Given the lack of research on the complete design and optimization of multifocal intraocular lenses (IOLs), we propose the design process of diffractive multifocal IOLs focusing on the intermediate distance, and then analyze and optimize the effect of substrate parameters on diffraction efficiency. Multifocal IOLs are mostly based on the superposition of different diffractive optical elements (DOEs) design from inside to outside. When human eyes are in a bright environment, the pupil is relatively small and the edge diffraction periods may not be involved in imaging. Meanwhile, the imaging changes in the transition region and the light interference in adjacent focal points lead to deteriorated visual quality. Thus the multifocal design method with pupil size independent into the IOL optical design becomes a research hotspot, on which many scholars have conducted research. Additionally, as the common view distance of human eyes is intermediate in daily life, optimization of the intermediate distance in multifocal IOL design has also become the focus. On the other hand, DOEs in IOL systems are usually designed with large curvature substrates to carry more diopters due to design space limitations. Combined with the softer material, the diffractive structure is mostly tilted and inclined to be perpendicular to the large curvature substrates, and then the effect of the substrates cannot be ignored. With the continuously improving requirements for visual quality, the future design of IOL substrates will certainly be more inclined to aspheric substrate as a method to improve image quality. In this way, the analysis and optimization of the effect of aspheric substrate parameters on the diffraction performance can bridge the gap between theory and practice in ophthalmic lens design. Through theoretical modeling and simulation analysis, we put forward the analysis and solutions in the above two aspects and hope that our study could serve as a model for the design of diffractive ophthalmic lenses such as multifocal IOLs.

On one hand, for the diffractive multifocal IOL design, we analyze the multifocal diffraction efficiency model through diffraction phase changes based on the scalar diffraction theory. Then we build a design model of multifocal IOL based on the Liou-Brennan human eye model through optical software and simultaneously optimize the modulation transfer functions (MTFs) at near, intermediate, and far distances. Generally, the complete design process of diffractive multifocal IOLs is established through the study of diffraction efficiency and MTF optimization. On the other hand, for the case where the diffractive structure is often tilted and perpendicular to the substrates in IOL design, the schematic design of diffractive IOLs with aspheric substrates is established. By the relationship in the schematic, we derive the expression of period radius and actual phase delay for diffractive IOLs with aspheric substrates. Furthermore, the expression of the actual diffraction efficiency is given for our built multifocal phase profile model. For the example parameters of multifocal IOL design, we analyze and compare the differences between the actual diffraction efficiency and the theoretical diffraction efficiency in terms of the diopters and aspheric synthesis factors. Finally, an optimization method is proposed based on assigning corresponding weights to different periods to compensate for the effect on diffraction efficiency.

Firstly, the diffraction efficiency distribution of multifocal DOE is obtained by the theory model of phase profile [Eqs. (6) and (7)], and the relationship between phase delay β₁, β_2, and diffraction efficiency at each order and overall orders in our experiment is analyzed [Figs. 1(a) and 1(b)]. The diffraction phase profile is obtained according to the focused optimization design of intermediate distance [Fig. 1(c)], and the results show that the diffraction efficiency of the obtained model reaches 0.2685, 0.3597, and 0.2223 at far, intermediate, and near focal points, respectively (Table 1). A multifocal diffraction design focusing on intermediate distance optimization is also obtained. Meanwhile, we establish and optimize a diffractive multifocal IOL system by Zemax, and the MTFs of far, intermediate, and near distances are 0.5528, 0.5840, and 0.5570 at 100 lp/mm, respectively which exceed the MTF of the Liou-Brennan model at 100 lp/mm (Fig. 2) with high imaging quality of IOL design. Then the effect model of diffraction substrate parameters is proposed for the multifocal DOE phase profile design (Fig. 4), and the expressions of ophthalmic lens period radius, actual phase delay, and actual diffraction efficiency for aspheric substrates are obtained. Additionally, analysis of the actual diffraction efficiency can be employed to pick the substrate diopters and aspheric synthesis factors for ideal diffraction efficiency (Fig. 6). We further provide an optimization method, and the results indicate that the optimized diffraction efficiency is in close agreement with the theoretical value and achieves our optimization objective (Fig. 7).

We conduct the diffractive multifocal IOL design and substrate effect analysis. Firstly, the theoretical model of multifocal DOE design is analyzed, and a multifocal IOL focusing on intermediate distance is designed. The MTFs of the IOL at three focal points of far, intermediate, and near distance are 0.5528, 0.5840, and 0.5570 at 100 lp/mm, and the diffraction efficiency reaches 0.2685, 0.3597, and 0.2223, respectively. Then according to the phase profile of multifocal DOE, a theoretical model of the effect of diffractive substrate parameters on diffraction efficiency is built, and the theoretical model in terms of both substrate diopters and substrate aspheric synthesis factors is analyzed. Finally, we propose an optimization method for the substrate effect, and the optimization example shows that the optimization equation can reduce the influence on diffraction efficiency caused by substrate parameters. The design and optimization of multifocal IOLs with high imaging quality are realized, and the ideas can be applied in designing diffractive multifocal IOLs and other multifocal ophthalmic lenses.