Improving the performance of multifocal diffractive lens designs by adding a peripheral piston

Abstract

Peripheral piston modulation in diffractive multifocal lenses suggests potential improvements in distance vision quality. Five lens designs—bifocal (BF), bifocal with piston (BFP), trifocal (TF), trifocal with piston (TFP), and a commercial refractive (RCN)—were compared using an adaptive optics visual simulator. Optical simulations revealed enhanced optical quality for distant objects with peripheral pistons, without compromising near vision. Visual performance and quality were assessed in eight cycloplegic young subjects. The peripheral piston was associated with trends toward improved high- and low-contrast visual acuity and visual preference scores at distance, suggesting functional and perceptual benefits over non-piston designs.

1. Introduction

Presbyopia, an inevitable consequence of aging, impairs the eye's ability to focus on nearby objects due to the diminished flexibility of the lens, typically manifesting in individuals in their early to mid-40s and significantly impacting daily activities such as reading and using electronic devices [1,2]. Traditional corrective measures, like reading glasses and bifocals, provide different optical powers for near and distance vision, but require the patient to take their spectacles in and out or move their eyes to look through different part of lens [3]. Multifocal corrections, available in contact lenses (CLs) and intraocular lenses (IOLs), offer an alternative by providing multiple focal points for far and near (bifocal corrections) or far, intermediate, and near (trifocal corrections) [3,4]. While monofocal corrections provide clear vision at only a single distance, typically far, multifocal corrections offer functional vision at different distances, at the expense of decreasing quality at far [5].

Commercially available multifocal contact lenses are generally limited to refractive designs, with different regions of the lens dedicated for far and near vision (e.g., “center-near” or “center-far”) [6]. On the other hand, the majority of current bifocal and trifocal IOL designs are diffractive [5,7]. Diffractive multifocal IOLs generate a specialized diffractive wavefront on one of the lens surfaces, consisting of concentric rings or echelettes. These structures generate a phase-wrapped defocus pattern by “wrapping” the phase beyond 2π radians, facilitating the creation of complex optical elements like diffractive lenses while maintaining optical continuity and minimizing artifacts. The diffractive surface splits incoming light into multiple diffraction orders, producing discrete foci at points of constructive interference along the optical axis. Diffractive multifocal IOL designs vary by the number of foci (e.g., bifocal, trifocal), the dioptric power of those foci, and the relative distribution of light among the foci, depending on the specific diffractive design. Some advantages of diffractive IOLs are their relative pupil size independence, improving the consistency of visual quality in different lighting conditions in comparison with concentric refractive zonal designs and reducing sensitivity to misalignments. A disadvantage of all multifocal wavefronts are their photic phenomena (e.g., halos and glare). Additionally, diffractive patterns are unique in that they also contribute chromatic effects to the retinal image [8–11].

Several design strategies are used to optimize light distribution in diffractive designs with the aim of improving contrast sensitivity, reduce aberrations, halos and/or glare [12,13]. These include combining light from different orders into a given focus, make use of the negative longitudinal chromatic aberration of the diffractive component to modulate chromatic aberration. Another strategy to modulate the light energy distribution especially for larger pupils (thereby addressing optical quality at low light conditions) is to employ phase apodization [14], whereby the step height of the echelette is progressively reduced towards the periphery of the lens, shifting energy from the near foci to the distance foci. In addition, in several commercial designs the diffractive element does not cover the entire optical zone, leaving an annular refractive region in the periphery.

Optimizing multifocal designs is challenging due to the need to balance image quality at both near and far distances, as improving one often compromises the other. Incorporating patient behavior and use-case scenarios into the design process can address these limitations. For instance, pupillary miosis causes the pupil to constrict with accommodative effort at near [15], while on the other hand, larger pupils occur during nighttime driving, where more visual discomforts are found with diffractive optics [16]. Reading requires viewing higher contrast stimuli compared to distance viewing tasks, where larger characters improve resolution and luminances higher than those encountered in low-light conditions enhance sensitivity. Conversely, compared to near tasks, outdoor environments are often dominated by distant objects and a range of spatial frequencies [17]. Considering all these factors, it becomes clear that distance vision is often more crucial than near vision in low-light conditions, where pupil sizes are larger.

