What radius does the conventional keratometer measure?

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Abstract
The reflected mire images used in conventional keratometry suffer from oblique astigmatism, resulting in separated sagittal and tangential image planes. Further complications arise if the cornea is assumed to be aspherical. To investigate the consequential effects on the readings--hitherto largely neglected--ray tracing methods were applied to two hypothetical models. One was representative of modern variable-doubling constructions and the other of the Javal-Schiötz design. Both are seen to require the tangential image plane to be focused. Given a spherical cornea, the measured tangential image height can be converted into an accurate radius reading by means of a linear calibration formula. In the Javal-Schiötz design, a non-linear correction is needed for this. Appropriately calibrated in these ways, each model is shown to give readings extremely close to the sagittal radius of curvature at the point of incidence when applied to corneae of conicoidal form. Extensive numerical results are tabulated and the detailed calculating schemes illustrated by worked examples.

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