Design concepts for advanced-technology intraocular lenses [Invited]

Abstract

An intraocular lens (IOL) replaces the natural crystalline lens during cataract surgery, and although the vast majority of implants have simple optics, “advanced technology” IOLs have multifocal and extended depth of focus (EDOF) properties. Optical concepts are evaluated here, with image contrast, focal range, and unwanted visual phenomena being the primary concerns. Visual phenomena with earlier bifocal diffractive lenses led to alternative diffractive designs (trifocals, etc.) and also to exploring increasing the depth of focus for monofocal IOLs using refractive methods, where although the defocus range might be more modest, visual phenomena are much less obvious. The designs cover a range of possibilities that might provide the best overall vision for patients with differing motivations, needs, and sensitivity to visual side effects.

1. Introduction

Intraocular lenses (IOLs) play a critical role in restoring vision for millions of individuals undergoing cataract surgery, where the natural crystalline lens is replaced by a transparent artificial lens. IOLs have evolved significantly since their inception, and modern IOLs are available in a variety of designs, with some broad categories being monofocal, multifocal, trifocal, and extended depth of focus (EDOF). This paper explores the design, development, and clinical applications of advanced IOLs, emphasizing recent innovations that address a variety of visual needs.

IOLs started out as simple rigid lenses with spherical surfaces, with little optical design apart from being a thick lens with a power. The initial lens implanted by Harold Ridley in 1949 was found to be too large and heavy, and early IOLs for both the anterior and posterior chambers rapidly converged on the optic format still widely used today, where the optic element is typically about 6 mm in diameter, and less than 1 mm thick, supported by thin flexible haptics [1]. The diameter often includes a peripheral flange region for IOLs with a lower refractive index in order to reduce incision size. [2].

The success of an IOL as a product depends on both a sound design, and verification of the optical properties of actual lenses during pre-clinical testing in the laboratory. For IOLs, National and International Standards specify the methods manufacturers must use to evaluate their lenses, making these Standards inherently relevant to optical design concepts. Notably, a new edition of the primary ISO 11979-2 Standard (3rd Edition) was released in October 2024 [3], continuing requirements from earlier versions where the modulation transfer function (MTF) remains the principal evaluation method (though alternative methods may be developed and applied). Over time, these evaluation methods have evolved, although the importance of the details have not always been discussed in the scientific literature, and the first section of the paper aims to consolidate and clarify the most essential parameters of the eye models used for IOL design, performance and quality control testing. We note that commercialization involves unique considerations not always relevant to broader scientific studies, a gap that the current study addresses.

There are hundreds of IOL designs in the patent and scientific literature, and many are either previously or currently available for use. Rather than providing a general review of IOLs, which now have an extensive, specialized literature, this paper focuses on advanced lens design concepts currently being implemented in commercial products. The concepts include diffractive principles behind state-of-the-art trifocal and sinusoidal diffractive IOLs, new concepts behind EDOF lenses including phase-shift, periodic refractive, wavefront extended and Isopure IOLs, and IOLs with improved quality in the periphery.

2. Eye models for evaluating IOLs

A primary initial concern about IOLs was the fabrication quality rather than the optical design, with power accuracy and optical quality being the most important issues. There are many methods to measure power, but the original ISO eye model in ISO 11979-2 [4,5] was used for a standardized modulation transfer function (MTF) test (Fig. 1). This test is configured in a manner where it appears to be also related to design characteristics, because an MTF evaluation at 100 lp/mm is used, which is equivalent to 30 cycles/° and 20/20 acuity for an average eye, but the initial use was solely for optical quality testing using a 3 mm diameter pupil and monochromatic light. The concept of a “performance evaluation” later became increasingly important, and aspheric and multifocal IOLs were evaluated using a similar eye model, with evaluations at different foci and with different pupil diameters. Wavefront measurements are typically not used directly for IOLs, and if a wavefront is available it is converted to an MTF for evaluation, with the MTF providing contrast information for the frequency range of interest. It is also typically the case that each power of an IOL model has a single design, even though each lens is used with a range of corneal powers, and axial lengths.

Fig. 1.

(a) Original ISO eye model using glass doublet. (b) ISO2 eye model with aspheric PMMA anterior lens (which also has a specific SA_IOL value). (c) An actual eye with an IOL. (d) Z35a eye model, with anterior PMMA lens and physical dimensions matching a real eye. (e) Z35b eye model with thin anterior PMMA lens.

The simulation of the eye in the ISO eye model is only from the IOL to the image (Fig. 1), with the anterior “corneal” lens physically much further in front of the IOL than a real cornea. The original ISO1 eye model used a glass doublet as the anterior lens, but the later ISO2 modification used an aspheric PMMA “corneal” lens to control spherical aberration (Fig. 1), but without addressing chromatic properties. These models are physically very different to a real eye, and care must be taken when relating image defocus to refractive error. Furthermore, the chromatic properties of the ISO model eyes are not the same as those of an eye even if polychromatic light is used. The chromatic aberration concern was addressed in ANSI Z80.35 [6] with the model eyes in Fig. 1(d) and (e), where the corneal power acts at approximately the correct physical distance from the IOL (called here the Z35a and Z35b eye models). Figure 1(d) takes advantage of the fact that PMMA has approximately the same dispersion as water, and the lens component is more robust than the thin meniscus lens in Fig. 1(e). Eye models like these can be used for either the design or analysis of the axial properties of IOLs, and an actual refractive error at the cornea would lead to the correct image defocus effects at the retina. Designs that have off-axis imaging criteria, such as those discussed below in sections 10 and 11, may have other requirements.

Optical “design” parameters are not always clearly stated in publications, or even in the IOL standards, and they include the following:

