Through-focus performance and off-axis effects in aspheric monofocal intraocular lenses

Abstract

This study aimed to determine the through-focus performance and the effect of misalignment on the optical quality of different aspheric monofocal intraocular lenses (IOLs). To this end, optical quality was assessed in three IOL models with different optic surfaces: standard aberration neutral model and two spherical aberration (SA) correcting, one of which utilizes higher-order aspheric terms. The optical quality was measured by means of the modulation transfer function at 3- and 4.5-mm pupils and under monochromatic and polychromatic light with different corneal SA. The optically derived range of vision and tolerance to misalignment were also tested. The study demonstrated that the type of IOL surface affects the monofocal implant's performance. Although a standard primary-SA correction may improve scotopic image quality, misalignment may diminish this advantage. The higher-order aspheric surface used to correct SA provided an improved performance against decentration and offered a higher optical quality than the aberration-neutral design when tested in a model eye. The latter, however, demonstrated a high tolerance to misalignment, offering a slight extension of the range of vision, potentially resulting from uncorrected optical aberrations.

1. Introduction

Cataract surgery with the implantation of intraocular lenses (IOLs) stands as one of the most frequently performed surgical procedures worldwide [1]. Despite significant advancements in presbyopia-correcting technology, monofocal lenses continue to be a preferred choice in standard cataract surgery [2]. The widespread preference for monofocal IOLs can be attributed to their cost-effectiveness, uncompromised distant optical quality, and low rate of photic disturbances such as halos and glare. [2,3] As well as often having different and distinctive optic and haptic geometries, current monofocal lenses can show diversity in the use of different optical technologies, which can include the induction of spherical aberration (SA), spectral-filtering or chromatic dispersion properties [4,5]. The degree of IOL's SA corretion appears of particular significance, given its interaction with the patient's corneal SA and its role in influencing the optical resolution and the depth of focus [4,6]. The long-established spherical design of monofocal IOL introduces 4th order SA, potentially diminishing visual quality. In contrast, the more modern monofocal IOLs feature an aspheric design, with negative SA (aberration-correcting IOLs) or no SA (aberration-neutral IOLs) to counteract or leave corneal primary SA intact in an effort to improve visual quality, particularly under scotopic conditions [4,5]. Another option is to use a non-prolate surface that utilizes higher aspheric terms to alter the SA in the optic center to a different extent than at the periphery [7–9]. This approach claims to lower the impact of SA on vision while enhancing the IOL tolerance to postoperative misalignment [7,9].

The emergence of tilt and decentration correlates with the reduction of visual acuity (VA); hence, [10] the alignment of the IOL with respect to the ocular axis may help to attain optimal visual performance after cataract surgery. Although it is suggested that minimal tilt, e.g., 2.89°, and decentration, e.g., 0.27 mm, [11] may not significantly affect visual function, it has been demonstrated that a large misalignment of the IOL can have a measurable effect on VA [11]. Clinical data and optical simulations further underscore the human eye's sensitivity to IOL tilt and decentration, with notable aberrations arising from deviations as low as 0.5 mm decentration, leading to noticeable visual symptoms [12,13]. A recent review indicates that 10% of patients experience tilt exceeding 5° and decentration over 0.5 mm after IOL implantation [14]. In conclusion, it should not be overlooked that even in routine cases, suboptimal IOL alignment may be expected postoperatively, and it will have the potential to reduce visual quality.

Besides influencing the IOL's performance under off-axis conditions, the optical surface geometry can affect the depth of focus by inducing or reducing SA. In terms of monofocal optics, it has been shown that SA correction compromises near vision compared to a standard spherical IOL [15]. Recently, the SA concept has been implemented in refractive extended depth of focus IOLs by introducing controlled amounts of positive and negative SA of the 4th and the 6th order [16]. One may wonder, however, whether implementing a complex aspheric design in a monofocal lens would also affect the patient's range of vision. Consequently, our study involved objective assessments of this distinctive aspherical monofocal design and its impact on the depth of focus and compared it against monofocal IOLs that use a standard SA-correcting and an aberration-neutral IOL approach. These assessments were conducted under both monochromatic and polychromatic conditions, employing two corneal models: one configured as an aberration-free cornea and the other representing the typical positive SA level observed in the human cornea (approximately +0.28 µm at 6 mm) [17]. Furthermore, we explored the impact of IOL misalignment, characterized by a tilt of 5 degrees and a decentration of up to 1 mm, on the IOL performance, with each factor evaluated separately.

