Fractal-structured multifocal intraocular lens

Abstract

In this work, we present a new concept of IOL design inspired by the demonstrated properties of reduced chromatic aberration and extended depth of focus of Fractal zone plates. A detailed description of a proof of concept IOL is provided. The result was numerically characterized, and fabricated by lathe turning. The prototype was tested in vitro using dedicated optical system and software. The theoretical Point Spread Function along the optical axis, computed for several wavelengths, showed that for each wavelength, the IOL produces two main foci surrounded by numerous secondary foci that partially overlap each other for different wavelengths. The result is that both, the near focus and the far focus, have an extended depth of focus under polychromatic illumination. This theoretical prediction was confirmed experimentally by means of the Through-Focus Modulation Transfer Function, measured for different wavelengths.

Fig 1. FIOL design.

a) Top left: Triadic Cantor set developed up to three steps, S = 3; b) FIOL fractal zones distribution for S = 2, obtained through the coordinate transformation r = b√(x) c) FIOL diffractive profile obtained with K = 3 (see the main text for details).

Fig 2. FIOL proof of concept.

a) Theoretical profiles of the anterior and posterior FIOL surfaces (green line). The red line is the diffractive profile of the FIOL, designed with S = 2 and K = 3 (magnified X5 in the vertical direction in order to show the relative heights of the diffractive steps); this profile was superimposed to a pure spherical profile of a monofocal IOL radius r = 12.42 mm (blue line). b) Interferometric image of the constructed lens.

Fig 3. Theoretical axial PSFs provided by a FIOL.

Results for a lens with distance power 19.5 D (Ad = +3,5D) with different pupil diameters (Φ) and three wavelengths: λ = 490 nm (blue line); λ = 555 nm (green line), and λ = 630 nm (red line). In each plot, the dotted lines are the PSFs (λ = 555 nm) of a monofocal 19.5 D IOL.

Fig 4. Theoretical visual MTF for the different pupil sizes.

These results were computed from the Fourier transform of the monochromatic PSF (the MTF) for the design wavelength λ₀ = 555 nm, weighted by the neural contrast sensitivity function [21].

Fig 5. Optical bench for in-vitro testing.

The object test was mounted on a linear translation stage. As the FIOL to be tested was placed at the image focal plane of L2 we called it: Badal lens. This configuration guaranteed that the angle subtended by the test object, and consequently the spatial frequency assessed in the TF-MTF, was constant for all vergences and equal to 14 cpd. The retinal image was recorded with an X5 microscope and a CMOS camera.

Fig 6. Experimental TF-MTF.

FIOL’s TF-MTF for 14 cpd obtained in the optical bench (Fig 6) with 4.5 mm pupil for different wavelengths. Zero defocus corresponds to far vision.