• (a)Aspheric IOL designs are typically described as having a certain amount of “spherical aberration” (such as 0.28 µm, 0.2 µm, or -0.28 µm, -0.2 µm, etc.), and the IOL standards envisage this to be the OSA Zernike spherical aberration for a 6 mm diameter entrance pupil of a real eye [7]. The beam converges down to approximately 5.3 mm diameter at the IOL, and that is what is modeled in the ISO2 model eye from the IOL onwards [3,4,8,9]. The standard includes a table where the conic constant of the anterior ISO2 lens surface can be adjusted to provide different “SA_IOL” values, using SA_IOL as shorthand for this complicated parameter in microns that is unique to IOL designs. The sign is always positive for the model eye, and negative for the IOL, despite a positive value often being used. In publications, the term spherical aberration (SA) can mean many different things, and even test equipment for IOLs may provide parameters that do not match this particular definition [10]. There are also many papers relating SA to depth of focus [11,12].
• (b)The ISO2 model eye illustrates some relationships that have become important for IOLs. The Zernike spherical aberration term is only valid for a specific aperture, and it includes an r⁴ component for primary spherical aberration, and also a linked r² paraxial defocus component, whereas some IOL designs control r² and r⁴ characteristics independently (r is radial distance). A conic constant (cc) is used on the anterior corneal lens of the ISO2 eye model to create the aberration, and the model eye then provides the correct aberration level for any pupil diameter, relative to the paraxial focus of the cornea. A real cornea is also often modeled as having a conic constant, though to a 1^st order approximation a term cc*r⁴ /(8*R³) can be used instead, where R is the radius of curvature [13]. The use of a conic constant tends to hide the fact that the main effect is related to spherical aberration. This also suggests that an optical design optimization might have difficulties with both a conic constant and an aspheric r⁴ term, in a similar manner to the conflict between curvature and an r² term (and if a lens had an r² aspheric term, the effect would be added to the power).
• (c)The MTF has become the main evaluation method for ophthalmic optics because it can be evaluated specifically over the range of interest for vision, with wavefronts converted to MTFs because of this ability. The “best focus” has traditionally used the peak 50 lp/mm MTF location for a 3 mm aperture for IOLs, with no strict alternative for EDOF lenses. Another traditional evaluation is to trace rays at different heights and plot their axial intersections (aperture vs defocus), and although this is easy to calculate, the effect on vision may be difficult to interpret (though the related radial power is sometimes evaluated for an IOL alone).
• (d)It is common to defocus the image plane on an MTF system to evaluate the image quality as an object gets closer. ANSI Z80.35 [6] provides equations that can be used to convert the defocus value in mm for the model to the refractive error in diopters at the cornea of a real eye. Publications are not always clear about this topic, and sometimes defocus is plotted as a power change at the IOL instead (with the effect at the cornea being about 0.7 times the effect at the IOL).
• (e)When testing an IOL, power is measured in collimated light without a converging lens, with the measurement characterizing the IOL alone. This test method can also be used for measurements at other wavelengths [14]. Although the chromatic properties can be compared to calculations for the IOL design with collimated light, when modeling the clinical behavior of a diffractive lens in an eye, where a diffractive lens of about 3 D is added to an eye of about 60 D, a realistic eye model must be used instead.
• (f)The early emphasis on lens testing also led to the use of single monochromatic MTF values at 50 lp/mm or 100 lp/mm to characterize a lens, because these correspond to 20/40 and 20/20 vision (or 15 cycles/° and 30 cycles/°) [3]. More recently, many parameters have been considered for their importance to vision [7,15–17], and one particular concept was included in ANSI Z80.35, and it is a reference for the new ISO 11979-2, with broad agreement that the area under the MTF curve up to 50 lp/mm (20/40, not 20/20) correlates well with Visual Acuity (MTFarea) [18]. This recognizes that when a judgement is made about a letter on an acuity chart, it involves many spatial frequencies, and the lower ones are often important. An equation that can be used to estimate clinical visual acuity (VA) from polychromatic laboratory measurements is given, but the MTFarea parameter can also be used directly, and other scaling methods are possible. This can be used for both designing and evaluating IOLs.

The overall outcome from this history is that real schematic eyes can be used for design purposes (Fig. 1(c)), and eye models like Z35a and Z35b can be used for both design and evaluation activities on-axis, particularly where chromatic properties are needed. Off-axis aberrations have traditionally seen little evaluation (though see sections 9 and 10 here). Astigmatism is not directly addressed in this paper, but it is a particular clinical concern, with patient satisfaction being higher when astigmatism is corrected, with most IOL designs also having astigmatism correcting versions, typically using a conventional refractive toric surface.

The terminology used to classify IOL designs is in flux [19], and this paper primarily discusses (i) monofocal IOLs with enhanced depth of focus (mono-EDOF), (ii) extended depth of focus IOLs (EDOF), which intend to provide intermediate vision, and (iii) multifocal IOLs, including bifocal (MIOL), and trifocal, which might also be called full visual range (FVR). All these non-monofocal lenses are in a broader category of simultaneous vision IOLs (SVIOLs), which distinguishes them from potential future IOLs that may have components that change shape or move to provide dynamic accommodation. The word “focus” was used above to define EDOF, rather than “field” [19], and using the acronym avoids having to choose between these 2 terms that are both widely used.

Image contrast, focal range, and visual phenomena are perhaps the main reasons to choose one design over another. A traditional monofocal lens that has optimal asphericity provides excellent vision at just one focus, but other designs extend good image quality to intermediate distances, perhaps with limited visual disturbances, and others provide good image quality over a large range of distances and pupil diameters, but perhaps with more visual disturbances. Patients who are more motivated to be spectacle-free are less likely to consider visual phenomena to be bothersome.

3. General principles for diffractive IOL designs

There are many papers that discuss diffractive optics [8,20,21], and the underlying concept goes back to Augustin Fresnel in the 1810s, where the wave theory of light has oscillations repeating after 1 wavelength (Fig. 2). Regions bounded by 1 wavelength differences in distance between object and image points came to be called Fresnel zones. Fresnel himself did not envisage diffractive lenses, but an early example of a diffractive imaging surface is the “Fresnel zone” plate, where alternating opaque and transparent half-period zones, with no refractive material at all, can form an image with about 10% of the input light energy (Soret, 1875) [22]). If the opaque regions are changed to transparent zones that delay the phase by half a wavelength, then about 40% of the light goes to each of two images (Wood, 1898) (illustrated later in Fig. 3(e)), which is the same energy distribution as a basic multifocal IOL. A diffractive lens works through what might be separately called diffractive and interference effects, but essentially there are specific distances from the lens that are an integral number of wavelengths away from all the zone boundaries. This gives a family of potential focus locations, and if the same phase delay is put across all the zones, so that there is a repeating structure, the energy goes to the image locations (the powers) that give the best overall match for being in phase.

Fig. 2.

Standard bifocal IOL in schematic eye, illustrating the wavefront when viewed from different focus locations, and the resulting MTF plots. Monochromatic evaluations at the design wavelength of 0.546 um. The zone boundaries are at incremental distances from the near focus of 1 wavelength, but the lens material within each zone redirects the light to the intermediate point, and the conflicts set up by this geometry results in about 40% of the light going to the distance and near focus at this wavelength.

Fig. 3.

The Fourier transform of a linear grating (inset) provides a convenient method for estimating the diffraction efficiency of a diffractive lens. The lens zones have equal areas, and the linear grating represents the radial lens surface relief profile plotted against the square of the radius. These are monochromatic calculations at the design wavelength. (a) Underlying monofocal. All energy in original focus. (b) Step heights 1 wave. All energy to near focus. (c) Standard bifocal with 0.5 wave steps. 40.5% energy to each focus. (d) Example of trifocal concept, with alternating steps 0.3 and 0.7 waves. There is an additional focus halfway between the original foci, with a period of the grating now being 2 original periods. (e) Phase reversal zone plate, with same energy balance as (c) at design wavelength, but different focus locations, and different chromatic properties. (f) Sinusoidal trifocal, with different characteristics to (d).

Figure 2 illustrates this for a standard bifocal IOL, and the zones essentially spread out very small phase delays in a wavefront physically across the surface of the lens, and with modern lathes it is easy to directly adjust the phase. The diffractive effects are similar to a linear grating used with collimated light (Fig. 3), where the grating steps are at the square of their radial locations on the lens, and a Fourier transform of the linear phase structure gives theoretical diffraction efficiencies into the different diffraction orders [20,22]. The traditional zone boundary radius r for the ith zone is given by ${r_i}^2=2i\cdot {\lambda }_0\cdot f,$ with ${\lambda }_0$ design wavelength, and f focal length.

Specific reference examples are depicted in Fig. 3 using the design wavelength: (a) With no additional phase structure the light goes to the original focus; (b) With 1 wavelength delays at the steps (which match the zone boundary locations), the light is all redirected into the +1 diffraction order; (c) Reducing the steps to ½ wave, 40.5% of the energy goes to each of the 0 and +1 orders; (d) Alternating the steps to have 0.3 and 0.7 waves there are 3 foci with fairly equal energies (one type of trifocal, but not one pursued as an IOL [22]), and because pairs of zones now form a repeating structure, one of those foci is halfway between the others; (e) A phase-reversal zone plate with ½ wave steps sends 40.5% of the light into each of two foci on either side of the original focus. (f) A sinusoidal structure sends light to 3 foci in the -1, 0, and +1 orders for a grating where 2 zones form a single period. Other step heights give different results, and at different wavelengths there are changes in both the angle of diffraction for a linear grating, which corresponds to lens power, and the energy directed to the different orders. The energy into different orders cannot be chosen arbitrarily, but a design can be chosen from available results.

