the corneal thickness by measurement of the width of the image slit given by the anterior and posterior surfaces of the cornea (Figure 2), that is, through the measurement of the width of the optical section formed on the cornea.

From the ray tracing in Figures 1 and 2, it would be possible to derive an expression which gives us the corneal thickness, e, depending on the measurement conditions, as well as on the characteristics of the biomicroscope. This relationship can be derived from simple trigonometry:

(1) Formation of the Slit on the Cornea As can be seen in Figure 1, calling H AB=segment between A and B, and C AC=segment between A and C, and taking into account the following geometric relations:

C Hcos(3 - ~)

h - cos(3) h = cos(3) C = H c o s 3 - a)

where: e+e+(~-/3)=~ ~ fi=e+~ we obtain the following relationship between h and H:

h - Hcos(e) cos( + (1)

being the angle of incidence of the light; H the width of the slit measured perpendicularly (~=0), that is, the section of the incident light beam at the corneal plane; h the width of the slit projected at a given angle (~) on the first corneal surface; and e the angle subtended by the image of the slit (h) from the projection lens. Note that when ~=0, h=H, so the measurement cannot be done.

F _CC

(2) Corneal thickness calculation According to the ray tracing shown in Figure 2".

s = h + 2x (2)

where h is given by equation 1, and x is:

sin(b') } /esin(b)= x = etan(b') = e v/1 _ sin2(b') x =

sin(b) = ncsin(b') n ~ / 1 sin2(b)

4

so the value of 2x in equation 2 will be:

2x = 2esin(b)__ (a)

i n ~ - sin2(b)

substituting for 2x from equation 3 into 2, and taking 1 into account yields:

S Hcos(e) 2esin(b) cos(e) + sin2(b)

where:q+~+(rc-b)=~ ~ b=q+~

Thus, the corneal thickness, e, is given by the following expression:

[Scos(e + ~) - Hcos(e)] ( n ~ - sin2(v + ~) e = (4)

2cos(c ÷ ~)sin(v + ~)

S being the width of the optical section measured on the cornea with the graticule, nc=1.377121, and q the angle subtended by h from the image of bulb's filament. The angles e and q are constants depending on the biomicroscope characteristics.

H !

LP

A .

h

Figure 1. Formation of the projection (h) of the slit (H) on the cornea: F: Light source, LC: collimating lens, LP: Projection lens. Ray diagram for the Haag-Streit optical pachometer.

I b!

i b'i iile h i

S

Figure 2. Relationship between the corneal thickness (e) and the width of the optical section (S) measured on the cornea with given illumination angle &). Symbols as in Figure 3. Note that, since F is nearer to the cornea than LP: b > fl, q > e, but a=~.

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A SIMPLE TECHNIQUE FOR MEASUREMENT OF CORNEAL THICKNESS

Method The width S of an optical section of the cornea was measured using a narrow slit of width H that when projected onto the cornea has a width h=h(H, ~), as given by equation 1. To this end, we took a fixed value of H small enough for the approximation of the cornea as a piano-parallel plate to hold. To simplify our computation, the value of H=I mm was used. Thus, the first step was to obtain a slit on the first corneal surface plane with a width of I mm (for ~=0). For this purpose, the focusing rod was mounted in its support and the eyepiece focused upon it; the illumination and observation arms were both set perpendicularly to the rod (e=0 ~ h=H), and then the diaphragm width was varied until its image (slit) on the rod had the expected width of 1 mm (measured with the graticule). Once this value was obtained, we measured the distance between the projection lens and the cornea (dl), and the distance between the image of the bulb's filament and the cornea (de), thus obtaining the values of angles e and rl (Figure 3), (*):

Both angles depend on the characteristics of the slit lamp (through dl and d2), as well as on the width H of the working slit.

These two parameters, dl and d2 can also be obtained by requesting this information from the agent of the manufacturer of the biomicroscope.

In order to measure dl, the slit was projected and

focused on the rod, and then, since the projection lens in the illumination arm is easily accessible in any biomieroscope (see instrument manual), we used a mfllimetre ruler to measure firstly the distance between the projection lens and the mirror, and secondly the distance between the mirror and the rod. Thus, dl will be the addition of these two distances. Regarding d2, the image of the bulb cannot be focused on the rod given its closeness to the mirror, so an accessory device was required. This device was an optical bench and a black target. The optical bench was put in front of the observation and illumination arms, perpendicularly to them, and the black target was displaced along it until the image of the bulb's filament was perfectly focused on the target. Then, the distance between the mirror and the target was measured with the ruler, and the value of dz was derived as the subtraction between the mirror-rod distance and the mirror-target distance.