In this study, we introduce a less-commonly-discussed approach to enhancing distance image quality for large pupils while maintaining near image quality: modifying the peripheral piston to optimize constructive interference. For the purpose of the current study the term “piston” refers to a constant optical phase shift introduced across the peripheral zone of the lens, which does not alter the slope or vergence of the light rays but adjusts the phase alignment relative to the central diffractive zone. Similar to the famous Young’s two-slit experiment [18], matching the phase between two regions of the optical zone will maximize constructive interference, resulting in a smaller, more concentrated Point Spread Function (PSF), and subsequently a higher Modulation Transfer Function (MTF) at the distance focus, especially for mid-to-high spatial frequencies. Here we consider the two regions of the optical zone to be a central circular zone containing the diffractive multifocal, and a peripheral plano zone with different levels of piston (i.e., constant optical phase). Peripheral piston modulation may enhance far-distance visual quality under low-light conditions by utilizing the larger pupil diameter to increase the contribution of the peripheral optical zone. The phase shift introduced by the piston may align the wavefront in the peripheral zone with the central diffractive region, potentially optimizing constructive interference and improving the optical performance for distance vision.

Adaptive optics (AO) visual simulators equipped with Spatial Light Modulators (SLMs) enable precise control of optical wavefronts, making them ideal for testing and optimizing multifocal lens designs [19,20]. This study utilizes a custom AO visual simulator with an SLM to test whether peripheral piston adjustments in diffractive IOL designs enhance visual function and quality.

Evidence supports the efficacy of using SLMs in AO systems for lens simulation. Vinas et al. (2017) showed high correlation between visual quality from real lenses and SLM-simulated phase maps [15]. Similarly, Vedhakrishnan et al. (2021) demonstrated the ability of an SLM-based AO visual simulator to project multifocal patterns onto the pupil of the eye for testing vision with multifocal contact lenses, effectively reproducing the vision achieved with the real contact lenses on eye [21]. Such simulators provide a realistic experience of multifocal vision, helping patients manage expectations pre-implantation and enabling iterative design testing without manufacturing each prototype.

In this study we used a SLM to simulate bifocal and trifocal IOLs without and with a peripheral piston (constant phase of 0.25λ for the bifocal and 0.28λ for the trifocal, where λ = 555 nm) and compared visual performance (high and low contrast visual acuity) as well as visual preference across designs in a group of patients with simulated presbyopia (paralyzed accommodation with cycloplegic drops). Our findings specifically focus on the impact of peripheral piston modulation on diffractive lenses. The results were also compared against a refractive multifocal pattern. This simulation is important as it enables the examination and optimization of lens designs before actual manufacturing, allowing experimental validation of the theoretical benefits of the design modifications, thereby reducing the risks and costs associated with producing suboptimal lenses.

2. Methods

Visual performance was assessed at distance (0.0 D), monocularly using an AO visual simulator in monochromatic light (λ = 555 nm, 5 nm bandwidth). High contrast (100%) visual acuity, low contrast (10%) visual acuity, and visual preference were assessed through five different IOL designs: (1) bifocal (BF), (2) trifocal (TF), (3) bifocal with peripheral piston (BFP), (4) trifocal with peripheral piston (TFP), and (5) one center-near refractive (RCN). Performance through all the designs was compared with a monofocal design. These IOL designs were simulated and mapped onto a Spatial Light Modulator in a custom-built monocular Adaptive Optics Visual Simulator (AOVS). The AOVS's internal aberrations were corrected using a deformable mirror, and all tests were performed with the subjects’ native higher-order aberrations while the spherical equivalent was corrected using an electrically tunable focus lens. The optimal focus for each subject was determined by adjusting the tunable lens as they viewed a Maltese cross target positioned at optical infinity and illuminated with 555 nm light

2.1. Theoretical optimization of the peripheral piston

To determine the optimal value of peripheral piston for subsequent vision testing, we first performed a simulation to theoretically assess the impact of peripheral piston on through-focus image quality under monochromatic incoherent light.

The multifocal patterns consisted of phase-wrapped defocus defined over the central 5 mm of the optical zone, with an annulus of peripheral piston (inner diameter of 5 mm and outer diameter of 6 mm), as illustrated in Fig. 1. Details of dioptric add-power and phase height are listed in Table 1. Peripheral piston was varied in magnitude from 0.0 to 1.0 waves at 555 nm. The optimal piston values identified through these simulations were 0.25 waves for the bifocal design and 0.28 waves for the trifocal design, which were used in subsequent evaluations. The maximum optical phase heights (Table 1) of the phase-wrapped multifocal wavefronts were chosen such that the relative percent energy distribution would be for the bifocal 50/50 (far/near) and for the trifocal 54/23/23 (far/intermediate/near) for a pupil diameter of 5 mm or less.

Fig. 1.

