The Stiles-Crawford Effect of the First Kind: Photoreceptor Optical Waveguides & Pupil Apodization Dynamics

The relative luminous efficiency $\eta(r)$ of a ray of light entering the pupil at a radial displacement $r$ (in millimeters) from the peak sensitivity locus is modeled by:

$$\eta(r) = \eta_{\text{max}} \cdot 10^{-\rho \cdot r^2} \implies \text{At } r = 3.0\ \text{mm} \ (6\ \text{mm Pupil Edge}), \ \eta \approx \mathbf{0.20\text{ to } 0.25}$$

The apodization parameter $\rho \approx 0.05\text{ to } 0.08\ \text{mm}^{-2}$ in healthy photopic cones. A ray entering the periphery of a $6.0\ \text{mm}$ entrance pupil produces less than one-fourth the visual sensation of an identical central ray!

Cone inner segments have a higher refractive index ($n_1 \approx 1.40$) than the surrounding interstitial matrix ($n_2 \approx 1.34$). Like telecom fiber optics, cones capture light via Total Internal Reflection (TIR):

$$\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right) \approx \sin^{-1}\left(\frac{1.34}{1.40}\right) \approx 73.2^\circ$$

Rays entering obliquely from the pupil margin hit the inner segment at angles exceeding the numerical aperture waveguide limit, leaking out into the extracellular space without stimulating photopigments in the outer segment.

Because spherical aberration ($Z_4^0$) and coma ($Z_3^{\pm 1}$) reside overwhelmingly in the marginal peripheral rays of the dilated pupil, the Stiles-Crawford effect apodizes (damps) these rays before they reach consciousness. Without SCE-I apodization, nighttime dilated visual acuity would be degraded by over $40\%$ from marginal optical flare.