These same characteristics are present for the diffractive lens, where the structure is scaled by radius r, rather than r², and images are moved to different distances along the optical axis, with different energies. The zones have equal areas, which matches the linear grating. One useful reference point with a diffractive lens is that a diffractive power of an IOL of 3.4 D approximately corrects the chromatic aberration of an entire eye, with a power of about 60 D. This means that a diffractive IOL with an add power of 3D to 4 D largely corrects longitudinal chromatic aberration of the entire eye for just that focus, though the energy balance still changes with wavelength. More broadly, the many types of diffractive IOL can reduce or increase the power change with wavelength for one or more foci, with the energy balance between the foci always changing at the same time.

The chromatic behavior for diffractive lenses that have periodic zone boundary placements can be contrasted with more general “Fresnel lenses”, which have that name because Augustin Fresnel was also involved with enormous lighthouse lenses, which are cut into segments of arbitrary widths in order to reduce size and weight. The 1 wavelength spacing of a diffractive lens makes the image quality well-behaved even as the wavelength changes, because the focus moves in order to retain the 1 wavelength dependence. This geometrical property is always there, even though the phase delay within the zones changes with wavelength. Any diffractive lens always has multiple diffraction orders when used with broadband light, and some diffractive IOLs deliberately target the m =  + 1 or m =  + 2 diffraction orders (see Section 5), while some more general monofocal diffractive lenses employ a multi-order diffractive concept [23]. In principle, diffractive zone boundaries can also be moved to compensate for spherical aberration with IOLs, but aberration adjustment with IOLs is more likely to be implemented as a refractive change using asphericity.

4. Trifocal diffractive IOLs

The development of trifocal intraocular lenses (IOLs) has revolutionized cataract surgery by enabling patients to achieve clear vision at near, intermediate, and far distances without the need for additional corrective lenses. The first commercially available diffractive trifocal IOL was the FineVision IOL [24] (BVI, USA). This uses a combination of refractive and diffractive optics, to achieve an efficient light distribution across three focal points for near, intermediate, and far vision. The base lens usually has a predetermined spherical or toric power, such as +20.0D, and incorporates asphericity to correct for corneal spherical aberrations, and the trifocal powers might be +20.0D, 21.75D, and +23.5D at the plane of the IOL.

The phase shift created by a diffractive surface is proportional to the height h(r) of the surface profile and the wavelength of light λ. The equation governing the phase shift ϕ(r) at a radial distance r from the optical axis is given by:

$$\varphi (\text{r})=(2\pi \ast \mathrm{h}(\text{r})\ast (\text{n}2-\text{n}1))/\lambda$$ (1)

where h(r) is the height of the lens surface at radius r, n1 and n2 are the refractive indices of the surrounding medium and the IOL material, respectively, and λ is the wavelength of light, typically 550 nm. This equation forms the foundation for designing the diffractive profiles like those used in the FineVision IOL. The height profile varies in a zonal manner, and the trifocal lens is also apodized, where the step heights decrease with increasing radial location (Fig. 4). The general equation is:

$$\text{H}(\text{r})=\mathrm{a}\ast (1-({\text{r}}^3/{\text{R}}^3))\ast \lambda /(2\pi \ast (\text{n}2-\text{n}1))\text{mod}[(\text{f}-{\text{r}}^2+{\text{f}}^2)\ast 2\pi /\lambda ,2\pi ]+\pi$$ (2)

where a is an amplitude parameter that controls the design, R is half the lens diameter, and f is the focal length associated with a diffraction order. Trifocal IOLs combine two diffractive profiles, balancing light between near, intermediate, and far distances. The focal lengths for near and intermediate vision are determined by f = n1 / P, where P is the diffractive add power in diopters. For a near vision power of +3.50D and an intermediate power of +1.75D, the focal lengths are calculated as follows: f1 = 1.334 / 3.50 ≈ 0.3811 m; f2 = 1.334 / 1.75 ≈ 0.7623 m. These focal lengths are used to design the diffractive profiles H1(r) and H2(r), which manage the light distribution to the near and intermediate foci, respectively. The FineVision patent describes the height profiles for the near and intermediate foci as using the following equations (Fig. 4).

$$\text{H}1(\text{r})=\text{a}1\ast (1-({\text{r}}^3/{\text{R}}^3))\ast \lambda /(2\pi \ast (\text{n}2-\text{n}1))mod[(\text{f}1-{\text{r}}^2+\text{f}{\text{l}}^2)\ast 2\pi /\lambda ,2\pi ]+\pi$$ (3)

Fig. 4.

Cross section representation of a trifocal apodized diffractive profile.

This profile focuses light for near vision, corresponding to approximately 300 mm (+3.50D).

$$\text{H}2(\text{r})=\text{a}2\ast (1-({\text{r}}^3/{\text{R}}^3))\ast \lambda /(2\pi \ast (\text{n}2-\text{n}1))mod[(\text{f}2-{\text{r}}^2+{\text{f}}^2)\ast 2\pi /\lambda ,2\pi ]+\pi$$ (4)

This profile manages intermediate vision, focusing light at approximately 600 mm (+1.75D).

Both profiles are superimposed onto the lens surface to create the trifocal functionality, and using a1 = 0.44 and a2 = 0.27 the lens is designed to distribute 84% of the light efficiently among the three focal points, allocating roughly 43% of the light to far vision, 28% to near vision, and 15% to intermediate vision as percentages of the focused energy for a 3mm pupil (Fig. 5). This allocation ensures that patients can function across a wide range of activities without the need for additional corrective lenses. The apodization comes from the gradual reduction in diffractive step heights from the center to the periphery of the lens, which optimizes the distribution of light between the near, intermediate, and distance foci, particularly under varying pupil sizes. In bright conditions (small pupils), light is primarily directed to the central portion of the IOL, which maximizes the benefit of trifocality. The apodization aligns with natural pupil dynamics, and under dim conditions (large pupils), apodization ensures that less energy is directed to near and intermediate, and more to far vision. The lower step heights also decrease unwanted light artifacts due to scattering at the steps themselves.

Fig. 5.

Light distribution (%) versus pupil diameter of an apodized trifocal IOL: Only 9% of the light in a 4.5 mm dilated pupil is used for intermediate distance.

An alternative version of the FineVision design also addresses chromatic aberration by adjusting the height of the diffractive zones. This reduces chromatic aberration in varying lighting conditions, enhancing the clarity of vision at all distances. However, the increased step height is more susceptible to increased straylight and perceived glare [25]. A different type of trifocal is the Panoptix IOL (Alcon, Fort Worth, TX, USA), which has a quadrifocal profile, with the majority of the light between distributed between the 0th, + 2nd, and +3rd orders. This functions like a trifocal design with an intermediate focus positioned closer to the near focus than for the other trifocal designs [26].

Clinical studies have demonstrated that trifocal IOLs provides superior visual outcomes over bifocal IOLs, with patients reporting high satisfaction rates for near, intermediate, and far vision [27]. Trifocal IOLs improved uncorrected near visual acuity compared to EDOF IOLs. Uncorrected distance and intermediate visual acuity, halos, and glare were not statistically different between both groups [28]. In particular, patients have noted improvements in their ability to perform daily tasks such as reading, computer work, and driving without requiring glasses.

5. Higher order diffractive IOLs

Typical diffractive bifocal intraocular lenses (IOLs) rely on the 0^th and +1^st diffraction orders to produce images for distance and near vision, respectively. In these designs, the 0^th order contributes to distance vision by utilizing the high-power refractive carrier lens, forming an image of distant objects. Meanwhile, the +1st order contributes to near vision by combining the refractive carrier's power with the diffractive element to create a focused near image.