Illustration of the 2-zone distribution in the IOL: Central zone (5-mm diameter) with the diffractive multifocal wavefront and a 1-mm width annular region, with flat phase of 0, 0.25λ or 0.28λ peripheral piston.

Table 1. Parameters of diffractive bifocal and trifocal patterns. ^a .

	Add-Powers [Diopters]	Maximum Optical Phase Height [waves at 555 nm]	Diameter of Diffractive Pattern [mm]	Relative Diffraction Efficiency (% energy in far/intermediate/near)
Diffractive Bifocal	0.0 (far) 2.0 (near)	0.50	5.0	(50/none/50)
Diffractive Trifocal	0.0 (far) 1.0 (intermediate) 2.0 (near)	0.55	5.0	(54/23/23)

^a Parameters correspond to the diffractive bifocal and trifocal lens profiles used in this study. Add-powers indicate dioptric powers, phase height is at 555 nm, diameter represents the diffractive zone, and diffraction efficiency shows energy distribution.

Cross-sections of the diffractive multifocal wavefront patterns investigated in this study are shown in Fig. 2. The diffractive bifocal is shown in Fig. 2(a) – 2(c), and the diffractive trifocal is shown in 2d – 2f. As an illustrative example, 0.0, 0.5 and 1.0 waves at 555 nm of peripheral piston are shown in the left, center and right columns of Fig. 2.

Fig. 2.

Cross-sections of diffractive bifocals (top row) and trifocals (bottom row) with various amounts of peripheral piston: 0.0, 0.5 and 1.0 waves (from left to right).

MATLAB (MathWorks, 2023a) computer simulations of optical quality with these lenses were performed with a 6-mm diameter pupil in monochromatic light at 555 nm wavelength. Simulations were performed assuming a diffraction-limited, aberration free eye-model. The monochromatic PSF was computed using Fourier Optics theory, as described by Chen et al., [22] and the Strehl Ratio, defined as the maximum value of the normalized monochromatic PSF, was used as the optical quality metric. An aberration-free, non-apodized amplitude pupil was used, and the wavefront phase was defined as the multifocal profiles described in Table 1. Illustrative examples of multifocal wavefront with various magnitudes of peripheral piston are shown in Fig. 2. The Strehl Ratio was calculated in 0.1 D steps, by modifying the defocus term of the wave aberration. Through-focus Strehl Ratio was obtained in a range between -0.5 D to +2.5 D (positive values indicate near object distances).

2.2. Adaptive optics visual simulator

We utilized a custom-developed Adaptive Optics Visual Simulator (AOVS) at the Center for Visual Science, University of Rochester, to evaluate multifocal lens designs by simulating their optical effects. A detailed description of this instrument can be found in a recent publication [23]. In summary, the AOVS features a supercontinuum laser source (LEUKOS ROCK 450-4, France) equipped with acousto-optic tunable filters (Optics and Photonics Gooch & Housego, UK) to select specific wavelengths of 555 nm for visual stimuli and 830 nm for aberration measurements. The supercontinuum laser provides temporal incoherence through its broad spectral bandwidth, while spatial coherence was disrupted by introducing a holographic diffuser. A Hartmann-Shack wavefront sensor (HASO 32 OEM, Imagine Eyes, France) measures ocular aberrations, and, an electromagnetic deformable mirror (MIRAO 52e, Imagine Eyes, France) with 52 actuators corrects which, for the purposes of the current study, corrects the internal optical aberrations of the instrument. Lens designs, including those with peripheral piston, are projected using a reflective phase-only Liquid Crystal on Silicon Spatial Light Modulator (LCoS-SLM, Holoeye, Germany). Visual stimuli are presented via a Digital Micromirror Device (DMD) with a 2.5-degree angular subtend. Pupil alignment is managed using a LED ring illuminator and CCD camera, which allows pupil visualization with an overlaid cross-hair and rings. The stimuli are viewed through an artificial pupil with a fixed 6 mm diameter, limiting the effective pupil diameter from that obtained by cycloplegia.

2.3. IOL design simulations

The wavefront maps corresponding to the diffractive multifocal lens designs defined below were simulated on the SLM of the AOVS setup. The designs (shown in Fig. 3): (1) A diffractive Bifocal lens (BF); (2) a diffractive Trifocal lens (TF); (3) A diffractive Bifocal lens with a peripheral piston (BFP); (4) a diffractive Trifocal lens with peripheral piston (TFP); and (5) a commercial refractive center-near lens (RCN; Dailies Total1, Alcon). All lens designs were simulated for a total aperture diameter of 6 mm. The BF, TF, BFP, and TFP designs featured a 5-mm central diffractive zone, with the outer 1 mm in the BFP and TFP designs allocated for the non-zero peripheral piston. The RCN design, however, utilized the entire 6-mm aperture without a distinct peripheral zone.

