## ABSTRACT

A method is described of measuring the birefringence of the intact cornea using light reflected obliquely from its posterior surface. The value obtained (0-0037) is in reasonable agreement with the results obtained by using transmitted light and from corneal sections. The change in birefringence with an increase in intraocular pressure from 10 to 40 mm. Hg is about 7 % of this. The change in birefringence was also assessed by changes in the density of the photographic image of the reflected light from the surface, and this affords a possible way in which the intraocular pressure could be measured in the human subject without touching the eye.

## A. THE MEASUREMENT OF THE RETARDATION OF THE CORNEA

Preliminary experiments on the change of corneal retardation with changes in intra-ocular pressure have been described elsewhere (Stanworth, 1949, 1950). Theoretical considerations, together with measurements of the retardation of the cornea at different pressures with transmitted light passing in various directions, led to the conclusion that in order to obtain the maximum change in retardation, measurements should be made in the central zone of the cornea, preferably with a horizontal light path so that the fibres having the main birefringent effect on the light are the vertical ones. In the intact eye, of course, some intra-ocular surface has to be used as a reflector so that the light can reach the observer. In order to avoid the effect of variations in the depth of the anterior chamber and enable the light to be confined to the central zone, the posterior corneal surface was used, the light path being a symmetrical one in the centre of the cornea (Fig. 1). The theoretical basis of the method is as follows.

### (1) The retardation for obliquely reflected light

Let the incident plane polarized light be represented by *u*_{1} = *A* cos *ait* in the plane of incidence, and *v*_{1}*=B* cos *ωt* perpendicular to the plane of incidence.

*P*) on the posterior surface, is given by where ø is the retardation produced by the cornea of the vertical component compared with the horizontal component.

*I*and

*R*are angles of incidence and refraction for incident light at anterior surface.

*I*

_{1}and

*R*

_{1}are angles of incidence and refraction at posterior surface. This is the form of the general expression for an elliptical vibration ; that is, The sign of

*N/M*depends on the relative signs of

*A*and

*B*and the sign of tan (

*I*

_{1}+

*R*

_{1}).

From the known curvature and thickness of the cornea the length of the light path and the values of *I*_{1} and *R* can be calculated for any angle of incidence, the average of the latter being the average angle between the light pathway and the optic axis of the cornea. If then the constants of the elliptically polarized emergent light can be measured, the birefringence of the cornea can be calculated.

### (2) Methods of measurement of the ellipticity of the emergent light

The most accurate methods of measurement of elliptically polarized light involve the use of some kind of half-shade device; in the present instance, however, the observed field is not uniform, and such devices cannot be used. In addition, the positions of the principal axes of the light vary with the retardation and have to be determined for each measurement. The possible methods that can be used are, therefore, both less accurate and less facile than those in general use. The method adopted was to place a quarter-wave plate with its fast axis along the major axis of the emergent ellipse, thus converting the light to plane-polarized light, the azimuth of which was then measured. The ellipticity (e) of the light is then given by the clockwise angle between the major axis, and this azimuth.

The disadvantages of the foregoing method are :

(i) In equation (2), used for determining the numerical value of ϕ, a given change in ϕ will lead to only a small change in

*e*when θ is small. The maximum sensitivity will be when sin 2θ = ±1, i.e. or .(ii) A change in the retardation will, in general, lead to a change in the position of the major axis of the ellipse. The whole procedure for the measurement of the ellipticity should therefore be repeated. Since, however, in the present case, the change in the retardation is relatively small, it was usually sufficient to assume that the position of the axes remained constant, and to take the change in analyser position as a measure of the change in ellipticity. It would obviously be an advantage, however, if the position of the axes remained constant with a change in retardation.

*M = ±N*, tan

*i= ±*1 and tan 2

*i*= ±∞. So, from equation (3), tan 2θ= ±∞ for all values of i.e. for all values of ϕ. And, from equation (2) tan ϕ = ± tan 2e, i.e. This arrangement is that used by Goranson & Adams (1933). In view of these considerations, the plane of polarization of the light entering the cornea was always arranged empirically so as to give a value of θ as near as possible to ± 45

^{0}.

*i*= 45° or 135

^{0}, depending on the sign of cos ϕ.

Since, as described above, a half-shade device cannot be used, the determination of the azimuth of the axes of the ellipse may not always be accurate. To avoid an error from this cause, the quarter-wave plate can be rotated from one side to the other of the estimated position, the least numerical value for the rotation of the analyser—from the position parallel to the axis of the quarter-wave plate to the new minimum position after the insertion of the quarter-wave plate—being a direct measure of the ellipticity of the incident light. That this is the case can be shown as follows :

Let elliptically polarized light with principal axes *a* and *b* fall on a quarter-wave plate with its fast axis at an angle α to the major axis of the ellipse, and then on an analyser at an angle *e’* to the fast axis of the plate.

