Multifocal intraocular lenses (IOLs) are now recognized as a powerful solution that can be proposed to patients who need cataract surgery and wish to become spectacle independent.1–9 A number of these advanced IOLs have been introduced onto the market, each with their own advantages and disadvantages, depending on the proposed solutions and the physiology of the intended patient. The diversity of available IOLs makes them complex to analyze. In this study, we focused on multifocal IOLs based on diffractive technology. The profile of the diffractive grating and some optical metrics, such as the longitudinal chromatic aberration (LCA) generated by IOLs, is discussed. Each IOL is made of a specific biomaterial, characterized by its Abbe number, with specific refractive shape and diffractive profiles. In most of the diffractive multifocal IOLs, a hybrid refractive–diffractive design is presented. Light energy is split between a number of foci, typically dedicated to far, intermediate, and near vision for trifocal IOLs. In most designs, the far foci receive light that appears to be purely refracted (0 order of diffraction), whereas the other foci (intermediate and near) are obtained through a combination of diffracted light (first and second order of diffraction). Bifocal IOLs exhibit only two foci, with various addition powers. As an example, the Tecnis ZMB00 (Johnson & Johnson Vision Care, Inc.) is a bifocal diffractive IOL. Its far vision is provided by refraction, whereas its near vision is driven by a combination of refraction and diffraction. Another example is the Tecnis Symfony (Johnson & Johnson Vision Care, Inc.). This is a bifocal IOL,7 which is a fully refractive–diffractive IOL without any purely refractive focus. Because the far and intermediate foci are close enough together in the Tecnis Symfony, an overlapping is observed in modulation transfer function (MTF) through-focus curves for small pupils. This gives a continuous vision from far to intermediate. At larger pupil diameters, this IOL presents distinct peaks. This type of IOL is referred to as an extended depth-of-focus (EDOF) IOL.7 In addition, trifocal IOLs have been developed to offer good visual performance over a broader range of vision through the definition of three foci. This is the case for the FineVision (PhysIOL, S.A.), AT LISA tri (Carl Zeiss Meditec AG) or PanOptix (Alcon Laboratories, Inc.) IOLs,9 for instance.
In the IOL literature, most of the in vitro optical characterizations have been performed in monochromatic green light, which corresponds to the most sensitive domain of light for the human eye. However, the natural visual environments of the human eye are polychromatic. White light comprises the different colors and wavelengths of visible light, ranging from red (650 nm) to violet (400 nm). The way the different wavelengths are handled by optical components leads to LCA, causing an additional aberration to all higher-order geometrical aberrations. However, the exact consequences on visual acuity are not demonstrated in this paper and remain to be explored in further studies.
Refractive or diffractive focalization leads to opposite signs of LCA. The combination of both of these principles offers an opportunity to reduce or compensate the LCA generated by the multifocal IOL. Diffraction theory predicts that addition powers and the amount of light distributed to foci are dependent on the wavelength of the incident light.
In this study, we investigated the basic structure of the diffractive patterns of various multifocal IOLs and explored, on an optical bench, the behavior of these IOLs in relation to various light wavelengths.
Materials and Methods
Multifocal Intraocular Lens Descriptions
Seven IOLs were studied and compared. For comparison with purely refractive components, two monofocal IOL with two characteristic biomaterials and Abbe numbers were also included in the study. The study was limited to a base power labeled to 20.0 diopters (D). This corresponds to the far focus power of a multifocal IOL used to achieve emmetropia in an “average” pseudophakic eye.
- Pupil-Independent Fully Diffractive Bifocal Multifocal Intraocular Lens The Tecnis ZMB00 is a pupil-independent, fully diffractive bifocal multifocal IOL, with a +4.00 D addition power. It is a single-piece C-loop IOL, made of hydrophobic material with ultraviolet (UV) filtration. The optic body diameter is 6.0 mm and the overall diameter is 13.0 mm.
- Extended Depth-of-Focus Multifocal Intraocular Lens The Tecnis Symfony ZXR00 is a bifocal multifocal IOL made of a diffractive step-like optical profile, intended to extend the range of vision while being combined with a proprietary technology to correct chromatic aberrations. It is a single-piece C-loop IOL, made of hydrophobic material with UV filtration. The optic body diameter is 6.0 mm and the overall diameter is 13.0 mm.