Fig. 3.

Wavefront maps of diffractive multifocal patterns used in this study, from left to right: bifocal (BF), bifocal with peripheral piston (BFP), trifocal (TF), and trifocal with peripheral piston (TFP). The yellow dashed line corresponds to a 6 mm diameter pupil diameter.

The near add in the BF/BFP and TF/TFP lenses was 2 D, and the intermediate add of TF/TFP lenses was 1 D (see Table 1). For the visual simulations, the peripheral piston of the BFP and TFP was 0.25λ and 0.28λ, respectively (which predicted optimal performance in the computer simulations, see section 3.1 and Fig. 5). RCN was an aspheric refractive center-near design with 0 D distance power and a mid-add of 1.03 D, featuring a smooth aspheric transition to the peripheral distance zone [6,24].

Fig. 5.

Strehl ratio at selected object distances (far, intermediate and near foci) as a function of peripheral piston height (similar computational conditions as in Fig. 4).

These phase maps were generated as grayscale images for 6 mm pupil and 555 nm wavelength using MATLAB and then mapped onto the SLM. The SLM operates by altering the phase of the reflected light waves, thereby creating a virtual lens with the same optical characteristics as the designed phase map. To ensure continuous phase modulation without abrupt discontinuities, a 2π-wrapping technique is applied. In this process, the optical phase is cyclically adjusted so that any phase exceeding 2π radians is wrapped back within the 0–2π range, maintaining smooth phase transitions across the optical zone.

2.4. Subjects

A total of eight subjects (age 25.4 ± 1.1 years) participated in the study, with a mean spherical refractive error of -0.78 ± 2.07 D and astigmatism below 0.5 D in all cases. To control for accommodation, each subject was cyclopleged with 1% Tropicamide ophthalmic solution, and assessments of visual acuity and preference were conducted exclusively for distance (0D) vision. Data collection was conducted over two sessions, each lasting approximately 1.5 hours.

The study was conducted in accordance with the tenets of the Declaration of Helsinki and received approval from the University of Rochester Institutional Review Board. Written informed consent was obtained from all participants prior to their involvement in the study.

2.5. High and low contrast visual acuity measurements

Visual acuity (VA) measurements were conducted at distance (0 D) to evaluate the visual performance through the simulated IOL designs across two contrast conditions. High and low contrast VA (100% at 10%, respectively) were measured using a logMAR chart with tumbling letter ‘E’ optotypes presented (200 ms duration) in a 4-Alternative Forced Choice (4AFC) paradigm, and subjects’ task was to identify the correct orientation of the optotype from four possible options. A QUEST algorithm was used for thresholding VA, and the average of last six points were averaged to determine the logMAR VA. Vision testing was performed with monochromatic light (555 nm) and a luminance of 85 cd/m².

2.6. Visual preference test

The visual preference (VP) test was conducted to assess subjective perceived visual quality of a natural image (a scene of country houses, subtending 2.5°) across five simulated lens designs (BF, BFP, TF, TFP, and RCN). VP was measured using a 2-Alternative Forced Choice (2AFC) method with confidence-weighted scoring. Subjects were presented with randomized pairs of lens configurations generated through the Spatial Light Modulator (SLM), with each lens design paired against the other four designs. Each pair was repeated 16 times, resulting in a total of 64 trials per design. For each trial, subjects selected their preferred image and rated their confidence using a weighted scale: ± 10 for very sure, ± 5 for moderately sure, and ±1 for not sure. If a subject consistently preferred a single design and assigned the maximum confidence score (+10) for all trials, the highest possible score for that design would be 64 × (+10) =  + 640. Conversely, consistently disliking a design with the maximum confidence score (-10) would result in 64 × (−10) = −640.

2.7. Statistical analysis

Data were analyzed using MATLAB software. Descriptive statistics, including means and standard error of means, were calculated for all key variables. A single-factor ANOVA was conducted to assess differences in VA across the lens designs for each contrast condition. VP scores were calculated using a confidence-weighted scoring system, integrating participant responses and confidence levels into aggregated scores. Post-hoc pairwise comparisons for VA and VP were conducted using Bonferroni correction to adjust for multiple comparisons. Linear regression analysis was employed to examine correlations between VA and VP. Statistical significance was defined as p < 0.05 for all analyses.