Five dl and dz measurements were done, and by averaging the obtained distances, d1=(100+3) mm, and d2--(40±1) mm values were obtained. These values yield the following ~ and q angles:

c = arctan = arctan = 0.28650

r /= arctan = arctan = 0.7162 °

The following step is to choose the value of ~. With our graticule we can measure variations of 0.05 mm in the value of S. The minimum value of S which can be measured with our graticule (AS) determines an experimental error in the value of the corneal thickness (Ae), that is, a minimum variation in corneal thickness which our method can discern. Since this value Ae

dt

14 '1

d2

~ LP

H H

Figure 3. Calculation of the angles e and q from the geometrical configuration in Figures 1 and 2. Note that H is equal in both cases because the slit in the cornea acts as the entrance pupil.

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C ALBARRAN, R MONTI~S-MICO, A.M. PONS, A GENI~ AND A. LORENTE

depends on the value of c~, we have used the values of that gives the minimum error Ae in the measurement of corneal thickness within the precision of our device. Figure 4 shows the dependence of the error Ae with e in the measurement of the corneal thickness, for H=I nun. It can be seen that the optimum angles are around 40 ° (range 35-45°), given that these values yield lower thickness variations, and consequently better accuracy. Nevertheless, the piano-parallel plate approximation precludes large angles. Therefore, we restricted our- selves to values between 30 and 40 °, namely c~=30, 35 and 40 ° .

Since the values of H, e, 11 and e are known, we are able to measure S on the cornea (Figure 2) and calculate the corneal thickness, e, from equation 4. For this purpose, the observation arm remained perpendicular to the cornea (as in the H measurement), while the illumination arm was put at e degrees (where e=30, 35 or 40°). The subject was required to look at the slit lamp fixation point, and once the cornea was focused, the value of S was measured.

When the slit was projected on the cornea with the illumination arm at e degrees, an image of the diaphragm (slit) was formed on the anterior corneal surface (A), and a second image was formed on the posterior corneal surface (B). The width of these two images depends on the H value, and the distance between them depends on H and ~. The measured distance S was the distance between the two opposite edges of these two projections (A and B) of the diaphragm (slit) over the two corneal surfaces (Figure 5).

In order to ensure that the central corneal area was being measured, the graticule had several circles into which the pupil, depending on its size, was centred (Figure 6). Thus, the fixation point and the chin rest were moved until the cornea was centred on the graticule.

Results With each of the three illumination angles above, and taking always H=I mm, we made four measurements of S for each of the five subject's right eyes involved in the study. Three of these subjects were emmetropic (ALV, RMM and CAD), while the other two were ametropes (AMP: R E - 5 .50/ - 1.00 x 180 V.A.6/6, AGS: R E - 1.75/ -0 .5 x 180 V.A. 6/6). When the meaurements were made, none of the subjects exhibited any corneal abnormalities.

Table I shows the mean and standard deviation of the measurements.

Corneal thickness e~ was calculated using equation 4 for each of these three mean values So, and the average

Figure 5. Optical section on the cornea showing the two images of the slit in the two corneal surfaces, and the S distance.

0.1

0.09

0.08

0.07

o.o6 E ~" 0.05

LU 0.04

0.03

0.01

20 2; 3'0 3'5 4~3 4'5 5; 5; 60 Angle (°)

Figure 4. Representation of the experimental error (for a typical value of H=I mm) in the measurement of the corneal thickness with our method, versus the inclination angle for the illumination system. Figure 6. Graticule used in the S measurement.

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A SIMPLE TECHNIQUE FOR MEASUREMENT OF CORNEAL THICKNESS

of the values ca, with the corresponding standard deviation, was taken as the value of the corneal thickness (Table 1).

Finally, for the purpose of comparison, we measured corneal thickness using a Haag-Streit optical pach- ometer.

Table 2 shows corneal thickness measured with a Haag-Streit optical pachometer and with our simple procedure for each of the subjects. The difference between both the results of the two procedures is small enough to make our method applicable in daily practice as a technique for excluding the existence of a pathologic corneal thickness.

To make the application of this method easier in the consulting room, it is possible to prepare tables of corneal thickness corresponding to several values of and S. This would avoid having to resort to equation 4 and computation of the angles ~ and q. We include two tables for two different values of H (Tables 3a and b). It should be borne in mind that these tables are valid only for the Magnon SL-250 slit-lamp which was used in our measurements, or any other lamp with a similar illumination system. For other slit-lamps it would be necessary to calculate e and q, and to compute the tables using equation 4.

