We have verified that the Pilkington Diffrax lens optically behaves as a diffractive bifocal contact lens. The longitudinal chromatic aberration of the lens is similar to that predicted by theory, both on and off the eye. The over-refraction with the lens on the eye is similar to the distance subjective refraction, which is also as predicted.
Atchison et al.1 investigated whether the Hydron Echelon contact lens exhibited the optical properties expected of a diffractive bifocal lens. Their experiments revealed two lines of evidence which confirmed the diffractive nature of the lens. First, the longitudinal chromatic aberration of the lens was opposite in sign to that of the eye and had magnitude predicted by the theory of diffraction. Second, the power of the bifocal addition, measured as an over-refraction with an automated refractor of eyes wearing the lens, was also predicted by theory. This over-refraction was similar to the subjective distance refraction, which was also expected on theoretical grounds because the zero order (distance) refraction should contain the majority of light intensity for near-infrared radiation used by automated refractors.
The purpose of the present study was to test whether the other commercial diffractive bifocal contact lens, the rigid Pilkington Diffrax lens, also behaved as a diffractive lens.
The methods were similar to the previous study1. Diffrax lenses used were plano power lenses (in air), one each with a back centre optic radius of 7.5, 7.6, 7.7, 7.8, 7.9 and 8.0mm. The specified addition of the lenses was +2.00D. The distance and near powers of the lenses were measured using a focimeter with the lenses placed in a wet cell. Seven interference filters isolated narrow wavelength bands between 420nm and 694nm.
The right eyes of six young subjects were used for refraction and longitudinal chromatic aberration measurements. The lens selected for each subject was according to the manufacturer's instruction, which is to select a lens with a back central optic radius 0.1mm steeper than the flattest corneal radius of curvature measured with a keratometer. Three wore the 7.8mm lens, two wore the 7.7mm lens and one wore the 7.6mm lens. For each of three subjects, a single vision Menicon SP lens was used as a control lens. The same back central optic radii was selected as for the Diffrax lens.
The experimental procedure was as follows. Keratometer readings were taken on the right eye and a contact lens selected. One drop of 1.0% cyclopentolate was instilled in the eye. After cycloplegia was attained, subjective and automated refractions were performed, in that order. Chromatic aberration measurements were then taken. The Diffrax contact lens was then placed in the eye and the refractive error measurements were repeated. For three subjects, a Menicon SP control lens of -3.00D power (in air) was then placed in the eye and the measurements were repeated.
Subjective refraction measurements were made with a 5mm artificial pupil. Automated refractions were made with the Canon AutoRef R1, which operates at 950nm. Results were expressed as Automated refraction minus subjective refraction, and then converted to an equivalent sphere (sphere + half cylinder).
Figure 1. Focimeter results showing addition power as a function of wavelength for the 6 Diffrax contact lenses. Various symbols correspond to different back centre optic radius (in mm). Theoretical results for a diffractive bifocal with an exact addition of +2.00D at 556nm are shown by the solid line.
Longitudinal chromatic aberration was measured by the best focus method using a 140mm focal length achromat Badal lens and a target consisting of two vertically oriented hairs, illuminated by a projector lamp whose output by modified by interference filters. About 6 determinations of distance and near foci were made alternatively at each of 7 wavelengths (only one focus was present for both the no lens condition and the Menicon lens condition). Results were converted to mean refractive error.
Hyperbolic curves of the form Rx = a + b/(
+ c), where Rx is the chromatic aberration in dioptres and
is the wavelength, were fitted by method of least-squares to the mean
data of all subjects for the no contact lens condition, the Diffrax
lenses with distance targets, and the Diffrax lenses with near
targets. Hyperbolic functions have been used successfully to describe
ocular chromatic aberration previously2
and fitted the data well for all conditions. In order to reduce the
inter-subject variance due to residual refractive errors, the
following normalization procedure was followed. Each data set was
fitted with a hyperbolic curve and then shifted vertically along the
refractive error axis so that the hyperbolic curve passed through
zero dioptres at 556nm. The data for all subjects were then pooled to
obtain mean and standard error estimates at each wavelength.