- Apodized Hydrophobic Fully Diffractive Intraocular Lens The FineVisionHP POD F GF is a double C-loop multifocal IOL with 5 degrees of angulation, made of PhysIOL proprietary hydrophobic G-free material,10 with UV filtration and a blue-light blocker. The optic body diameter is 6.0 mm and the overall diameter is 11.4 mm. In addition to its far refractive power, FineVisionHP provides two foci for intermediate and near distance vision, with addition powers of +1.75 D and +3.50 D, respectively.
- Apodized Hydrophilic Fully Diffractive Intraocular Lens The FineVision POD F is a double C-loop multifocal IOL with 5 degrees of angulation, made of hydrophilic (meth)acrylic material, with UV filtration and a blue-light blocker. The optic body diameter is 6.0 mm and the overall diameter is 11.4 mm. In addition to its far refractive power, the FineVision POD F provides two foci for intermediate and near distance vision, with addition powers of +1.75 D and +3.50 D, respectively.
- Hydrophobic Fully Diffractive Trifocal Longitudinal Chromatic Aberration–Corrected Intraocular Lens The LCA–corrected FineVision multifocal IOL (PODLGF) is a double C-loop lens with 5 degrees of angulation, made of PhysIOL proprietary hydrophobic G-free material, with UV filtration and a blue-light blocker. The optic body diameter is 6.0 mm and the overall diameter is 11.4 mm. In addition to its far refractive power, the LCA–corrected FineVision provides two foci for intermediate and near distance vision, with addition powers of +1.75 D and +3.50 D, respectively. This IOL has been specially designed to minimize chromatic aberration for far and intermediate vision.
- Hydrophobic Partially Diffractive Trifocal Intraocular Lens The trifocal Acrysof IQ PanOptix TFNT00 is a UV-filtering and blue light-filtering foldable diffractive multifocal IOL. It is a hydrophobic acrylic single-piece IOL, with a 6.0 mm optic, two open-loop haptics, and an overall diameter of 13.0 mm. The diffractive structure is located within the central 4.5 mm of the anterior surface and distributes the incoming light into +2.17 D intermediate and +3.25 D near addition powers.
- Hydrophilic Partially Diffractive Trifocal Intraocular Lens The AT LISA tri 839MP is a trifocal diffractive IOL, with +3.33 D for near addition and +1.66 D for intermediate addition at the IOL plane. This multifocal IOL has an aspheric design, with an overall diameter of 11.0 mm and an optic diameter of 6.0 mm. The IOL presents an asymmetric light distribution: light is distributed between distance and near foci within the whole optical zone. On the other hand, in the central 4.34 mm zone, light is divided among distance, intermediate, and near foci.
- Hydrophilic Monofocal Intraocular Lens The MicroPlus (PhysIOL, S.A.) is an aspheric monofocal IOL with 2 degrees of haptic angulation, made of hydrophilic (meth)acrylic material, with UV filtration and a blue-light blocker. The IOL has 4 closed haptics.
- Hydrophobic Monofocal Intraocular Lens The MicroPure (PhysIOL, S.A.) is an aspheric monofocal IOL with 2 degrees of haptic angulation, made of PhysIOL proprietary hydrophobic G-free material with UV filtration and a blue-light blocker. The IOL has 4 closed haptics.
Because the diffractive profile has a strong impact on the optical properties of a given IOL, the topology of each diffractive IOL was measured. Topography measurements were acquired using an optical profilometer (Bruker Contour GTI). The IOLs were measured in the Interferometry VXI mode, with a 20× magnification objective and a 0.55× zoom lens and total magnification of 11×. The field of view of a simple image was 0.6 × 0.4 mm2. To cover the whole radius of the lens, image stitching was applied. Equidistant images were taken along the IOL radius. An image composite was generated automatically by the calibrated instrument software. Relative positions of the images were recorded by the motorized stage encoder of the optical profilometer. The recording process was performed without changing the view angle. From the completely reconstructed profile, the main IOL curvature was evaluated and removed to extract the experimental diffractive profile. The height and position of each diffractive step were evaluated and made in correspondence with the diffractive Fresnel IOL add-focus and phase relationship.11,12Figure 1 shows this process. Height correction has been applied to take into consideration the view angle associated with the IOL curvature along the radius.