Due to the periodic nature of diffractive structures, their focusing power is linearly dependent on wavelength. It is higher for the longer wavelengths and lower for shorter wavelengths. Therefore, positive diffraction orders induce longitudinal chromatic aberration (LCA) with a sign opposite to that of the cornea and the refractive carrier lens. The LCA induced by a diffractive profile can be described by the equation:

$$LCA=\frac{-m\cdot |\mathrm{\Delta }\lambda |}{{\lambda }_0}\cdot P({\lambda }_0,1),$$ (5)

where m represents the diffraction order, Δλ is the wavelength range of the broadband spectrum, and P(λ₀, 1) is the power of the diffractive structure at the design wavelength ${\lambda }_0$ .

These configurations help reduce longitudinal chromatic aberration (LCA) at near focus in bifocal designs, or at both intermediate and near focus in trifocal lenses. However, the LCA at the distance focus (m = 0) remains unaffected.

In recent years, alternative designs have been developed to address the effects of the eye’s LCA at the distance focus. These designs utilize diffractive steps with increased heights, to induce a larger phase difference in the incoming wavefront and shift the main interference locations by one or more diffraction orders. By utilizing the reversed LCA that is available for positive diffraction orders, these designs partially compensate for the LCA of both the cornea and the refractive carrier lens, even at the distance focus.

Figure 6 illustrates this approach applied to a typical bifocal profile, where about 81% of the energy is equally distributed between the 0^th and +1^st diffraction orders. In the first-order bifocal design shown in Fig. 6(a), with an addition power of +3.50D, there are inherent trade-offs due to the compensation of longitudinal chromatic aberration at the distance focus, as predicted by Eq. (5). While the power variation of the diffractive element is linearly dependent on wavelength, the eye's change in optical power with wavelength follows a nonlinear, hyperbolic pattern [29], typically resulting in a natural LCA of around 1.7D between 400 nm and 700 nm, varying slightly with IOL material. Shifting the distance focus by one diffraction order can result in overcompensation of the eye's natural LCA (Fig. 6(b)), potentially leading to increased LCA at the near focus and degrading image quality.

Fig. 6.

Phase profile of a bifocal IOL, with a periodic pattern in r² (a), with a step size of half a wavelength (π) that distributes 81% of the diffracted light between two main diffraction orders m = 0 and m =  + 1 (b). The height of the period of the phase profile was increased by one wavelength (2π) (c), to shift the distance diffraction order from m = 0 to m =  + 1 and the near diffraction order from m =  + 1 to m =  + 2 (d).

To obtain a more balanced compensation of longitudinal chromatic aberration at both the distance and near foci, one potential approach is to reduce the power of the diffractive element. This adjustment narrows the through-focus range, resulting in a design that shares similarities with the first extended depth of focus (EDOF) IOL introduced to the market [14]. Figure 7 illustrates the impact of LCA correction across three different bifocal designs.

Fig. 7.

Effect of longitudinal chromatic aberration (LCA) correction achieved by a diffractive bifocal intraocular lens (IOL) under the following conditions: (a) distance focus at the 0th diffractive order with an addition power of +3.50D; (b) distance focus at the +1st diffractive order with an addition power of +3.50D; and (c) distance focus at the +1st diffractive order with an addition power of +1.75D. Defocus is referenced to the IOL plane. Calculations were performed using the Liou & Brennan eye model, incorporating a cornea, with the IOL immersed in an aqueous medium, designed to compensate for the total spherical aberration of the cornea.

.

In a typical trifocal design, the 0^th, + 1^st and +2^nd diffraction orders are used to generate the distance, intermediate and near images, respectively. This is achieved through a diffractive structure with a repeating pattern composed of two parabolic zones. The width of the trifocal period is therefore twice of that of a bifocal with the same near power $({r_i}^2=4\mathrm{\Delta }{\lambda }_0\cdot f)$ , where the power of the diffractive structure at each diffraction order is given by $P({\lambda }_0,m)=m\cdot P({\lambda }_0,1)$ . As a result, the power of the trifocal diffractive structure at the diffraction order m =  + 1 is effectively halved, compared to a bifocal design.

Shifting the profile by one diffraction order allows the +1^st, + 2^nd, and +3^rd diffraction orders to be utilized for distance, intermediate, and near vision, respectively [30]. This diffraction order shift, results in less overcompensation of longitudinal chromatic aberration at the near focus, compared to the first-order bifocal design, as predicted by Eq. (5). However, for typical near add powers around +3.50D, a slight overcompensation at the near focus may still occur.

An example of a trifocal IOL utilizing the +1^st diffraction order for distance focus is shown in Fig. 8. In this example, the diffractive profile has a focusing power of +1.75D, generating a diffractive addition of +1.75D for the m =  + 1 order, + 3.50D for the m =  + 2 order, and +5.25D for the m =  + 3 order. To compensate for the extra +1.75D introduced by the diffractive element at all focal distances, the base power of the refractive carrier is reduced by the same amount. For instance, a 20D lens at the distance focus would consist of a + 18.25D refractive carrier combined with +1.75D added by the diffractive element. This design closely mirrors the FineVision trifocal IOL with LCA correction [31].

Fig. 8.

Phase profile of a trifocal IOL, with a periodic pattern in r² made of two distinct zones (a), that distributes 84% of the diffracted light between three main diffraction orders (c), with order +1 being used for distance. Its chromatic behavior is illustrated on the right plot (b). Defocus is referenced to the IOL plane. Calculations were performed using the Liou & Brennan eye model, incorporating a cornea, with the IOL immersed in an aqueous medium, designed to compensate for the total spherical aberration of the cornea.

This design approach can be extended to any N-Focal configuration and to higher diffraction orders, as in the case of the Tecnis Synergy [32,33].

Compensating for longitudinal chromatic aberration at the distance focus can provide advantages, such as enhanced perceived contrast in distance vision. However, these benefits may be reduced in the presence of significant higher-order aberrations [34] or increased levels of transverse chromatic aberration [35]. Additionally, another potential trade-off is the greater manufacturing complexity, as the taller diffractive structures may lead to more challenging fabrication processes.

6. Sinusoidal diffractive IOLs

The continuous nature of a sinusoidal trifocal profile, such as the Acriva Trinova IOL (VSY Biotechnology, The Netherlands), gives the surface a smoother profile without abrupt steps between adjacent zones. Benefits of this design approach may include easier manufacturing, and reduced light scattering, due to the absence of transition zones. Another advantage seems to be the superior diffraction efficiency obtained with this continuous profile compared to a more conventional parabolic trifocal profile.

Gori et al. (1998) [36] derived an analytical expression for a periodic sinusoidal shape profile known as the “optimum triplicator”, which can achieve a diffraction efficiency as high as 92.56%, across diffraction orders m = -1, 0 and +1, corresponding to distance, intermediate and near foci, respectively. The Phase profile of the optimum triplicator, defined in terms of the radial coordinate r and for a unit grating period, is expressed as follows:

$$\phi (x,a)=ta{n}^{-1}[\alpha \cdot \sin (2\pi x)]$$ (6)

where $\alpha$ modulates the profile's amplitude, thereby influencing light distribution between distance and near foci, and x represents the normalized period length in r² space $\left(\frac{r^2}{2\cdot {\lambda }_0\cdot f}\right)$ .

In 2020, Holmström et al. [37] introduced an additional parameter s, which can be used to shift the profile in the radial r² space $\left(x=\frac{r^2-s}{2\cdot {\lambda }_0\cdot f}\right)$ . This adjustment modifies the shape of the first zone of the diffractive profile, providing another degree of control over energy distribution across the diffraction orders m = -1, 0 and +1, for realistic apertures of limited size. A thorough analysis of the Acriva Trinova sinusoidal profile can be found in Vega et al. [38].