2. Materials and methods

2.1. Intraocular lenses

Three models of hydrophobic acrylic monofocal IOLs were evaluated: an aberration-neutral enVista MX60 (Bausch + Lomb Incorporated, Rochester, NY, USA), an SA-correcting Tecnis ZCB00 (Johnson & Johnson Surgical Vision, Inc., Santa Ana, CA, USA) and CT LUCIA 621P (Carl Zeiss Meditec AG, Jena, Germany) with a non-prolate optical surface that affects the effective SA correction depending on pupil diameter. Two samples of each lens model were included. All lenses had the same refractive power of 20D.

The material of the enVista MX60 has a refractive index of 1.55 and 36.9 Abbe number. According to the manufacturer, the MX60 biconvex optics yield aberration-neutral ray propagation, although no further information is given on conditions under which the IOL design was optimized. The Tecnis ZCB00 has a refractive index of 1.47 and a higher Abbe number equal to 55. The ZCB00 was designed using a “physiological eye model” in order to correct 0.27 µm of 4^th-order SA, as a close level was observed in the normal population [17]. The CT LUCIA 621P's refractive index is 1.49, and the Abbe number is 51. By contrast to the other two models, CT LUCIA 621P's asphericity induces SA that evolves from high to low negative primary SA, while the position in the pupil plane changes from center to periphery. This is achieved through a non-prolate surface featuring higher-order aspheric terms [9]. After upscaling the values to an equivalent SA correction at a 6 mm diameter, the correction is -0.24 µm at 3 mm, which decreases to -0.16 µm at 4.3 mm and further reduces to -0.08 µm at 5 mm. This peripheral SA increase was introduced to lower the IOLs’ sensitivity misalignment compared to standard SA-correcting platforms [18]. The optical design of the CT LUCIA was optimized using a schematic eye model proposed by Liou and Brennan. [19] This approach was implemented by Carl Zeiss and is now referred to as ‘ZEISS Optic’ (ZO).

2.2. Testing procedures

The modulation transfer function (MTF), a recognized optical-quality metric, [20] was applied to assess the IOLs’ performance. Measurements were conducted using an OptiSpheric IOL PRO2 device (Trioptics GmbH, Germany), whose design adheres to the standards outlined in ISO 11979-2, [20] and provides the MTF with a precision of ±2%. A schematic illustration of the device is available elsewhere [21]. The assessment was performed along two perpendicular meridians, corresponding to a crosshair target projected onto a monochromatic camera (VA-1MCM120-A0-C; Vision Systems Technology, Vista, CA, USA). Images of two line spread functions were captured and analyzed using OptiSpheric software (Trioptics GmbH, Germany). The software performed a Fourier transform on these images to generate the MTF and phase transfer function (PTF). The results of the two meridians were averaged due to the rotational symmetry of the tested IOLs.

The optical quality was tested under three spectral and SA conditions. One involved using a cornea model with +0.27 µm of 4^th order SA (ISO-2) at 5.15 mm and polychromatic light originating from a polychromatic light-emitting diode source. Furthermore, the spectral components were weighted to resemble the V-lambda curve using an additional filter. Since the polychromatic condition more closely corresponds to the clinical situation, it was also used for subsequent testing of the depth of focus and IOLs’ tolerance to misalignment. However, to study the design characteristics of the monofocal IOLs, we also applied monochromatic 546-nm testing involving the +0.27-µm and aberration-free (ISO-1) corneal models. Under these three conditions, we analyzed and compared the MTF at 3 and 4.5 mm obtained using a 50 lp/mm criterion.