Index of Refraction and Abbe Number
All the IOLs studied in this paper are made of different biomaterials, presenting advantages and disadvantages in terms of biocompatibility, transparency, UV filtering, and so forth. From the imaging point of view, materials have different refractive indices and Abbe numbers. Both parameters are complementary because they act on the chromatic properties of an IOL and on the phase shift of light traveling through it. The higher the Abbe number, the lower the chromatic aberration. Table 1 shows some parameters of the IOLs studied.
The optical bench used for this series of measurements was the PMTF (Power and Modulation Transfer Function bench, developed by Lambda-X) to measure image quality—MTF of diffractive multifocal IOLs.1 The PMTF optical bench is equipped with three monochromatic light sources, at three different wavelengths (480 nm, 546 nm, and 650 nm ± 2 [SD]). The apparatus complies with International Organization for Standardization (ISO) number 11979-213 and ISO number 11979-914 requirements. Measurements were performed with a model cornea, displaying zero spherical aberration (0 μm of longitudinal spherical aberration), to assess the optical performance of the IOLs themselves, excluding the potential influence of the cornea lens. Residual chromatic aberration generated by the optical bench was calibrated and was removed from the through-focus curves.
The PMTF enables MTF measurement at different apertures (2.0 mm, 3.0 mm, 3.75 mm, and 4.5 mm), focal planes (through-focus curve) and spatial frequencies.
In the experimental setup, the tested multifocal IOL was placed in an 11.0 mm diameter lens holder before being inserted into a quartz cell filled with aqueous sodium chloride 0.9%. The anterior side of the IOL was placed facing the incident light. The lens holder guaranteed a tilt-free orientation of the IOL under inspection. The device automatically detects the optical axis of the IOL with 0.2 mm of lateral precision.
The through-focus MTF curves were recorded at 50 cycles/mm at a 3.0 mm aperture in accordance with ISO standard recommendations.
Intraocular Lens Surface Topography
Diffractive topographies were obtained once the main IOL curvature had been extracted. Figure 2 shows these topographies. All the multifocal IOLs studied in this paper were found to present diffractive profiles, and a number of these exhibited alternating step height variation.
In diffractive multifocal IOLs, the main curvature provides the main power of the lens. It is often associated with far vision, which is mainly driven by the refractive elements of the IOL. There are, however, a few exceptions, which can be found in the case of the Symfony and LCA–corrected FineVision IOLs. These cases will be discussed in more detail later in the paper. The diffractive profiles were superposed on the main curvature of the lens to give rise to the addition power for intermediate and/or near vision. It is worth noting that one or more diffractive profiles can be combined to give one or more additional foci, respectively.
As mentioned previously, all the multifocal IOLs studied in this paper exhibit diffractive profiles, even the EDOF Symfony IOL. The Symfony clearly behaves like a diffractive bifocal IOL. The extension of range of vision, claimed by the manufacturers to be provided by this IOL, derives from the close position of the far and intermediate foci along the optical axis. The EDOF effect is amplified when the pupil is small.
Bifocal Diffractive Intraocular Lenses
Both Tecnis IOLs (ZMB00 and EDOF Symfony) exhibit a bifocal diffractive design; however, the Symfony presents a shorter grating frequency compared with the ZMB00. This reflects the lower add power of the Symfony IOL. This property was confirmed by measurement of the MTF through-focus curves. On these diffractive bifocal Tecnis IOLs (ZMB00 and EDOF Symfony), a simple structure is observed. This structure is typical of a simple diffractive IOL added to the main refractive lens. As described earlier, the refractive lens provides the main IOL power. Step positions define annular zones within the diffractive lens. Each of these zones have an equal effect on the focus, hence the fact that the pitch distance between two steps is inversely proportional to the square root of the added power and is proportional to the square root of the step number. It is for this reason that the added power is higher (roughly double) in the case of the ZMB00 compared with the Symfony IOL.
Trifocal Diffractive Intraocular Lenses
Trifocal diffractive IOLs present a double diffractive structure, which corresponds to a combination of two diffractive patterns. The AT LISA tri 839MP, FineVision POD F, FineVisionHP POD F GF, and LCA–corrected FineVision all have two addition powers with a ratio of two (eg, 1.75 D, +3.50 D). This harmonic relationship translates into a steady geometric variation of high and low step heights.
The position of diffractive steps along the IOL radius depends on the square root of the step number, as shown in the following relationship:
where ρq is the step position on the radial axis, q is an integer associated with the step number, λ0 is the design wavelength, and F the diffractive focal length in meters.
