Aberrations of chick eyes during normal growth and lens induction of myopia

Abstract

Understanding the control of eye growth may lead to the prevention of nearsightedness (myopia). Chicks develop refractive errors in response to defocusing lenses by changing the rate of eye elongation. Changes in optical image quality and the optical signal in lens compensation are not understood. Monochromatic ocular aberrations were measured in 16 chicks that unilaterally developed myopia in response to unilateral goggles with −15D lenses and in 6 chicks developing naturally. There is no significant difference in higher-order root mean square aberrations (RMSA) between control eyes of the goggled birds and eyes of naturally developing chicks. Higher-order RMSA for a constant pupil size exponentially decreases in the chick eye with age more slowly than defocus. In the presence of a defocusing lens, the exponential decrease begins after day 2. In goggled eyes, asymmetric aberrations initially increase significantly, followed by an exponential decrease. Higher-order RMSA is significantly higher in goggled eyes than in controls. Equivalent blur, a new measure of image quality that accounts for increasing pupil size with age, exponentially decreases with age. In goggled eyes, this decrease also occurs after day 2. The fine optical structure, reflected in higher-order aberrations, may be important in understanding normal development and the development of myopia.

Appendix: derivation of equivalent angular blur

Geometrical image blur on the retina is proportional to the first derivative of the wavefront aberration. Therefore, the power of each term in the geometrical angular blur is a factor of the pupil radius less than the power in the Zernike expansion of the wavefront aberration. It is an angular measure of the blur on the retina.

For spherical defocus:

$$ W = {\sqrt 3 }Z_{5} {\left( {2\frac{{r^{2} }} {{r^{2}_{{\max }} }} - 1} \right)} $$

$$ \frac{{\partial W}} {{\partial r}} = {\sqrt 3 }{\left( {4\frac{r} {{r^{2}_{{\max }} }}} \right)}Z_{5} $$

where W is the wavefront aberration, r is the radial position of a ray in the pupil and Z ₅ is the Zernike coefficient for spherical defocus. The ray at the edge of the pupil would have r = r _max The radius of the corresponding blur circle is

$$ {\text{blur}} = \frac{{4{\sqrt 3 }}} {{r_{{\max }} }}Z_{5} . $$

This is the equivalent blur due to defocus, a new measure. Following the definition of equivalent defocus (Thibos et al. 2002c), the equivalent blur due to higher-order, 3rd order and 4th order aberrations are all defined as

$$ {\text{Equivalent}}\;{\text{blur}} = \frac{{4{\sqrt 3 }}} {{r_{{\max }} }}{\left( {{\text{RMSA}}} \right)} $$

where RMSA is the root mean square aberration present. In the presence of a single aberration, RMSA is equal to the Zernike coefficient. The definition of equivalent blur is an approximation assuming that all blur is due to defocus and hence it is only exact for defocus. All other equivalent blur calculations apart from defocus are approximate.