3. Results

3.1. Theoretical simulations of the effect of the peripheral piston

Through-focus Strehl ratio from computer simulations is shown in Fig. 4 for diffractive bifocal (left) and trifocal (right) wavefronts for three values of peripheral piston. The results show that peripheral piston has a significant impact on optical quality at distance (0 D), and not at other foci (e.g., intermediate and near). At 0D, maximal constructive interference resulted in the highest Strehl ratio at 0.25λ of peripheral piston. Alternatively, 0.75λ led to a dip in distance image quality due to maximal destructive interference.

Fig. 4.

Through-focus Strehl ratio for diffractive bifocal (left) and trifocal (right) wavefronts, for 6-mm pupils, assuming diffraction-limited optics.

Figure 5 shows the effect of peripheral piston height on Strehl ratio at specific object distances (i.e., the foci of the bifocal and trifocal). The largest effect of peripheral piston was on distance vision at 0 D, with a negligible effect at intermediate and near.

Based on these simulations, we can conclude that the 0^th order of diffraction (pertaining to the focus at 0 D) equals piston optical phase to the average phase height of the wavefront map. The Strehl ratio was maximum when the inner and outer zones interfered constructively. Thus, optical quality at 0 D was maximized for a peripheral piston height of 0.25 and 0.28 waves, for the diffractive bifocal and trifocal wavefronts, respectively. These values of peripheral piston height were used for subsequent vision testing and optical metrology.

3.2. High and low contrast visual acuity

The VA measurements in patients at 100% and 10% contrast levels showed significant variations across the lens designs, as depicted in Fig. 6. A one-way ANOVA revealed statistically significant variations in VA across lens designs for both 100% and 10% contrast conditions (p < 0.01 for each), demonstrating that lens type has a distinct impact on VA independent of contrast level.

Fig. 6.

Distance visual acuity (logMAR) for different lens designs under 100% (dark symbols) and 10% contrast (light symbols) conditions. Lens designs include monofocal, Bifocal (BF), Bifocal with piston (BFP), Refractive Center Near (RCN), Trifocal (TF), and Trifocal with piston (TFP). Symbols represent average across subjects. Error bars represent standard error of the mean.

The monofocal lens showed the best VA among all designs, with a logMAR VA of -0.22 ± 0.02 (Standard Error of the Mean, SEM) for 100% contrast (p = 0.01 when compared to the multifocal lens average) and 0.16 ± 0.06 for 10% contrast (p < 0.01 relative to the multifocal lens average).

At the 100% contrast condition, the BFP lens showed a slight improvement in VA compared to the BF lens (p = 0.41), with a logMAR value of -0.10 ± 0.06 for BFP versus -0.09 ± 0.05 for BF. Similarly, the TFP lens demonstrated a modest improvement over the TF lens (p = 0.27), achieving a VA of -0.14 ± 0.04 compared to -0.11 ± 0.06 for TF. The RCN lens exhibited the greatest degradation in VA among the multifocal lenses, with a logMAR VA of 0.01 ± 0.04. Pairwise comparisons revealed statistically significant differences between the RCN lens and other multifocal lenses (p < 0.05 for all comparisons).

At 10% contrast condition, the BF design recorded a VA of 0.38 ± 0.05, with the BFP lens showing a slightly better performance at 0.36 ± 0.06 (p = 38). The TF and TFP designs had almost similar VA values of 0.33 ± 0.06 and 0.32 ± 0.06, respectively. The RCN lens demonstrated the lowest performance among all multifocal lens designs, with a VA of 0.46 ± 0.06 logMAR, showing a significant difference specifically in comparison to the TFP design (p = 0.02).

Figure 7 illustrates the change in VA (logMAR) with peripheral piston lenses (BFP and TFP) relative to their standard counterparts (BF and TF), shown in the y-axis as the difference in VA (logMAR), with negative values denoting improved VA and positive values indicating deterioration. Results are presented for both high and low contrast conditions. In high contrast conditions, the trifocal design showed greater improvement with the addition of peripheral piston, whereas in low contrast conditions, bifocal designs exhibited more benefit with piston. However, the differences between bifocal and trifocal designs were not statistically significant, regardless of contrast condition (p > 0.5 for both condition).

Fig. 7.

Difference in visual acuity (logMAR) between BFP and BF and between TFP and TF, for both 100% contrast (dark bars) and 10% contrast (light bars). Positive values indicate visual acuity improvement due to the addition of the peripheral piston. Error bars indicate SEM.