Figures 3 to 5 show the step positions of the investigated diffractive IOLs as a function of their number order and associated added power. Dots represent the experimental data, whereas the solid lines correspond to the theoretical curves, based on the above formula.
Chromatic Properties of Diffractive Intraocular Lenses
As the following mathematical relationship shows, the diffractive added power is wavelength-dependent:
where p is an integer that represents the maximum phase modulation as a multiple of 2π, λ0 is the design wavelength, F0 is the focal length (in meters) at the design wavelength, m is the considered order of diffraction, and λ is the wavelength of interest.
The refractive focus is wavelength-dependent because of its refractive index dependency, as seen in Equation 2. However, it can be seen that the diffractive foci are also wavelength-dependent but in the opposite way: the focus position is inversely proportional to the considered wavelength. In the case of a refractive–diffractive IOL, the chromatic aberration appears as a combination of both effects, and it can be theoretically balanced.
The amount of light energy distributed on each focus is fully dependent on the diffractive structure of the IOL and its height, the wavelength of use, and the variation of the refraction index between the IOL and its surrounding medium. The energy associated with a particular focus is linked to the diffraction efficiency of the IOL. This efficiency is directly connected to the phase modulation undergone by the light when it passes through a periodic structure, as in the case of a sawtooth grating, for instance. The phase modulation is given by the following relationship:
where λ is the wavelength, Δn is the refractive index difference between the inner and outer media, and h0 is the local thickness crossed by the light.
For a specific wavelength, a 2π phase modulation will give the maximum diffraction efficiency. This implies that in most the cases, the step will have a height given by:
In the case of a low diffraction order value, an approximation of the diffraction efficiency can be given by the well-known diffraction efficiency law of the sawtooth grating:
where Symbol, m is the diffraction order, and p= Δn h/λ0, which produces an optical phase difference of pλ0 or a maximum equivalent phase shift of p2π.
In practice, none of the diffractive IOLs has the maximum grating amplitude at the design wavelength, because, for the IOLs to be effective, the different foci must be present together. The phase modulation given by the surface profile therefore then determines how the incident energy is distributed through the various diffraction orders. In most of the IOLs studied, the step height is lower than h0 to distribute light onto the zero order (often associated with far focus) and the first orders (intermediate or near).
Through-Focus Modulation Transfer Function Curves
Figures 6 to 12 show MTF through-focus curves recorded at a pupillary aperture of 3.0 mm, a spatial frequency of 50 LP/mm and three wavelengths: 480 nm, 546 nm, and 650 nm under an ISO 1 cornea. The green curve is taken as the reference. As can be seen in most of the graphs, the MTF peaks in three wavelengths (red, green, blue) and over the different foci, exhibiting, in most cases, an offset compared with the behavior in green light. These shifts are attributable to chromatic aberration. The order in which the peaks are displayed is associated with the dominant process (refractive or diffractive) occurring for the creation of a specific focus. As an example, in most of the multifocal IOLs, far foci (except for the Symfony IOL), red-maximum appears for lower power values and blue-maximum for higher values. This red–green–blue distribution is the signature of a refractive dominant process. Inversely, in most of the near foci, blue appears first, whereas red has the highest power (blue–green–red). In that case, the dominant process is diffractive. Peak positions (power) are driven by a Bragg-like law or the kinoform law (Equation 1), whereas the efficiency of the diffractive profiles is mainly driven by the step height and its relative value compared with wavelength. This is especially visible in the case of the Symfony IOL, which becomes monofocal for far focus in red light and monofocal for intermediate focus in blue light. This IOL is bifocal in green light and is fully driven by a diffractive chromaticity. Because of a large step height in the case of the Symfony IOL, the energy balance is more sensitive than for the other multifocal IOLs.
For each IOL and each associated focus, the measured power is reported in relation to the wavelength used (the B graphs in Figures 6, B, to 12, B). The slope of the lines is directly associated with the magnitude of the longitudinal chromatic aberration, and its sign depends on the dominant process: refractive or diffractive. A negative slope relates to a refractive process, whereas a positive slope is directly associated with a diffractive one.
Some foci present a slope very close to zero, which corresponds to a compensation of the refractive and the diffractive LCA. Hence, these foci are said to be chromatically corrected.
The chromatic properties of the different IOLs characterized in this study are summarized in Figure 13. For each focus, chromatic effects were computed as a variation of power shift according to the wavelength. Therefore, histogram bars in the positive range of the graph correspond to foci that exhibited less power in blue light than in red light, and vice versa for the bars in the negative range.
