Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system

Abstract

We have used a modified double-pass apparatus with unequal entrance and exit pupil sizes to measure the optical transfer function in the human eye and have applied the technique to three different problems. First, we confirm that in the eye the double-pass spread function is the cross correlation of the input spread function with the output spread function [ J. Opt. Soc. Am. A 12, 195 ( 1995)]. Consequently, when entrance and exit pupil sizes are equal, phase information is lost from the double-pass images. Second, we show that in double-pass measurements the eye behaves like a reversible optical system. That is, when entrance and exit pupils are equal, the double-pass image results from two passes through an optical system having a transfer function that is the same in both directions. To test for reversibility in the living eye we have used a double-pass apparatus with different exit and entrance pupil sizes (one of them small enough to consider the eye diffraction limited), so that the ingoing and the outgoing transfer functions are different. The measured image quality was unchanged when the pupils were interchanged, i.e., when the first-pass entrance pupil size becomes the second-pass exit pupil size, and vice versa. Third, the technique provides a means for inferring the complete optical transfer function of the eye, including the phase transfer function, and the shape of the point-spread function.