The through-focus (TF) assessment was performed solely in the polychromatic condition featuring SA. The United States Air Force (USAF) resolution target was imaged through each IOL using the monochromatic camera integrated into the metrology device. First, the TF MTF was obtained at the following spatial frequencies: 25, 50, and 100 lp/mm. Then, we calculated the weighted optical transfer function (wOTF) [22] across the range of frequencies (f) from the measured MTF and PTF at each defocus point from +1D to -1.5D, taking into account the neural contrast sensitivity function (CSF), which was derived from a work by Campbell and Green [23].

$$w\mathrm{O}\mathrm{T}\mathrm{F}={\displaystyle \frac{1}{150}{\sum }_{f=1}^{150}MTF\left(f\right)\cos \left(PTF\left(f\right)\right)CSF\left(f\right)}$$ (2)

The wOTF has demonstrated a robust correlation with clinical defocus curves [22] and was applied as a parameter to calculate simulated postoperative visual acuity (simVA).

Furthermore, the effects of misalignment on the polychromatic MTF were compared at 50 lp/mm and USAF images. To this end, an IOL under test was decentered by 0.2 mm, with a maximum of 1 mm off-axis shift. A figure demonstrating a decentered lens in our metrology study can be found in an earlier publication [24]. The IOLs were decentered into a vertical direction; thus, only the sagittal (vertical) component of the crosshair target was analyzed. In a separate analysis, the IOLs were placed on a customized insert featuring a 5° tilt, and the MTF was remeasured, with the two meridians averaged. The orientation of the tilted insert was not standardized during placement. Although the decentration effects were measured at the position of the best focus of the centered sample, the introduction of the tilted insert required repositioning the lens in the system and realigning its focus.

3. Results

3.1. Three-condition MTF analysis

The MTF curves derived at the best focus at 3- and 4.5-mm apertures are compared in Fig. 1. In short, at a pupil size of 3 mm and under ISO-2 and polychromatic light, the CT LUCIA and ZCB00 produced higher MTF values, with the mean ± standard deviation of 0.46 ± 0.01 and 0.47 ± 0.00 at 50 lp/mm, respectively, while the enVista's MTF was 0.38 ± 0.01 at 50 lp/mm. The enVista IOLs displayed the lowest MTF in monochromatic ISO-2 condition (MTF@50 lp/mm = 0.61 ± 0.00). However, the other two models had similar MTF values at 50 lp/mm, with the ZCB00 showing 0.73 ± 0.01 and the CT LUCIA, 0.75 ± 0.01. In the ISO-1 condition featuring monochromatic light, the CT LUCIA performed better at 50 lp/mm (MTF = 0.78 ± 0.01) than the other monofocal IOLs.

Fig. 1.

Modulation transfer function (MTF) levels of the studied IOLs at the best far focus for each measurement condition. The dotted lines show the values of each lens separately; the solid lines refer to the average of two samples. ISO-1 = aberration-free cornea; ISO-2 =  + 0.27 µm cornea; Poly = polychromatic light; Mono = monochromatic light.

At a pupil size of 4.5 mm, the ZCB00 produced the highest MTF values among the three models in polychromatic light, with an average level of 0.34 ± 0.00 at 50 lp/mm. The CT LUCIA had an MTF of 0.26 ± 0.01. However, the aperture increase affected the enVista's performance most, showing the lowest MTF at 50 lp/mm of 0.18 ± 0.00. In a monochromatic ISO-2 setting, the ZCB00 still showed the highest and the enVista the lowest MTF values. After introducing the ISO-1 cornea, the CT LUCIA's and enVista's MTFs were 0.73 ± 0.05 and 0.63 ± 0.03, while the ZCB00 showed the poorest optical performance, with an average level of 0.36 ± 0.01 at 50 lp/mm.

3.2. Polychromatic TF performance

Figure 2 presents the TF MTFs tested at three spatial frequencies and the 3-mm pupil. Given the monofocal design of the lenses, the curves showed one peak of maximum MTF that corresponds to the best (distance) focus. The CT LUCIA and the ZCB00 displayed comparable TF MTF peaks across the three spatial frequencies and the studied conditions.

Fig. 2.

