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Editor,—Garway-Heath *et al* described a “keratometry and ametropia” method to correct measurements of optic disc size for ocular magnification.1The new method implies that the refraction, the power of the lens, and the power of the cornea are all independent (uncorrelated) variables. Table 2 on page 644 (Summary of ocular biometry) clearly demonstrates that this is not always the case; in fact, the variance of the lens power was almost the same as the variance of the total power of the eye. The explanation has to be that the power of the lens and cornea were negatively correlated. Measurements of the corneal curvature were therefore of little use for their purpose. Garway-Heath*et al *noted that the improvement over the use of uncorrected measurements was moderate, but they failed to draw the obvious conclusion: if correction is necessary, and correction based on spectacle refraction is considered unsatisfactory, correction based on measurements of the axial length of the eye is the only alternative—and quite feasible in these days when ultrasound biometry is used to predict intraocular lens power for cataract surgery.

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Editor,—Bengtsson raises an interesting question about the nature of the complex interaction between the ocular refractive components. He is correct in stating that the new “keratometry and ametropia” method to correct for ocular magnification assumes that the power of the lens and the power of the cornea are independent (uncorrelated). Linear regression analysis of data pooled from our three patient groups (209 eyes) confirms this (Fig 11, significance of regression p = 0.21) and the finding is consistent with previous reports. The power of the lens and the power of the cornea are also unrelated to refractive error.

The refractive power of the eye depends on the refractive power of the cornea, the equivalent power of the crystalline lens, and the distance between the two (F_{e} = F_{1} + F_{L} − [(w/n).F_{1}.F_{L}], where F_{e} = refractive power of the eye, F_{1} = refractive power of the cornea, F_{L} = equivalent power of the crystalline lens, and w/n is a function of the distance of the crystalline lens from the cornea). If two random variables are added to produce an outcome, then the variance of the outcome is the sum of the variance of those variables if they are independent (if there is a degree of positive correlation the variance is higher than the sum, and if there is a degree of negative correlation the variance is lower than the sum). Bengtsson points out that the variance of the lens power is almost the same as the variance of the total power of the eye, and concludes that the power of the lens and cornea must be negatively correlated. There are, however, three variables that contribute to the equivalent power of the eye, the third variable being the term [(w/n).F_{1}.F_{L}]. Table 11 summarises the means and standard deviations for each variable in the pooled data.

The term [(w/n).F_{1}.F_{L}] is highly positively correlated with the power of the lens (*r*
^{2} = 0.73, p <0.000) and less so with the power of the cornea (*r*
^{2} = 0.32, p <0.000). Since this term is subtracted from the other two, it will tend to decrease the overall variance. This partly explains why the variance of the refractive power of the eye is lower than the sum of the variance of lens and corneal powers.

In order to maintain emmetropia in an eye, variables such as corneal power, lens power, and axial length have to be balanced. The relation between corneal power and lens power is modified by axial length.

Both corneal power and lens power are negatively correlated with axial length (*r*
^{2} = 0.17, p <0.000 and* r*
^{2} = 0.36, p <0.000 respectively), so that both corneal power and lens power decrease with increasing axial length. One might therefore expect corneal power and lens power to be positively correlated. However, if axial length is constant, corneal power and lens power have to be negatively correlated to maintain emmetropia. Figure 12 plots lens power against corneal power for the 48 eyes from our combined data set that have an axial length between 23.0 and 23.5 mm.

There is a significant negative correlation (*r*
^{2} = 0.26, p <0.000) between lens and corneal power in this group with relatively constant axial length.

This modifying effect of axial length accounts for the lack of correlation between corneal power and lens power.

Finally, Bengtsson states that we failed to draw the obvious conclusion that ocular magnification correction based on axial length measurement is the only alternative to less satisfactory methods. In our recommendations at the end of the paper, we state that the axial length method should be used in preference to methods that rely on only keratometry and ametropia. We agree with Bengtsson that this is quite feasible these days, with ultrasound biometers readily available in most ophthalmology units. We would urge manufacturers of optic nerve head imaging instruments to include the facility to make corrections on the basis of axial length. The advantage of the new keratometry and ametropia method reported in our paper is that it has little systematic bias with respect to other methods, and is therefore preferable to the other methods when axial length is not known.

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