Lens measurements of the longitudinal chromatic aberrations associated with the diffractive addition are shown in Fig. 1, together with the theoretical chromatic aberration for a +2.0D addition at 556nm. All lenses show similar additions, which are linearly related to the wavelength as predicted by simple diffraction theory1.
Figure 2. Difference in refractive errors between the control contact lens condition and the no contact lens condition, plotted as a function of wavelength for three subjects. Ordinate values correspond to the refractive error results for each condition measured with a Badal optometer minus subjective refraction in dioptres.
Refractive errors of subjects are plotted as a function of wavelength in Figs 2 and 3. Fig 2 shows the difference in refractive error between the Menicon (control) lens and no lens conditions for three subjects. There is little change with wavelength, showing that the presence of a single vision low powered contact lens has little effect on the eye's chromatic aberration. With no contact lens in place, the refractive error averaged across all 6 subjects increased by 1.89±0.10D between 420nm and 694nm (Fig 3). A similar amount of 2.04D±0.34D was obtained for Diffrax lenses with distance targets (Fig 3). However, for Diffrax lenses for near targets the mean refractive error only increased by 1.09±0.25D between 420nm and 694nm (Fig 3). These results indicate that the Diffrax lens canceled about 0.8D of the eye's chromatic aberration for near targets. Consequently, the addition power of the Diffrax lens increased significantly with wavelength. The mean increase was 1.05D±0.27D (+1.21D at 420nm to +2.16D at 694nm).
Figure 3. Refractive errors plotted as a function of wavelength for the no contact lens condition, the Diffrax lenses for distance targets, the Diffrax lenses for near targets, and the theoretical predictions for near. Error bars show the mean +/- 1 standard error of mean results for 6 subjects after normalization (see Methods). The curve for the Diffrax lenses for near targets is displaced downwards from the normalized curve by +2.09D, which is the mean addition for the Diffrax lenses at 550nm. The curve for Diffrax lenses for distance targets plus theoretical additions is based on a +2.00D addition at 556nm.
The fitted curves are as follows (wavelength
No contact lens +1.838 - 0.593/(
Diffrax lenses for distance targets +1.449 - 0.381/(
Diffrax lenses for near targets -1.457 - 0.152/(
Diffrax lenses for distance targets with theoretical additions
+1.449 - 0.00360*
As a further test of the diffraction contact lens theory, we attempted to predict the Diffrax results for the near condition. This prediction was computed as the sum of the theoretical addition power expected if the lenses behave as diffraction bifocals1 and the Diffrax results for the distance condition. The prediction is shown by the dashed curve in Fig. 3, which makes a reasonable fit to the mean experimental data (symbols).
Autorefractor minus subjective refraction results were within the range +0.35D to -0.06D across all subjects and all conditions (no lens, distance Diffrax, near Diffrax and Menicon).
The results show that the Diffrax bifocal contact lens, like the Hydron Echelon bifocal contact lens, has the optical properties expected of a diffraction bifocal. The longitudinal chromatic aberration corresponding to near vision is similar to the predicted amount for the lenses by themselves (Fig 1) and on the eye (Fig 3). Our automated refractor results are similar to distance subjective refraction results. These support the theoretical intensity pattern of the Diffrax lens type (Fig 4), for which about 75% of the light at 950nm, where the Canon R1 refractor operates, is in the zero (distance) diffraction order. About 12% in the first order, with smaller amounts in other orders.
Figure 4. Theoretical intensities as a function of wavelength in different diffraction orders for the Diffrax lens type. A step size of 275nm is assumed.
We thank Professor Michael Freeman, inventor of the Diffrax bifocal lens, for providing the results to produce Fig. 4. We thank our subjects, and Mark Lucey and Lawrence Stark for assistance. LNT was supported by a travel grant from the University of Queensland and by N.I.H. grant EY05109.