Through focus modulation transfer function (MTF) of monofocal IOLs recorded at three spatial frequencies and the two apertures. Measurements were conducted in polychromatic light using an ISO-2 cornea lens. The dotted lines show the values of each lens separately; the solid lines refer to the average of two samples.

Conversely, the enVista lens demonstrates diminished peak characteristics, showing slightly higher MTFs at hyperopic defocus and at -1D. This translated into a simVA improvement at +1 and -1D, with a logMAR difference of about 0.03 logMAR, as shown in Fig. 3. Differences can also be noticed in the recorded USAF resolution target images presented in Fig. 4, which confirms the equivalence of the far-focus images in terms of subjective image quality: the simulated VA values at varying distances fell within the -0.09 to -0.08 logMAR.

Fig. 3.

Simulated visual acuity (simVA) as a function of spectacle defocus. Measurements were conducted in polychromatic light using an ISO-2 cornea lens. The dotted lines show each lens’ values separately; the solid lines refer to the average of two samples.

Fig. 4.

Polychromatic United States Air Force target images recorded at 3 mm using an ISO-2 cornea lens.

3.3. IOL decentration

Figure 5 presents the loss of the optical quality calculated at each decentration point and the 3- and 4.5-mm pupils under the polychromatic condition. The MTF loss was defined as the difference between the on-axis MTF value at 50 lp/mm compared to its decentered position. Notably, the CT LUCIA and the enVista exhibited a relatively modest MTF reduction of up to -0.03 when subjected to 0.8-mm decentration, with a more pronounced difference after a 1-mm shift (Fig. 5). Still, the enVista response to decentration demonstrated substantial variability between the samples as indicated by their deviation. The ZCB00 demonstrated a more substantial MTF loss after testing under off-axis conditions, where a 0.4-mm decentration of the ZCB00 had a similar impact as an 0.8-mm decentration of the CT LUCIA and the enVista. The comparison at 4.5 mm appears close to effects observed at a smaller pupil, with a marginal uptick of the enVista's MTF by a value of 0.01 at 1 mm decentration. Note the device's accuracy of 0.02 MTF value. Fig. S1 presents the MTF values measured at each point assessed. The impact of decentration on the USAF image quality is also presented in Fig. S2-3.

Fig. 5.

The modulation transfer function (MTF) loss at 50 lp/mm measured with the study IOLs under lens decentration and compared to the on-axis value at 3 mm (left panel) and 4.5 mm (right panel). Measurements were conducted in polychromatic light using an ISO-2 cornea lens. The error bars indicate standard deviation.

3.4. IOL tilt

The MTF values for the three monofocal lens models at the 3 mm aperture exhibited a slight reduction following a 5° tilt. Under conditions of polychromatic illumination, the ZCB00 and CT LUCIA displayed a comparable MTF loss at 50 lp/mm after the tilt: 0.47 ± 0.00 to 0.46 ± 0.00 and 0.46 ± 0.01 and 0.44 ± 0.02, respectively. The enVista's MTF values were lower, but also with virtually no effect of 5° tilt, showing 0.38 ± 0.01 before and 0.37 ± 0.00 after this misalignment. A comparable effect was observed at 4.5 mm, with the ZCB00, enVista, and CT LUCIA showing the reduction of the MTF at 50 lp/mm from 0.34 ± 0.00 to 0.32 ± 0.01, 0.18 ± 0.00 to 0.17 ± 0.01, and 0.26 ± 0.00 to 0.25 ± 0.00, respectively. The corresponding USAF images are presented in Fig. S3.

