Allometry and scaling of wave aberration of eyes

The scaling of root mean square (RMS) wave aberration in an isometrically growing eye is investigated, along with changes due to measurements made at different relative pupil sizes. It is found that, relative to an initial state, if an eye expands in all directions by the factor k, and the wave aberration is then measured at a relative pupil size which has changed over the pupil size used for the original measurement by a factor b, the new wave aberration will be increased or decreased by a factor kb(n), where n is the exponent relating RMS wave aberration, to pupil radius, r, in the equation: RMS=qr(n) in the initial eye. This implies that, if wave aberration is measured in a growing eye with a constant measurement pupil size, the measured RMS will decrease by the factor 1/k(n-1).