3.3. Visual preference

The results in Fig. 8 illustrate the VP scores for BF, BFP, TF, and TFP. One-way ANOVA indicates a significant effect of lens design on VP scores (p < 0.01). The BFP lens recorded a VP score of 26 ± 40.60, slightly higher than the BF lens, which had a score of 21.57 ± 36.83 (p = 0.43). The TFP lens achieved the highest VP score of 209.86 ± 59.51, which was marginally statistically higher than the TF lens score of 147.43 ± 44.79 (p = 0.06). In contrast, the RCN lens exhibited a markedly negative VP score of -404.86 ± 128.09, indicating a perceptual disfavor among participants compared to other lenses (p < 0.05 for all cases).

Fig. 8.

Visual preference scores for the different lens designs (BF, BFP, RCN, TF, and TFP). Positive values indicate higher preference, while negative values reflect lower preference. TFP exhibits the highest preference score, while RCN shows the lowest. Error bars represent SEM.

The BFP lens exhibited a minimal increase in VP with a mean benefit of 4.43 ± 46.65 over the BF lens (Fig. 9). In contrast, the TFP lens showed a larger improvement (Fig. 9), with a mean increase in preference score of 62.43 ± 42.98 over the TF lens.

Fig. 9.

Benefit in visual preference scores for BFP compared to BF and TFP compared to TF (differences). Positive values indicate an improvement in visual preference with the addition of the peripheral piston. Error bars represent SEM.

3.4. Visual acuity vs. preference score

In Fig. 10, the relationship between high contrast VAs (HCVA, logMAR) and VP scores are shown across different lens designs, with each point representing individual data. Among the designs, the TFP lens generally exhibited more negative VA values and higher positive preference scores, suggesting a tendency toward both better visual performance and perceived visual quality. The regression fit line reveals a negative correlation between HCVA and VP (r = 0.39, p-value = 0.01). This modest correlation suggests that while there is a statistically significant association between HCVA and VP, it is relatively low, indicating that VA alone may not fully capture subjective visual quality. The spread of data points highlights the variability in participants’ experiences, underlining the necessity of assessing both visual function and perceptual quality to gain a more comprehensive understanding of visual performance and satisfaction.

Fig. 10.

Correlation between high contrast visual acuity (logMAR) and visual preference scores across different lens designs: BF, BFP, RCN, TF, and TFP. Individual data points are shown as solid circles, with subject IDs (e.g., S1, S2) labeled inside the symbols. The regression line represents the fitting of the individual data.

4. Discussion

4.1. Differences between bifocal and trifocal lenses

In this study, we compared the bifocal with peripheral piston (BFP) to the bifocal (BF), and the trifocal with peripheral piston (TFP) to the trifocal (TF), across three key metrics: high contrast VA, low contrast VA, and perceived VP. The measurements at 100% contrast indicated that TFP achieved the highest high contrast VA values, reflecting slightly sharper retinal image quality. The observed mean improvement in high contrast VA was -0.03 logMAR for TFP compared to TF, while for BFP compared to BF, the change was -0.01 logMAR. Although these differences are small, the improvement was slightly more noticeable in the TFP lens compared to BFP.

Low contrast VA (10% contrast) assessments provided further insights into the performance limitations of bifocal designs, particularly under challenging viewing conditions. In this setting, both bifocal lenses demonstrated a significant reduction in VA, whereas the trifocal designs, including TFP, maintained relatively stable performance. This resilience in low contrast conditions is especially relevant for situations where contrast sensitivity plays a critical role, such as low-light environments. Although the addition of a peripheral piston did not lead to substantial improvements in low contrast VA within the scope of our selected tasks, it remains possible that this feature could yield perceptual benefits under different visual assessments that emphasize contrast sensitivity.

In addition to the objective VA measurements, subjective evaluations through VP scores demonstrated a notable favorability for trifocal lenses, particularly the TFP design. Across the designs, TFP achieved the highest preference scores, suggesting that participants experienced greater satisfaction and visual comfort with this lens configuration. Interestingly, while differences in VA between designs were small and clinically negligible, the preference tests revealed a bias toward piston designs, indicating that these differences may still be perceived by subjects. This finding is supported by the preference score comparison in Fig. 6, where TFP shows a clear advantage over its bifocal counterpart with peripheral piston (BFP). The weak correlation between high contrast VA and VP, as shown in Fig. 7, underscores the idea that VA alone does not fully account for subjective visual quality. The observed variability in preference scores across individuals highlights the subjective nature of visual quality, supporting the need to assess both objective and subjective metrics for a more comprehensive evaluation of lens performance.

