2.1 Optical principles for in-vivo assessment of LCA

The variation of the optical power of the eye with wavelength quantifies its LCA. An estimation of LCA can be obtained from the experimental measurement of the chromatic difference of refraction (CDRx) [20] from two object vergences (L_B, L_R) of the retinal conjugates of the source commonly for a short (blue, B) and a long (red, R) wavelength within the visible range

Although CDRx is a slight underestimation of the chromatic difference of focus in most eyes [19], many reported studies consider it as a useful estimation of LCA for practical reasons, and so we will do in this work. It is crucial to refer CDRx to the wavelength range used in the experiments before comparing results from different studies. In this study, we consider the range given by B = 455nm and R = 625nm, which corresponds to CDRx ≈1.2 D in normal, healthy eyes, according to the results adjusted from several experimental subjective studies reported by [1].

For the measurement of CDRx in eyes with no accommodation, we combine an autorefractor with a Scheiner disc because it allows better assessment of focus than assessing blur [15]. The Scheiner disc, named after Christoph Scheiner (1619), is a double pinhole aperture with the two pinholes separated away less than the pupil diameter. The disc is placed close to the eye and centered to the pupil. The subject looks through the disc at a distance spotlight, which in our setup is an illuminated narrow slit. Figure 1 shows the basics of the Scheiner principle applied to an eye that, being emmetropic for the green light (a), becomes myopic for the blue (b) and hyperopic for the red (c) as a consequence of LCA. Thus, while the subject perceives one single green image of the slit illuminated with green light –because the two pencils converge on a common focus on the retina (a)-, they perceive two separate images of the same slit for either blue or red illumination –because the retina intercepts the two pencils after or before they converge (b, c).

Chromatic refractive error using Scheiner disc. An eye that is emmetropic for the green light (a) becomes myopic for the blue (b) and hyperopic for the red (c) as a consequence of LCA. The subject perceives a single image of a slit in (a) but two images in (b) and (c).

Figure 2(a) depicts a scheme of the optical setup and how it would work for an ideal emmetropic eye without LCA. A white light source illuminates the slit placed at the front focal plane (F) of a lens. An achromat lens is used to not contribute to LCA. The emmetropic subject is looking through the Scheiner disc at the image of the slit formed at infinity by the lens. Such image at infinity conjugates the unaccommodated emmetropic eye’s retina. Should the eye be virtually free of LCA, the two pencils would converge on a common focus on the retina and the slit would be seen singly for all wavelengths. For a normal eye affected by LCA, a refractive error raises when looking at the slit test, which appears doubled, either under blue (Fig. 1(b)) or red (Fig. 1(c)) lights.

Scheme of the autorefractor combined with a Scheiner disc. (a) Ideal LCA-free emmetropic subject looking at a distance test that is the image through the achromat of the slit at F. Normal emmetropic subject affected by LCA with test placed at the object conjugate through the achromat of their far point: (b) O_R, under red light, and (c) O_B, under blue light.

To compensate the amount of ametropia induced by a given wavelength illumination, the subject needs to shift the slit away from F until an axial point O that conjugates – through the achromat lens and for such a wavelength- with their far point. Figures 2(b) and 2(c) show these adjustments, done for the red and the blue light, successively. In paraxial approximation, from Newton’s lens formula zz'=−f2, with z and z’ accounting for the positions of object O and image O’ from the front and back focal planes (z = FO, z’ = F’O’) respectively, and f the achromat focal length, we obtain the vergence of the far point, which is given by

where k corresponds to the distance between the achromat and the cornea (Fig. 2(b)), which is assumed to be constant. We recall that distances in the direction of light propagation are considered positive, otherwise negative, in Eq. (2). If z_i = 0, then L_i = 0. From the chromatic shift (X) (Fig. 2(c)), we use Eq. (2) to calculate object vergences L_i for i = {R, B} and substitute in Eq. (1) to obtain CDRx.