While the “s” parameter adds flexibility, it does not enable independent control of energy distribution among the three foci using only parameter α. To address this limitation, Xing et al. [39,40] proposed a revised phase function incorporating an additional sinusoidal term with a period half that of the first. This formulation includes two new amplitude parameters for tuning the overall sinusoidal profile and the secondary sinusoidal term. The improved sinusoidal phase function is:

$$\phi (x,a)=P_0\cdot ta{n}^{-1}[\alpha \cdot \sin (2\pi x)+C_0\cdot \text{sin}(4\pi x)]$$ (7)

Figure 9 illustrates two sinusoidal profiles based on Eq. (7), each with its corresponding diffraction efficiency.

Fig. 9.

Comparison of two sinusoidal profiles based on Eq. (7) (in a and c), and their respective diffraction efficiencies (in b and d). The profiles use parameter sets P0 = 1.0, α = 2.6572, C0 = 0 and s = 0 mm2 for a) and P0 = 1.2, α = 2.6572, C₀ = -0.5 and s = 0.422 mm² for c), both with focusing powers of -1.75D, 0D and +1.75D at diffraction orders m = -1, 0 and +1, respectively.

In contrast to diffractive designs that use positive diffraction orders for distance focus, lenses utilizing a negative diffraction order to focus at distance require an increase in the base power of the refractive carrier to counterbalance the negative power introduced by the diffractive element across all focal distances. For example, in a 20D lens, the refractive carrier power would be adjusted to +21.75D, with the diffractive element contributing -1.75D to achieve the desired total power.

A key trade-off with the continuous sinusoidal profile is that it achieves distance focus using the negative 1st diffraction order instead of the conventional 0th order. Consequently, this profile introduces longitudinal chromatic aberration (LCA) at the distance focus with the same sign as that produced by the cornea and the refractive carrier, as described by Eq. (5). This increases the cumulative LCA at the distance focus and reduces LCA compensation at intermediate and near foci, compared to a 0th order parabolic trifocal design.

Figure 10 presents through-focus MTF plots at 50 c/mm, comparing the performance of a sinusoidal profile under both monochromatic and polychromatic conditions.

Fig. 10.

Through focus MTF at 50 c/mm, under monochromatic and polychromatic conditions for a sinusoidal profile modelled by Eq. (6), using parameters P₀ = 1.2, α = 2.6572, C₀ = -0.5 and s = -0.422 mm², with focusing powers of -1.75D, 0D and +1.75D at diffraction orders m = -1, 0 and +1, respectively. The model eye uses a physiological cornea based on the Liou & Brennan eye model [41]. Polychromatic calculations are based on the methods described by Ravikumar et al. [42], sampling the visible spectra in 5 nm steps (61 wavelengths). Defocus is referenced to the IOL plane.

While the sinusoidal profile demonstrates higher diffraction efficiency relative to parabolic trifocal profiles, this advantage may not fully extend to real-world polychromatic lighting conditions.

7. Phase shift design for extending the depth of focus

The design of intraocular lenses is a constantly evolving field, where advanced optical techniques are employed to optimize light usage and enhance visual perception. Multifocal IOLs have progressed from bifocal [43,44] to trifocal designs [45], offering simultaneous correction for distance, intermediate, and near vision, greatly improving spectacle independence. However, a key challenge remains: achieving distance vision quality comparable to monofocal lenses while ensuring a seamless transition from distance to intermediate vision. To meet these demands, the criteria in Table 1 were identified.

Table 1. Key Requirements Based on Patient Needs.

	Photopic	Mesopic
Distance	Satisfying correction at 20/20	Monofocal-like correction
From distance to intermediate	Continuous correction	Functional correction

One method to extend the depth of focus that has attracted considerable attention in areas like infrared imaging, lithography, and optical design, is the phase mask technique [46]. Annular phase shift zones can introduce controlled blurring that remains consistent across different focus positions, and this extends the depth of focus while keeping the point spread function (PSF) nearly constant. This consistency ensures stable image quality over a broad defocus range, and Fig. 11 illustrates a simplified phase shift template [47] in the optical path difference (OPD) space at the entrance pupil for a model eye. The template consists of an inner and outer zone, where the outer zone is similar to the lens design of the underlying monofocal IOL, and it is primarily used for distance vision under mesopic conditions. In photopic conditions, when the pupil is smaller, the inner zone—with distinct curvatures and a phase shift step at a mm, a width of b mm, and a height of c µm—modifies the wavefront, creating an interference pattern. By optimizing these parameters, the inner zone corrects distance vision and provides a relatively continuous range of correction from distance to intermediate.

Fig. 11.

Schematic representation of a design template in the optical path difference (OPD) space at the entrance pupil of the model eye. The template comprises an outer zone that replicates the monofocal lens design, and an inner zone that incorporates a phase shift step to modulate the wavefront, generating an interference pattern.

Table 2 summarizes a pseudo-optimized design example. For the optical analysis, the photopic and mesopic iris pupil sizes were set to 3.0 mm and 4.5 mm, corresponding to entrance pupil diameters of 3.4 mm and 5.1 mm, respectively. Figures 12(a) and 12(b) show the through-focus MTF performance of the phase-shift design compared to a standard monofocal design in an eye model [41]. Figure 13 simulates retinal blur images of a 20/40 tumbling E at various distances for different designs. The results indicate that the design successfully balanced patient requirements for distance and intermediate vision under both mesopic and photopic conditions, as outlined in Table 1.

Table 2. Pseudo-Optimized Design Example: Parameter Summary.

ri (mm)	hi (µm)	a (mm)	b (mm)	c (µm)
1.20	0.80	0.80	0.20	-0.20

Fig. 12.

Through-focus MTF performance comparison of the lens design in an eye model, λ= 550 nm: (a) For small photopic pupil size (3.0 mm), showing the modulation transfer function across different focal points. (b) For large mesopic pupil size (4.5 mm), illustrating the MTF under low-light conditions.

Fig. 13.

Simulated retinal blur images of a 20/40 tumbling E at a wavelength of 550 nm: Comparison between monofocal and phase-shift designs under different pupil sizes. The images illustrate the visual performance for (a) small photopic pupil (3.0 mm) and (b) large mesopic pupil (4.5 mm)

Figure 14 simulates the perceived halo effect during night driving. The phase-shift design significantly reduces the halo typically associated with bifocal lenses, bringing it to a level comparable to monofocal lenses.

Fig. 14.

Simulation of the retina-perceived halo effect under night driving conditions, with a typical car’s headlights at 50 meters away. The simulation assumes a scotopic entrance pupil size of 6 mm and a wavelength of 550 nm. The contrast sensitivity of rods spans approximately 4 log units of light intensity, from threshold to saturation. The phase-shift design is compared to a typical bifocal design and a monofocal design to evaluate halo mitigation under these conditions.

While Table 2 demonstrates the feasibility of using phase shift technology to achieve the design goals, other variations utilizing the phase mask technique [48] can also meet similar objectives. The design process follows classic lens design principles, including template selection, merit function establishment, parameter optimization, and tolerancing. Success depends on factors such as pupil size selection [49,50], incorporating contrast sensitivity into optical calculations [51], modeling visual artifacts like halos, and learning from prior IOL designs. Ultimately, it is the combination of these elements that has made this technique effective in the design of EDOF IOLs.