As expected, Figure 13 shows that in most cases, the longitudinal chromatic aberration related to the far foci (blue bars) was found to be negative and directly linked to the Abbe number of the IOL biomaterial. In the vast majority of the multifocal IOLs studied, we found that far vision was controlled by the intrinsic refractive behavior of the biomaterial (zero order of diffraction). Hence, the magnitude of the LCA in refractive cases was shown to be proportional to the Abbe number (Figure 13). The only exception in this study related to the Symfony IOL, which was found to exhibit a modified, positive LCA for both foci. This reflects the fact that in this specific case, the IOL was found to be totally diffractive. All the other IOLs exhibiting a zero order far focal point showed a negative LCA directly correlated with the Abbe number of the IOL biomaterial. For the sake of comparison, LCA was also measured on two refractive monofocal IOLs (MicroPlus and MicroPure). These IOLs are made from the same materials as the FineVision and FineVision IOLs, respectively. As expected, the LCA associated with these IOLs was found to be fully refractive and to have the exact same value as the refractive far focus of the related trifocal IOLs (FineVision and FineVisionHP).
Four of the IOLs studied presented an interesting behavior in their correction of the longitudinal chromatic aberration, for at least one focus. These IOLs (FineVision, LCA–corrected FineVision, PanOptix, and ATLisa) presented a very low slope on the dispersion curve, mostly for intermediate focus. In the specific case of the LCA–corrected FineVision IOL, two foci were found to be LCA–corrected. Although the results were not extrapolated to clinical relevance, this LCA study complements other studies of the effect of energy distribution on diffractive IOLs between the different foci, especially in the case of spherical aberration and the effect of the apodization.15 More than the position of the peaks along the optical axis, the chromatic effect changes the MTF distribution in accordance to the wavelength.
In conclusion, in this study, we compared 7 different multifocal IOLs under three different wavelengths. Two monofocal IOLs were added as purely refractive IOLs for the sake of comparison.
First, the surface topography of the diffractive profiles was measured and interpreted in terms of step position and step height. Diffractive step position gives information on the focalization properties of an IOL, whereas step height provides insights into the energy balance between the different foci. MTF through-focus curves were then measured on an optical bench for three different wavelengths. Based on these results, the longitudinal chromatic aberration was assessed for each IOL and its associated foci.
From these measurements, it was shown that LCA is driven by two major processes: refraction and diffraction. The position of the specific wavelength MTF peaks and resulting dispersion curve revealed the dominant process. It was also observed that it was possible for the MTF balance between the different foci of a given IOL to be become strongly modified while changing from green to blue or red light.
In most of the multifocal IOLs studied, some of the foci were found to be refractive (in general, this was true for the far focus) and others were diffractive (intermediate and near foci). However, the Symfony IOL appeared to be an exception; in that case, all the foci were shown to be driven by a diffractive process. It is interesting to note that in some cases, it was possible for the LCA to be fully compensated. This was the case for the intermediate focus of the FineVision, PanOptix, and ATLisa IOLs, whereas the LCA–corrected FineVision IOL was found to be LCA–corrected for both far and intermediate foci.
Finally, it is well understood that chromatic aberration reduction can improve the image quality of any optical system under polychromatic light. However, in the specific case of the eye and its monochromatic aberration, the improvement of vision quality by LCA reduction has not yet been demonstrated. Hence, although the results were not extrapolated to clinical relevance, this study still offers the reader a new performance metric to characterize multifocal IOLs and their different foci.
What was known
- Diffractive multifocal intraocular lenses (IOLs) are powerful devices to replace the crystalline lens after cataract surgery. These IOLs reduce the spectacle dependence. Various diffractive multifocal IOLs are present on the market.
- Most of the optical characteristic of IOLs are presented in green light, which is the most sensitive part of the eye. However, the life is polychromatic and most of the optical systems present chromatic aberration because of the intrinsic refractive properties of the optical material or diffractive structure.
What this paper adds
- Longitudinal chromatic aberration (LCA) was driven by two major processes: refraction and diffraction.
- In some cases, and with some focus of the diffractive IOL, LCA can be fully compensated.
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Drs. Gatinel and Loicq have a proprietary interest in some of the discussed optical designs. This study has been performed under a collaborative agreement with Physiol. Dr. Willet has no financial or proprietary interest in any material or method mentioned.