The observed advantage of trifocal designs in our high contrast VA and VP measurements can be understood through the specific energy distribution in these lenses. The trifocal lenses used in this study featured an energy allocation of approximately 54% for distance, with 23% each for intermediate and near vision, whereas the bifocal lenses distributed energy equally between distance and near (50/50 split). This energy distribution could account for the trifocal’s enhanced performance at distance, as the far focus receives a higher percentage of the available light compared to the bifocal design. Importantly, we are not asserting an inherent superiority of trifocal lenses over bifocals; rather, this advantage appears closely linked to the specific percentage energy split and design characteristics of the trifocal lenses tested, while the differences in the structure of the halo produced by the defocused image from the near focus (BF) and the near and intermediate foci (TF) may also play a role in the observed functional and perceptual vision at far.

Intentionally, the diffractive design did not extent the entire optical zone, but was restricted to the central 5-mm, leaving a peripheral flat area of zero phase shift (BF and TF designs) or a non-zero phase (BF and TF piston designs). A smaller diffractive central region is common practice in several commercial designs, under the rationale that larger pupils are normally devoted to far vision, making multifocal optics and a near region unnecessary. This choice allowed us a direct comparison without differential effects attributed to the different extents of the diffractive component. However, the results should not be generalized to comparative performance of full diffractive designs with diffractive designs with annular piston. Further studies evaluating the effect of peripheral piston modulation across varying diffractive surface sizes and configurations would provide alternative comparative benchmarks.

4.2. Effect of the piston

This study found that the trifocal lens with peripheral piston provided both better visual performance and perceived visual quality compared to other designs, with 7/8 subjects achieving VA and VP scores better than 0, and 5/9 subjects achieving VA better than -0.1 logMAR and a VP score above 175. The addition of a peripheral piston in the bifocal design resulted in a slight but not significant improvement. The RCN design showed lower performance compared to the other designs, which may be partly attributed to its energy allocation for distance being less than that of the other simulated lens designs.

Peripheral piston surrounding diffractive multifocal wavefront introduces phase shifts in the peripheral zones, theoretically optimizing light’s constructive interference at distance and enhancing retinal image quality. This mechanism may result in sharper retinal images and improved high contrast VA, especially in low light conditions where the pupil may be larger than the diffractive region of an IOL’s optical zone. Studies on multifocal designs have shown that phase modulation can enhance the MTF, leading to better optical performance under conditions where sharpness is critical [25,26]. Alternatively, the effect of peripheral piston which was half a wave out of phase with optimal value (e.g., 0.75λ for the bifocal) resulted in maximal destructive interference, as seen by the dip in Strehl ratio at 0 D in Fig. 4.

In low contrast environments, where multifocal lenses often experience a decline in performance due to scattered light and reduced contrast sensitivity, peripheral piston modulation may still offer benefits by enhancing distance optical quality. The redistribution of light could potentially improve contrast sensitivity by enhancing the MTF in challenging visual conditions [27,28]. This improvement might be particularly relevant in dim lighting, where pupils dilate and visual performance tends to deteriorate.

The concurrence of the optimal piston level with the average phase height was an intriguing finding, as it appeared to maximize constructive interference for the bifocal and trifocal designs tested. This observation implies that the 0^th order of diffraction (allocated to distance vision) accrues phase equal to the average phase of the diffractive wavefront. Therefore, the bifocal condition, which varies in phase height between 0.0 and 0.5λ and has an average value of 0.25λ, had optimal distance image quality when the peripheral piston region also had a value of 0.25λ. A similar effect was observed in the diffractive trifocal. Although this effect was observed in the designs tested, further investigation is required to determine whether this relationship applies to other multifocal lens profiles. Factors such as energy distribution among diffraction orders and diffraction efficiency may influence the generalizability of using the average phase height as a predictor for optimal piston levels.

In real-life scenarios, patients with naturally larger pupils (exceeding 5 mm for the types of lens designs we used) would likely benefit from this effect. Larger pupil sizes increase the contribution of the peripheral zone, potentially resulting in sharper retinal images and improved visual clarity for distance, particularly under low-light conditions where pupil dilation occurs.