8. Periodic refractive extended depth of focus (PREDoF) design for presbyopia

A number of design strategies to overcome presbyopia have been proposed to address the growing demand for enhanced visual quality across a range of object distances. One of the earlier designs was based on the refractive principle, using multiple concentric power zones for far and near vision. Although this design improved near visual quality, significant concerns arose regarding the substantial loss in far vision quality and poor intermediate vision. Diffractive designs, such as bifocal and trifocal lenses, then gained much attention, as they provided sharper images at the designated focal points compared to the refractive bifocal design. However, these diffractive designs could still cause undesirable visual symptoms, known as “photic phenomena,” such as halos, glare, and starbursts [52,53]. This is because these designs rely on redistributing light energy to specific and discretely spaced focal distances, which results in significant blur at other distances. To minimize these visual symptoms, EDOF approaches [54–58], based on both refractive and diffractive principles, have recently emerged as a new trend in presbyopia correction. These EDOF lenses have been shown to significantly reduce photic phenomena. However, the range of depth of focus remains limited, and their performance can vary with changes in pupil size.

Recently, a new design concept was proposed for a periodic refractive EDOF (PREDoF) lens [59]. This approach offers two main advantages: (1) the distribution of light energy can be more precisely controlled throughout the depth of focus by adjusting the local refractive power, and (2) the periodic nature of the power profile across the lens reduces performance variation with different pupil sizes. The method begins with a power profile that is repeated periodically across the lens. The power profile can be designed based on specific requirements of retinal image quality through focus and the targeted depth of focus. Once the power profile is established, it can be converted into the wavefront (or phase) profile by using the relationship given by the equation below.

$$P(r)=\frac{1}{r}\frac{dW(r)}{dr}$$ (8)

where W(r) represents the wavefront, P(r) represents the local sagittal wavefront vergence (local refractive power) at a radial distance, r, from the pupil center, and dW(r)/dr represents the first derivative of the wavefront.

Figure 15 shows two different PREDoF designs as examples demonstrating the feasibility of controlling through-focus performance. Each design was optimized for retinal image quality within its respective depth of focus: 1.2 D and 2.5 D. These designs were based on power profiles derived from sawtooth (AP*((sawtooth(cyc*Θ) + 1)/2)^E) and sine (AP*(abs(sin(cyc*Θ))^E) functions, respectively, where AP denotes add power distributions ranging periodically from 0 to AP, cyc is the number of cycles and Θ varies between -2π and 2π across a 6 mm lens diameter, as shown in Fig. 15(a). The variable E is an exponent of the power profiles. The variables, AP and E can be adjusted to optimize the through-focus characteristics of a design based on individual needs. The Visual Strehl Optical Transfer Function (VSOTF) [60] under white light conditions was calculated from the wavefronts to represent through-focus retinal image quality, and the performance of the two PREDoF designs was compared to the diffraction-limited case (Fig. 15(b)). Both designs effectively improved intermediate and intermediate/near vision performance, while reducing the value of the parameter for far vision.

Fig. 15.

Two examples of the PREDoF designs for 1.0 D and 2.5 D DoF. (a) power and corresponding wavefront maps for 6 mm diameter and (b) theoretical through-focus retinal image quality evaluated by polychromatic visual Strehl optical transfer function (VSOTF) for a 4 mm pupil under monofocal i.e. diffraction-limited case (dotted line), 1.2D DoF (dashed line) and 2.5D (solid line) conditions. Defocus is referenced to the IOL plane. (c) shows through-focus retinal image quality for two designs based on the sine power profile ranging from 0 to 1.25D (top) and 0 to 2.25D (bottom). (d) shows through-focus retinal image quality of the 2.5D PREDoF design for three different pupil sizes, 3, 4 and 5 mm in diameter

The PREDoF design method demonstrated remarkable flexibility in creating refractive wavefronts that provide continuous and smooth through-focus retinal image quality over a range of depths of focus. Designs can be easily customized to meet the specific needs of individual patients by manipulating parameters associated with the periodic optical power profile (Fig. 15(c)), while also exhibiting a level of tolerance to changes in pupil size (Fig. 15(d)), lens decentration, and uncorrected aberrations in the eye. However, the well-documented trade-offs between overall image quality and the magnitude of depth of focus still exist, and investigating acceptable levels of optical blur that the presbyopic visual system can tolerate is crucial for further optimizing performance

9. Wavefront EDOF and multifocal IOLs

Deliberate modifications of spherical aberration can lead to EDOF lenses that can mitigate the effects of presbyopia without inducing nighttime symptoms [61–63]. A baseline sphero-cylindrical correction provides vision at distance, with the lenses either a) inducing positive or negative spherical aberration in the central pupil (zone I in Fig. 16(a)) for a wavefront EDOF lens), or b) inducing opposing spherical aberration in the center section and the annular central zone (zone Ia and Ib in Fig. 16(b)) for a wavefront multifocal lens.

Fig. 16.

(a) The pupil is divided into a circular central zone I and an annular peripheral zone II for wavefront EDOF lenses. (b) The central zone is divided into a center zone Ia and an annular zone Ib for wavefront multifocal lenses.

9.1. Wavefront extended depth of focus (EDOF) lenses

The wavefront characteristics provided by a wavefront EDOF lens across the pupil of the eye are expressed as [61] (Table 3)

$$\mathrm{W}(\rho ,\theta )=C_f{\rho }^2+C_s{\rho }^4\text{if}\rho <=2.25\text{mm}$$ (9)

where W(ρ, θ) is the wavefront error induced by a wavefront EDOF lens, ρ is the radial distance in the pupil plane (3 mm for a 6 mm pupil). C_f and C_s are constants, giving a focus shift of C_f ρ² and spherical aberration in the central pupil of C_s ρ⁴. There is a multifocal effect from the focus term, and other effects from the induced spherical aberration: 1) making the defocus effect asymmetric, 2) extending depth of focus up to around +0.5D when the eye’s pupil is relatively small, and 3) providing some mitigation for astigmatism and coma if significant in the central pupil [64]. The reading benefit is for well-lit conditions, and it is particularly significant for eyes with excellent acuity for distance. Table 3 lists 3 other specific examples: a truncated sinusoidal wavefront profile, a Gaussian wavefront profile, and a radial power profile of a Tayler series.

Table 3. Examples of presbyopia-correcting lenses that induce spherical aberration in the central pupil.

	Radial wavefront profile or radial power profile in the central pupil	Wavefront errors in the central pupil (zone I Fig. 16(a))	Comments
Wavefront profile of polynomials	W(ρ, θ) = Cf ρ2 + Cs ρ4 (ρ<2.25 mm)	W(ρ, θ) = Cf ρ2 + Cs ρ4	Inducing a focus shift, a spherical aberration,
Truncated sinusoidal wavefront profile	W(ρ, θ)= A* cos(b* ρ) (ρ<2.25 mm)	W(ρ, θ) =A – A*b2*ρ2/2! + A*b4*ρ4/4! - A*b6*ρ6/6! +…	Inducing a focus shift, a spherical aberration, and many higher order spherical aberrations
Gaussian wavefront profile	W(ρ, θ) = a* exp (- c*ρ2) (ρ<2.25 mm)	W(ρ, θ) =a - a*c2* ρ2 +a*c4* ρ4 - a*c6* ρ6 +…	Inducing a focus shift, a spherical aberration, and many higher order spherical aberrations
Radial power profile of a Tayler series	Φ(ρ) = 2.2862 + 1.1583 ρ -11.869 ρ2 + 11.356 ρ3 -3.0736 ρ4 (ρ<1.5 mm)	W(ρ, θ) =a constant - 1.1431 ρ2−0.3861 ρ3 +2.839ρ4 -2.2712 ρ5 +0.5122 ρ6 (ρ<1.5 mm)	radial power profile and radial wavefront profile are related by Φ (ρ) = -(1/ ρ) * dW/dρ