*1*of light passed by the analyser is given by Differentiating

*I*with respect to

*e’*for a constant value of a, we find that, for the maximum value of

*I*, where

*e”*indicates the analyser position for maximum intensity, and e” is between o and if

*b/a*is positive,

*e”*is between o and if

*b/a*is negative. From equation (4) differentiating

*e”*with respect to a we find that

*e”*has a maximum or minimum value when either

*b = a*(the condition for circulary polarized light) or

*e”*= 0 or (which can only be true if the incident light is plane polarized) or α = 0 or (which applies to any incident light). In the latter case it can easily be shown that if

*n*is an even integer (i.e. the quarter-wave plate has its fast axis along the major axis of the ellipse)

*e”*is at its maximum value if

*bfa*is positive.

But it was shown above that e” is then between o and , so *e* is the minimum numerical value of *e”* in a clockwise direction. Similarly if *b/a* is negative, *e* is the minimum numerical value of *e”* in an anti-clockwise direction.

These relationships are reversed if *n* is an odd integer, the quarter wave plate having its slow axis along the major axis of the original ellipse.

### Results

The Fresnel formulae used are only approximate, so it was considered necessary to verify the method experimentally. A piece of adhesive cellophane tape was fixed on a glass slide, and its retardation measured for normal incidence by transmitted light. The slide was then rotated, first about an axis containing the optic axis of the cellophane tape, and then about an axis at right angles to this, the retardation being measured for varying angles of incidence. The retardation was then measured by light reflected from the back surface of the glass slide; the maximum error was nowhere greater than 6 %. The experimental results with the cat cornea also showed that the method is reasonably accurate ; the retardation of the cornea in a pressure chamber (Stanworth & Naylor, 1950) was measured under constant conditions but with different positions of the polarizer. The calculated retardation varied by only *±* 10 mµ from the arithmetical mean.

The preliminary results (Stanworth, 1950) obtained by reflected light from a cornea suspended in a pressure chamber correspond to a birefringence of the corneal fibres of 0·0037 (for light of wave-length 540 mµ), almost all the results falling between 0µ0030 and 0µ0045. The change in birefringence when the pressure behind the cornea was raised from 10 to 40 mm. Hg averaged 0µ00012, i.e. about 3% of the total. The rate of increase in birefringence decreased at higher pressures, but this had little if any effect below a pressure of about 30 mm. Hg, i.e. over the physiological range.

The experiments were repeated with the whole eye suspended by sutures through the episclera, the pressure being varied through a needle inserted through the optic nerve and past the dislocated lens. In this case the change in birefringence for the above change in pressure was about 7 % of the total. It appears, then, that by far the greater part of the double refraction of the cornea is determined by the structure of the corneal fibre and only a relatively small proportion is due to stress.

## B. THE MEASUREMENT OF CHANGES IN RETARDATION BY PHOTOGRAPHY

Measurement of retardation by density of a photographic image can be very sensitive (Swann & Mitchison, 1950), and was used in the present case in an attempt to make the method sufficiently easy to envisage its application to the human subject.

*I*passed by an analyser at angle

*y*to the horizontal is To obtain the greatest rate of change of intensity with changes in retardation, MA and sin

*2*γ should have their maximum values, i.e.

*M=N*, and γ = 45° or 135°; in these circumstances, , and the polarizer is set as before.

In practice it was not convenient to set the polarizer in this manner, since the anterior specular reflex was not then at minimum intensity and tended to overlap the posterior reflex. The polarizer was set to give minimum intensity of the anterior reflex. Under these circumstances , and the rate of change of intensity is not at its maximum value.

Whatever the polarizer setting, the maximum change in intensity for a given change in ϕ will occur when . If the phase difference is between 0 and 180^{0}, the intensity should increase, but if it is between 180 and 360°, it should decrease, with rising pressure. If it is slightly less than 180^{0}, the slight initial increase in intensity will not produce any appreciable increase in density, and only the subsequent fall will be seen. If the initial phase difference is slightly lower still, a preliminary rise will be followed by a fall. The reverse will occur with an initial phase difference slightly less than 360°.

These predictions were confirmed by measurement, by an S.E.I. densitometer, of 500 photographs taken at different pressures, using the comea suspended as before and fast orthochromatic film (Kodak Ortho. X), at $12$ sec. exposures, in a specially constructed fixed focus miniature camera giving a magnification of x . Comeae with phase differences from 340 to 360° and o to 160^{0} showed an average increase in image density, with increasing pressure, of 0·13; those with a phase difference 180-330° showed an average fall in density of 0·15. Comeae with phase differences of 168, 100 and 330° showed a biphasic response.

These changes in density are sufficiently marked to make it possible to envisage an instrument which, although not recording the intra-ocular pressure directly, would nevertheless measure changes in its value in the human eye with a considerable degree of accuracy, without touching the eye.

## REFERENCES

*J. Franklin Inst*

*Brit. J. Ophthal*

*Acta XVI. Concilium Ophthahnologicum (Britannia)*

*Brit. J. Ophthal*

*J. Exp. Biol*