4. Discussion

Previous investigations have undertaken in vitro comparisons of various monofocal IOLs. Borkenstein et al. assessed the CT LUCIA 621P IOL under two corneal model conditions: the ISO-1 cornea without SA and the ISO-2 cornea characterized by a positive SA of 0.28 µm (5.15 mm) [25]. Their findings revealed that the MTF mean at 50 lp/mm with a 3.0 mm aperture was 0.797 (ISO-1) and 0.723 (ISO-2), and with a 4.5 mm aperture, it was 0.751 (ISO-1) and 0.505 (ISO-2) [25]. Consistent with the Borkenstein group's work, when assessed with a 3-mm aperture in our study, CT LUCIA 621P demonstrated an MTF of 0.78 under an SA-neutral corneal model and 0.75 after introducing SA. Regarding a 4.5 mm aperture, our assessment yielded MTF values of 0.73 and 0.41, respectively. In previous work by our group, we evaluated the optical performance by the metrics derived from the OTF of ZCB00 in polychromatic light. We found the MTF value of 0.50 ± 0.00 at 50 lp/mm and the 3-mm aperture, while at 4.5 mm, it reduced to 0.39 ± 0.01 at 50 lp/mm, [26] which is close to the level observed in the current study, confirming a high reproducibility of the ZCB00 optical parameters. Likewise, virtually no difference can be observed between blue-light filtering CT LUCIA 621 PY and its clear counterpart (CT LUCIA 621 P) in terms of optical quality [27]. In an assessment covering three spectral and SA conditions similar to those in the current study, the blue-light filtering model exhibited for the 3 mm aperture an MTF at 50 lp/mm of 0.49, 0.75, and 0.77 under polychromatic and monochromatic ISO-2, and monochromatic ISO-1 conditions, respectively [27]. This suggests that the performance of the two lenses is equivalent regardless of the chromatic condition.

The ZCB00 IOL has also been evaluated in clinical studies. Auffarth et al. presented the results of the European multicenter study and made a comparison between an enhanced-monofocal IOL and the ZCB00 [28]. In that investigation, 139 patients underwent bilateral implantation of one of the two models. They found a CDVA of -0.06 ± 0.01 logMAR in the standard-monofocal group, which agrees with our simulations. Likewise, the enVista demonstrated good visual results in a multicenter clinical evaluating 79 subjects, showing a CDVA of 0.01 ± 0.09 logMAR [29]. For the CT LUCIA 621 P lens, Hernández-Martínez and colleagues reported a mean Snellen corrected-distance VA (CDVA) of 0.89 ± 0.13 (equivalent to 0.05 logMAR) in their population, which is worse than our model predicted [30]. By contrast, the CDVA recorded 3 months post-surgery in the Garcia-Tomas study was 1.13 ± 0.11 (-0.05 logMAR), being close to the values predicted in our simulations [31].

The primary purpose of monofocal lenses is to restore vision after cataract surgery, offering one focus and intrinsically optimizing far vision. However, they also possess blur tolerance, ensuring a certain level of depth of focus, as shown in the current project and clinical studies [28,32]. The three IOL models we studied demonstrated the peak of simulated VA at 0.00D, which gradually worsened with increasing negative defocus. All IOLs produced a simVA of 0.06-0.08 logMAR at -1D, indicating minimal differences in their defocus tolerance. In the previously mentioned clinical investigation of the ZCB00, Auffarth et al. [28] showed a close correspondence to our simulated VA with a DCVA of 0.11 logMAR at -1D. The performance of ZCB00 in a case-control study revealed a VA of 0.07 logMAR at -1D [32]. Our results were consistent with those clinical findings, indicating a strong IOL component influencing the depth of focus of monofocal patients. However, the patients’ intermediate vision with monofocal lenses may also depend on other factors, such as optical aberrations. In the current study, a slightly improved tolerance to defocus of the enVista may result from its higher residual SA and/or lower Abbe number, yielding higher material dispersion. Increased chromatic aberration results in a broader defocus curve and improved intermediate vision in monofocal patients, as demonstrated by our group's recent research [33]. While a slight optical and visual quality deterioration can be noted at distance, such differences are not typically deemed clinically relevant. Furthermore, monochromatic higher-order aberration, pupil size, ocular biometry, and residual refractive errors [34–36] are also considered to be important factors affecting the eye's depth of focus, and this should be taken into account when interpreting the clinical implications of our findings.