9.2. Wavefront multifocal lenses

An alternative design concept is to use 2 different wavefront corrections [61] as

$$\begin{array}{ll}\text{W}(\mathrm{\rho },\mathrm{\theta })& ={\text{C}}_{\text{f}0}{\mathrm{\rho }}^2+{\text{C}}_{\text{f}0}{(\mathrm{\rho }/{\mathrm{\rho }}_0)}^4\text{if}\mathrm{\rho }<{\mathrm{\rho }}_0\text{mm in Zone Ia}\\ & ={\text{C}}_{\text{f}1}{\mathrm{\rho }}^2+{\text{C}}_{\text{s}1}{(\mathrm{\rho }/{\mathrm{\rho }}_1)}^4\text{if }{\mathrm{\rho }}_0<=\mathrm{\rho }<={\mathrm{\rho }}_1\text{in Zone Ib}\end{array}$$ (10)

where C_f0, C_f1, C_s0, and C_s1 are constants, 0.8 mm<= ρ₀ <=1.25 mm, and 0.9 mm<= ρ₁ <=2.25 (with an example being C_f0 ρ² for a focus shift of 1D, C_f1 ρ² for a focus shift of 0.37D_, C_s0 = 0.7 microns, C_s1= -1.11 microns, ρ₀ =1.15 mm, and ρ₁ =1.75 mm). These Spherical Aberration terms have opposite signs, meaning one of C_s0 and C_s1 is positive while the other is negative. This concept was implemented as the MiniWell IOL (SIFI, Italy), which induces spherical aberration of opposite signs in the central optical zones according to Eq. (10), with two foci for far and near shown in Fig. 17(a), while the focus for near vision by itself is EDOF for an aperture size of 3 mm. The through-focus MTF curves in Fig. 17 were are for a Mini Well IOL +20D measured using a NIMO system (Lambda X, Belgium) with two apertures. [62]. Clinical results of Mini Well IOLs in a multicenter trial were published in 2020 [63].

Fig. 17.

Measured through-focus MTF of a Mini Well IOL +20D for 50lp/mm (Blue) and 25 lp/mm (green). (a) 3 mm aperture. (b) 4.5 mm aperture. Defocus is referenced to the IOL plane.

The optical properties of a wavefront bifocal lens are not explained intuitively using geometrical optics. The design of wavefront multifocal lenses requires a balance that involves a range of focus locations and pupil diameters, and presbyopia corrections from +1.0D to about +3D can be created [64]. With an actual design, Fourier Optics can be used to: a) determine optical performance, b) calculate retinal images for an individual eye if its wave aberration is known, and c) determine the retinal image at nighttime with or without the eye’s aberrations (with simulation results indicating that halo and nighttime symptoms are similar to natural aberrations because the induced wavefront changes are relatively small).

Newer concepts for lenses that modify the wavefront have already been described in the patent literature [64,65] including non-diffractive trifocal lenses, EDOF improvements, and a reduction in pupil size dependency.

10. IOLs and peripheral optics

In the phakic eye, the crystalline lens is thick, with a gradient refractive index distribution, that produces a relatively high image quality over a large visual field [66]. Traditionally, IOLs have been designed to provide good image quality only in the central area of the fovea without considering their performance in the peripheral retina. Most current IOLs have biconvex designs and are thin to facilitate an easier implantation. These two facts are responsible for a degraded image quality in the peripheral retina in comparison to the natural eye. Although this has been known for a long time [67,68], there was little clinical attention, assuming that this degradation would not surpass the retinal and neural limits occurring in the periphery. However, Jaeken et al. [69] showed that patients implanted with biconvex IOLs experienced significantly larger astigmatism and defocus in the periphery compared to the fellow eye with their natural crystalline lens. More recently, Togka et al [70] showed that this optical deterioration also produces a significant reduction of the detection contrast sensitivity in the peripheral visual field.

Reduced visual quality in the periphery after cataract surgery may have significant consequences in the quality of life [71], being good peripheral vision necessary for many visual tasks, such as navigation, object recognition, simultaneous tracking of multiple objects at once, or saccade planning. In addition, a recent study has shown that a degraded peripheral optics can affect tasks such as navigating steps [72] and driving [73]. Moreover, impaired peripheral vision is associated with an increased risk of falls, highlighting its importance in overall visual performance.

The poor peripheral optics, and their visual effects in pseudophakic patients, led to the development of an alternative IOL that provides improved image quality for peripheral vision. The lenses were designed to mimic the peripheral performance of the natural crystalline lens, and they have an inverted meniscus design [74]. The radius of curvature of the posterior surface is smaller than that of the anterior surface by a factor that depends on IOL power, and Fig. 18 shows an example of this type of lens (ArtIOL, Voptica SL, Murcia, Spain) compared with a standard biconvex lens. Figure 19 shows the calculated point-spread functions at different eccentricities in a real eye, and two eyes implanted with a standard biconvex lens and an inverted meniscus IOL.

Fig. 18.

Optical coherence tomography images of pseudophakic eyes implanted with an inverted meniscus lens (ArtIOLs) (left) implanted in comparison with a typical biconvex IOL (right) implanted.

Fig. 19.

Point-spread functions (PSFs) as a function of eccentricity calculated for eye models of a phakic human eye model (top row).

These lenses have already been implanted in a large group of patients, showing an improvement of both image quality and peripheral contrast sensitivity. Figure 20 shows the average peripheral refraction in a group of patients implanted with standard biconvex lenses and with inverted meniscus lenses [75].

Fig. 20.

Mean values of peripheral spherical equivalent (left) and peripheral astigmatism (J0) (right) for eyes with ArtIOLs 25 (blue) implantation, and control (red) groups (CG). Error bars are standard deviation across subjects and are displayed as upper error bars and lower bars in one direction only to avoid overcrowding. Data from 12 to 19 degrees, coinciding with the excavation of the optic disc, were removed (from reference 10).

An additional observation with these new IOLs was that while implantation of a biconvex IOL seems to induce eccentricity-dependent shifts in the visual field, this is apparently less of an issue with the inverted meniscus IOLs [76]. Pre- and post-operative fundus retinal images of cataract patients were used to measure the displacement of retinal landmarks induced by IOL implantation as a function of eccentricity, finding that it was less noticeable for inverted meniscus lenses than for biconvex IOLs. This suggests that the world-to-retina mapping might be altered after standard IOL implantation, but not with reversed meniscus IOLs.

11. Multiconfiguration surface optimization: the isoplanatic and the isofocal concepts

A major advance in refractive IOL design a couple of decades ago was the use of at least one aspheric surface. Spherical IOL surfaces induced positive spherical aberration adding to that of the cornea, while aspheric surfaces allowed negative-spherical aberration inducing IOLs, mimicking the compensatory effect found in the young crystalline lens to balance corneal spherical aberration [77].

Taking this further, the optimization of a higher number of lens surface design parameters (i.e. radius of curvature and several conic constants) can use a higher number of degrees of freedom to optimize performance metrics that verify several conditions. This approach uses a multiconfiguration method whereby a composite merit function targets optimal retinal image quality, for example at both the fovea and multiple peripheral retinal eccentricities (Isoplanatic IOLs [78]), or for both distance vision and a specified intermediate/near focal range (Isofocal concept [79]). In addition to the optimization target, boundary conditions can also be imposed, which might be related to performance (e.g. pupil independency), or to provide some immunity to tilt, or to control the geometry (e.g. peripheral lens thickness, maximum vault, or integration with the haptic platform).