Conclusion In this study, we have developed a method for measuring corneal thickness. This method exhibits three interesting features: the most important one is the simplicity of the experimental set-up, since it requires only a calibrated graticule in the eyepiece of the biomicroscope and knowledge of its optical char- acteristics. Another desirable feature is its speed of use, since corneal thickness can easily be determined from the value of S alone, the measurement of which

Table 1. Means and standard deviations for the width of the optical section of the cornea, S, for each one of the angles studied.

Subject $3oo (ram) $35o (mm) $4oo (mm) e (mm)

RMM AMP AGS ALV CAD

1.60±0.05 1.75_____0.06 1.93__+0.05 0.56±0.02 1.63±0.05 1.78±0.05 1.93±0.05 0.59±0.01 1.58i0.05 1.73±0.05 1.90±0.05 0.54±0.01 1.60±0.05 1.75±0.05 1.93±0.05 0.56±0.02 1.60±0.05 1.75±0.06 1.90__+0.05 0.55±0.01

Table 2. Comparison between the measurements of the corneal thickness obtained with optical pachometry with our method for each of the subjects.

Corneal thickness (ram) Subject Optical pachometry Graticule method

RMM 0.56 ± 0.01 0.56 + 0.02 AMP 0.58 ± 0.01 0.59 ! 0.01 AGS 0.54 ± 0.01 0.54 ± 0.01 ALV 0.56 + 0.01 0.56 ± 0.02 CAD 0.55 ± 0.01 0.55 + 0.01

becomes faster with practice. Finally, this is a low-cost method, as the only requirement is the addition of a calibrated graticule to an instrument, the biomicroscope that is already present in any ophthalmic consulting room.

Regarding the strong correlation in normal corneas between our method and optical pachometry (Table 2), this is expected since the sources of error, such as the optical quality of the slit-lamp, the subjectivity of the measurement, ocular movements, etc., are nearly the same. This does not imply that the measurement precision of these methods is the same and we think that optical pachometry is more accurate than our technique. Thus, for example, if we measure oedema- tous corneas with our procedure, we would probably obtain very high and 'strange' measurements, indicating an abnormal cornea, which is the objective of this method.

In conclusion, we emphasise that the purpose of this paper was not to develop a more accurate corneal thickness measurement method, but one which is more simple than other methods which require a high level of technical knowledge or expensive accessory instrumen- tation. Our method has not been designed for research

Table 3. Corneal thickness corresponding to several values of S and ~, and for two different values of H (Tables 3a and b)

H=0.5 mm H=I mm 30 ° 35 ° 40 ° ~ 30 °

S S 35 ° 40 °

0.90 0.41 1.50 0.92 0.43 1.52 0.94 0.46 1.54 0.96 0.58 1.56 0.98 0.51 1.58 1.00 0.54 1.60 1.02 0.56 1.62 1.04 0.59 1.64 1.06 0.61 1.66 1.08 0.64 1.68 1.10 0.66 1.70 1.00 0.42 1.60 1.02 0.44 1.62 1.04 0.46 1.64 1.06 0.48 1.66 1.08 0.51 1.68 1.10 0.53 1.70 1.12 0.55 1.72 1.14 0.57 1.74 1.16 0.59 1.76 1.18 0.61 1.78 1.20 0.64 1.80 1.10 0.42 1.80 1.12 0.44 1.82 1.14 0.46 1.84 1.16 0.48 1.86 1.18 0.49 1.88 1.20 0.51 1.90 1.22 0.53 1.92 1.24 0.55 1.94 1.26 0.57 1.96 1.28 0.59 1.98 1.30 0.61 2.00

0.43 0.45 0.48 0.50 0.53 0.55 0.58 0.60 0.63 0.65 0.68

0.40 0.42 0.44 0.45 0A9 0.51 0.53 0.55 0.57 0.59 0.61

0.46 0.47 0.49 0.51 0.53 0.55 0.57 0.59 0.60 0.62 0.64

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C ALBARRAN, R MONTI~S-MICO, A~M. PONS, A GENI~ AND A. LORENTE

use given the higher accuracy of other techniques. It must be considered only as a gross measurement technique, analogous to the confrontation test in the visual field evaluation. Thus, our technique will be useful in detecting marked changes in corneal thickness which may indicate the need for more accurate pachometry. In other words, it is a technique for detecting relatively large corneal thickness abnormal- ities rather than for accurate corneal thickness measure- ment.

Adress for Correspondence R. Mont4s-Mic6, O.D. Departament Interuniversitafi de Optica, Facultat de Fisica, Universitat de Val6ncia, Dr. Moliner, 50 46100 Burjassot (Val6ncia) Spain.

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