The post-implantation misalignment of IOLs, decentration or tilt, can detrimentally affect the visual result, particularly for aberration-correcting lenses [5,18,37,38]. SA-correcting IOLs are held to be more susceptible to quality loss when placed in an oblique position. Still, the three lens models have different aspheric designs; thus, their tolerance to obliquity should differ [5]. Fujikado and Saika examined aspherical IOLs with different SA corrections (-0.27 µm, -0.17 µm, and -0.04 µm at 5.15 mm aperture) [37]. They found that the IOL with the lowest SA correction displayed a higher tolerance to misalignment [37]. Pérez-Garcia et al. also indicated that aberration-free IOLs showed the highest MTF for all misalignment values, and decentration proved to have a more significant effect on optical quality than tilt [5]. This observation aligns with the current study's results. Still, it is important to note that the CT LUCIA model also corrects SA; this can be seen in Fig. 1, reporting its optical quality in monochromatic ISO-2 condition at 4.5 mm, as its MTF level was between that of the aberration-neutral and -0.27 µm (at 5.15 mm aperture) compensating lens. Nevertheless, CT LUCIA's decentration effects were much smaller than the standard SA correcting lens, likewise in its blue-light filtering version, [27] and closer to the aberration-neutral approach. Borkenstein and colleagues found that comparing the ZCB00 and CT LUCIA 621P in centered, decentered (1 mm), and tilted (5°) positions, the effect of decentration was sensitive to the IOL design, being stronger for IOLs designs with higher SA-correcting values [25]. Our current investigation confirmed that an optical design optimized to minimize an SA contribution of IOLs (e.g., aberration-neutral) generally proves robust against decentration. However, we noticed the two enVista lenses had some variability in tolerance to decentration. One lens demonstrated slight improvement, while the other had a more pronounced degradation of the optical quality. This inconsistent response was confirmed through additional testing. Interestingly, both samples demonstrated nearly identical optical performance when centered, achieving high optical quality that meets industry (ISO) standards [20]. However, it is important to note that only two samples were assessed in this study. Therefore, further investigation on a larger sample size is required to confirm the noted differences. Another intriguing observation was that the enVista had worse MTF than the CT LUCIA at 4.5 mm in all conditions, despite the ISO-1 condition being most suited to the aberration-neutral model. This may result from discrepancies between such designs depending on the selected IOL optimization conditions, e.g., with or without model cornea or for a specific SA value. While further investigation is warranted, our results suggest that the complex SA pattern may provide a less variable performance across a spectrum of corneal SA values than a standard aberration-neutral lens.

5. Conclusions

Asphericity of optical surfaces is an important factor affecting the performance of monofocal IOLs under scotopic conditions and potential lens misalignment after implantation. The non-prolate surface design of the CT LUCIA proved robust against decentration with a comparable effect to the aberration-neutral enVista, showing an advantage under larger pupils. The latter demonstrated a minimally improved depth of focus, which could be attributed to its higher dispersion properties and/or uncorrected corneal SA. A high SA correction may, independent of lighting conditions, maintain a high image quality; however, one may lose the benefit with decentration exceeding 0.4 mm. Clinical studies are needed to define the role of IOL asphericity and its interaction with intrinsic eye aberrations and how this can be used in optimizing the postoperative performance of monofocal IOL patients.

Funding

Klaus Tschira Stiftung10.13039/501100007316; Carl Zeiss Meditec AG10.13039/501100002806.

Disclosures

G. Auffarth reports grants, lecture fees, and nonfinancial support from Alcon, Hoya, Kowa, and SIFI; grants and lecture fees from Santen and Johnson & Johnson; and grants from Carl Zeiss Meditec AG, PhysIOL, and Acufocus outside the submitted work. R Khoramnia reports grants, lecture fees, and nonfinancial support from Johnson & Johnson Vision Care, Inc., Rayner, 1stQ, and Alcon Laboratories Inc.; grants and lecture fees from Hoya Corporation and PhysIOL; lecture fees and nonfinancial support from Teleon, and lecture fees from Santen, Acufocus, Ophtec, and Bausch & Lomb outside the submitted work. G Łabuz reports non-financial support from Contamac outside the submitted work. W Yan has nothing to disclose.

Data availability

Data underlying the results is available within the figures of this paper. Numerical data can be made available upon reasonable request.

Supplemental document

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