The principal innovation lies in the development of a design strategy that employs a realistic refraction-dependent multi-surface computer pseudophakic eye model, and an IOL with surfaces described by a set of optimization variables, coupled with a multiconfiguration optimization approach. Unlike other methods that describe the IOL by its aberration values (e.g. 4th order spherical aberration or a combination of aberrations), this method approaches directly the optimization of IOL surface geometries, targeting retinal image quality, instead of specific aberrations, such as coma and astigmatism in the periphery, or spherical aberration. This leads to IOLs with smooth, continuous refractive profiles, which for example can improve peripheral image quality, or extend the depth of focus.

In the Isoplanatic IOL designs, eye models were defined for each IOL power, considering relations between refractive error, axial length and retinal shape. The optical target was defined as an optical quality metric evaluated simultaneously across the field of view between 0 and 10 deg in 2.5-deg steps, with weights ranging from 1 to 10. Boundary conditions enforced a given IOL power, and constrained the central and peripheral thickness of the IOL. The surfaces of the IOL were described by anterior and posterior radii of curvature, three aspheric coefficients (2^nd, 4^th and 6^th order), and central and peripheral IOL thicknesses, with a 6-mm diameter IOL optical zone. This design strategy was found to improve off-axis performance by between 0.2 and 0.6 um RMS in comparison to four leading IOL designs (Fig. 21), while also improving the axial performance in some cases.

Fig. 21.

Simulated optical performance (RMS wavefront error) as a function of field angle for commercial IOLs (black symbols and lines) and for new isoplanatic IOL designs obtained using a multiconfiguration approach to optimize performance in a range of eccentricities from 0 to 10 deg. The values represent averages for six anatomically realistic eye models, and error bars represent standard deviations. The insets represent the commercial IOL profile (black) and the new isoplanatic design, with the optimized radii of curvature and three conic constants per surface (red). The examples are for IOLs with 22 D power, and evaluations for a 4-mm pupil diameter. Original commercial IOL profiles correspond to: A Tecnis (J&J), B SofPort (B&L), C Acrysof SN60WF (Alcon), and D XL-Stabi-ZO (Zeiss). Anterior lens surface is at left. Data adapted from Barbero et al [78]

In the Isofocal IOL designs, eye models were defined for each IOL power, with the axial length adjusted to focus the retinal image for a corresponding monofocal IOL of the corresponding power. The optical target was defined as a retinal image quality metric evaluated simultaneously at eight different object plane locations (ranging from 5 to 0.4 meters) and with weighting coefficients ranging between 0.44 and 0.02. Boundary conditions were imposed on IOL central thickness, IOL vault, and limits to the surface asphericity. Optimization was performed for a 4.5 mm optical zone diameter. Each of the surfaces of the IOL were described by aspheric surfaces, with variables radius of curvature, conic constant, and four additional aspheric constants, from 4^th to the 10^th order. The optimization process followed a sequential routine, in a damped least mean squares algorithm. Figure 22 A shows a semi-meridian of the anterior and posterior IOL surface coordinates (left) of a 22D IOL design, and the corresponding power of a model cornea + IOL. The IOL proved to have a uniform performance (hence the name “isofocal”) in an ample range of object distances (MTF at 50 c/deg between 0.5 and 5 m shown in Fig. 22(B)). The IOL also showed high performance stability with pupil diameter.

Fig. 22.

Isofocal IOL designs and performance. Upper panels correspond to the first published Isofocal design (Fernandez et al. [79]) and lower panels to a commercialized design, the Isopure IOL by BVI-PhysIOL. A. Left Panel. IOL profile semi-meridian for a 22 D IOL power design (anterior IOL facing left). Right Panel. Corresponding IOL power of the computer eye model (cornea + IOL). B. Simulated optical performance (MTF at 50 c/mm) as a function of object location, for three different pupil diameters (PD). C. Commercial Isopure IOL (20 D) measured power (phase-shifting Schlieren Interferometry, NIMO TR1504, Lambda X), reported by Perez-Sanz et al [80]. D. On bench measurements of through-focus optical performance (correlation metric of an E-letter optotype) of the Isopure IOL (21 D) inserted in a cuvette (based on Rassow principle), in an Adaptive Optics system with a pupil-conjugate deformable mirror that simulated different amounts/signs of spherical aberration, -0.2um (-SA), 0 + 0.2um (+SA) for 4.5-mm, in comparison with no IOL (black line). Figs A and B are reproduced from Fernandez et al Optics Letters 2011 [79]; Fig. C is an adaptation from Perez-Sanz et al. [80]; Fig. D is reproduced from Lago et al. [81]

The lower panels of Fig. 22 show results for a commercial realization of the IOL (Isopure by BVI-PhysIOL), with radial power measurements in a physically manufactured 20-D IOL (Fig. 22 C, data from Pérez-Sanz et al. [80]), in comparison with an aspheric monofocal IOL (Micropure, by PhysIOL). On bench tests with Isopure IOL, immersed in a cuvette with a model eye, and “corneal” spherical aberrations induced or corrected in an Adaptive Optics (AO) system show expanded depth-of-focus with respect to a monofocal IOL, and a high degree of independency from corneal spherical aberration (Fig. 22, data from Lago et al [81]). The radial oscillations in the power profile (shown in both examples) are responsible for the relative immunity to changes in pupil diameter and corneal spherical aberration, in comparison to extended-depth-of-focus designs simply targeting a given magnitude of 4^th order spherical aberration in the IOL, and they demonstrate the strength of the multiconfiguration approach that aims to improve retinal image quality (over the defined range) by tuning a larger range of IOL design surface parameters.

12. Discussion

IOLs have been used for 75 years, with phacoemulsification, foldable IOLs, and optical measurement of the axial length, contributing to routinely successful surgery with excellent refractive results [82]. IOLs do not currently accommodate, yet many patients prefer to minimize their use of spectacles, or to not use them at all. Design concepts that reduce spectacle use have been evaluated here in an order that reflects historical developments, where multifocal IOLs initially provided a large “add” power for reading, but where clinical feedback led to smaller add powers and more foci in order to provide a single more continuous defocus range with reduced perception of visual phenomena. That led in turn to considering expanding the focal range for monofocal lenses as much as possible, while also leading to the idea that even modest increases in focal depth are valuable, particularly when distance vision is unaffected. Concepts that provide this broad range of characteristics for modern IOLs have been discussed in detail, and alternative methods are continuously being evaluated (e.g. [83–90]).

Funding

Fundação para a Ciência e a Tecnologia10.13039/501100001871 (FCT) (UIDB/04650/2020); Agencia Estatal de Investigación10.13039/501100011033 (PID2023-146439OB-I00); National Eye Institute10.13039/100000053 (R01EY014999, R01EY034151, P30EY007551, R01EY035009, P30EY 001319).

Disclosures

DG is a consultant for BVI, and receives trifocal lens royalties. GY holds a financial interest in US patent 20220260854. JL has financial interests in EU Patent # 2221747 B1 and its equivalent patents, based on the same patent application, granted in US, China, Japan, and Mexico, PCT publication #WO2020236330, US Patent Office Publication # 20240041652, patent licensing to Apolloptix inc, and receives royalties from SIFI. PA holds patents on the concept of inverted meniscus IOL (ArtIOLs) and has a financial interest in Voptica SL, the company commercializing these lenses. SM holds patents for the Isoplanatic (#WO2011151497A9) and Isofocal IOL ((#WO20140102352A1 and #WO2021048248, and receives royalties from the commercialization of the Isopure IOL (PhysIOL-BVI), based on the Isofocal concept. SM is a co-founder of 2EyesVision and consultant to Hoya, AzaleaVision and Adaptilens, which have interests in the IOL space.

Data availability

Data underlying the results presented in this paper are available on request to the authors.