The Stiles-Crawford Function for Small Foveal Targets

Abstract

Purpose:: To characterize the shape of the Stiles-Crawford function (SCF) in young, visually normal adults for the central 10-minute arc diameter foveal area and for a pupil size (3 mm) typical of common well-lit environments. The foveal SCF might mediate ocular accommodation to the vergence of light.

Methods:: The SCF was determined psychophysically in the left eyes of 28 adults with a twin-channel Maxwellian view system. The target was a flickering spot (548 nm; 10 min arc; 8 Hz) superimposed on a uniform circular field (7 deg). The beam for the flickering target always passed through the center of the natural 3-mm entrance pupil. The beam for the background passed through each of 21 pupil locations on a square sampling grid with a period of 0.75 mm. Data were fit with the numerically stable monomial form log₁₀ rho = a + bx + cy + dx² + ey² + fxy, where rho is the pupil transmittance, and x and y are the pupil coordinates. The frequency distributions of each of the SCF coefficients a through f did not depart significantly from the Gaussian (p > 0.05). Of the 15 possible correlations between coefficients a through f, five correlations were significant (p < 0.04). Thus, the coefficients are not independent.

Results:: The mean base-10 directionality of the SCF (rho value) was 0.035, with a standard deviation of 0.038. The median SCF peak was located 0.2 mm nasal (inter-quartile range 0.92 mm) and 0.3 mm superior (inter-quartile range 0.97 mm) from the entrance pupil center. Due to the nature of the Gaussian distribution of rho values, some SCFs were very flat and/or saddle shaped, and one was inverted. These shapes differ from the classical form, commonly assumed, in which log rho falls off as a second-order polynomial toward the pupil edge.

Conclusions:: The foveal SCF by psychophysical methods appears to be less peaked and of a more variable shape than currently thought.

Keywords: emmetropization • myopia • refractive error development