Jacobi–Fourier phase masks as ophthalmic elements to correct presbyopia

Purpose Investigations into the correction of presbyopia have considered lens design, clinical implications and the development of objective metrics such as the visual Strehl ratio. This study investigated the Jacobi–Fourier phase mask as an ophthalmic element in the correction of presbyopia. The goal was to develop a contact or intraocular lens whose performance was largely insensitive to changes in pupil diameter. Methods Numerical simulations based on Fourier optics were performed to evaluate three different Jacobi–Fourier polynomials, with the aim of providing a range of clear vision (1 Dioptre (D)). Performance was evaluated for three pupil sizes (6, 4 and 2 mm), while polychromatic images were simulated using three different wavelengths (656.3, 587.6 and 486.1 nm). The Neural Transfer function was included in the simulation. To validate the method and results, we used the Visual Strehl combined objective metric (VSCombined) currently used in visual optics. This metric gives more weight to the phase transfer function and is more suitable for non‐symmetrical phase functions. Results Numerical validation showed the suitability of the Jacobi–Fourier phase masks for extending the range of clear vision of presbyopic eyes, providing a visual acuity of at least 0.10 logMAR (6/7.5 Snellen) at all distances between 1 and 6 m. The results show a range of clear vision of 1D was not affected by changes in pupil size, an increase in retinal image contrast accompanied by image artefact reduction by increasing the radial order of the Jacobi–Fourier phase mask and a reduction of wavelength dependence of the retinal images. These results are supported by simulated images and the objective criterion VSCombined. Conclusions The use of Jacobi–Fourier phase masks as ophthalmic elements for presbyopic correction show promising results, with a good range of clear vision and reduced dependence on pupil size and chromatic aberration.