# A simple technique for measurement of corneal thickness

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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

109

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 =Hcos3- 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)

in~ - 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=~.

110

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 ima

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