4.3. Theoretical prediction vs. empirical results

The core question of this study relates to the effect of peripheral piston on visual performance. While theoretical simulations predicted substantial improvements in retinal image quality with the addition of the peripheral piston, the actual visual tasks demonstrated smaller benefits than the theoretical predictions. The comparison between bifocal lenses (BF vs. BFP) and trifocal lenses (TF vs. TFP) in Fig. 6 and 7 show that the peripheral piston improved VA in both bifocal and trifocal designs. However, the enhancement was more noticeable in the trifocal lenses (TFP), especially for high contrast VA, where the improvement was reflected in sharper retinal images.

One possible explanation for the less pronounced improvements lies in the Stiles-Crawford effect, which suggests that light entering the eye through the peripheral zones (e.g., between 5 mm and 6 mm in pupil diameter) contributes less to perceived image quality [29,30]. This effect may have diminished the influence of the peripheral piston, despite its potential to improve light distribution. Additionally, theoretical modeling assumed a diffraction-limited model eye, but in the experiments, subjects viewed the targets through the simulated lenses and their native higher-order aberrations (the deformable mirror in the AOVS only corrected for higher-order aberrations inherent to the system, not participants’ native higher-order aberrations). These uncorrected aberrations could have limited the potential benefits that the peripheral piston might otherwise provide and may be, at least in part, behind the observed inter-subject variability in the absolute VA and VP with the lenses and the relative effect of piston.

4.4. Relation between visual acuity and visual preference metrics

The weak correlation between individual high contrast VA and VP in Fig. 10 highlights the importance of VP testing when evaluating multifocal lens designs. Although there is a statistically significant association, the relatively low correlation value (particularly for some designs such as RCN) indicates that individual VA measurements alone are insufficient for fully capturing subjective visual experience. This variability suggests that while VA provides some idea about retinal image quality, it does not reflect individual visual comfort or satisfaction levels, which are critical factors in real-world visual performance. This measure is particularly relevant for advanced lens designs, where enhancements in optical quality may not straightforwardly translate to better user experience without subjective perceptual evaluation.

The individual data points show variability across different lens designs, with BF and BFP designs generally clustered around lower VP scores, despite relatively comparable high contrast VA. This indicates that while bifocal lenses may provide adequate sharpness, they are less favored by users, possibly due to higher visual disturbances. In contrast, trifocal lenses, especially those with peripheral piston modulation, consistently show higher VP scores, suggesting that despite similar or slightly reduced high contrast VA, the subjective experience is more favorable, likely due to reduced optical artifacts and/or visual discomfort. The RCN design, exhibited highly negative VP scores, illustrate that even with a not largely reduced VA (around 0.01 logMAR on average), user satisfaction can be significantly impacted if visual disturbances are prominent. Furthermore, the concentric RCN design with a relatively large central zone for near, may be less suited for distant vision, even if the fixed 6-mm pupil allows wider peripheral regions for distance than the smaller natural pupils usually found in presbyopes (Guillon et al., 2016, OVS). The comparison of VA logMAR and preference underscores the importance of considering both objective VA and subjective experience in evaluating lens designs. Overall, the data suggests that while VA remains important, VP is more heavily influenced by other factors present when judging perceived quality of natural images, making trifocal lenses with piston modulation particularly well-balanced in terms of both performance and perceptual quality.

4.5. Potential clinical benefits and limitations

Patients and clinicians may benefit from peripheral piston modulation being considered in multifocal IOL design, as the findings suggest potential improvements in patient satisfaction, while maintaining acceptable levels of high contrast VA. This balance between objective vision quality and subjective comfort could lead to fewer post-surgical complications related to visual discomfort and potentially reduce the need for corrective follow-ups. Lens design modifications, such as optimizing phase modulation across more zones or adjusting the degree of modulation, could further enhance visual comfort by improving light distribution.

A limitation of the current study was that all simulations and vision testing were performed in monochromatic illumination. While this was done to isolate the effect of peripheral piston modulation and avoid chromatic effects associated with phase wrapping (which in any case are also present in diffractive lenses), future work should include white light assessment to more closely reflect real-world viewing conditions.

While the tested profiles are suitable for presbyopia correction and could be deployed in IOLs or CLs, the potential application of such profiles in other contexts, such as myopia control, remains an area for future research.

Funding

Empire State Development Funds; Center of Emerging and Innovative Science (University of Rochester); Clerio Vision, Inc; National Institutes of Health, National Eye Institute10.13039/100000053 (NEI R01-EY035009,P30EY 001319); Research to Prevent Blindness10.13039/100001818 Unrestricted Funds to the Department of Ophthalmology.

Disclosures

SG: None; TZ: None; SA: None; GGM: Clerio Vision (E, F); LZ: Clerio Vision (E, F); SM: None.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.