Physiological chromatic model eyes for IOL characterization

Abstract

Accurate optical bench characterization of intraocular lenses (IOLs) under white-light conditions requires model eyes that reproduce both physiological spherical aberration (SA) and longitudinal chromatic aberration (LCA). Although current ISO and ANSI standards adopt a physiological reference for LCA under polychromatic testing, a rigorous framework is still needed to determine whether a complete bench system reproduces a physiologically meaningful chromatic baseline. To address this issue, we propose a chromatic model eye based on an achromatic doublet cornea compatible with standard ISO and ANSI geometries. Different physiological SA levels are obtained by selecting the posterior-surface conic constant while preserving physiological LCA. Longitudinal chromatic aberration is evaluated from the paraxial vergence of the exit-pupil wavefront of the complete optical system and referenced to the spectacle plane of the physiological reference eye. When implanted with IOLs spanning clinically relevant dispersion ranges, the proposed model reproduces the pseudophakic LCA of the ANSI Physiological benchmark over 400–700 nm, with deviations below 0.02 D for a high-Abbe IOL and 0.06 D for a low-Abbe IOL. Polychromatic MTF analysis showed trends consistent with the residual differences in LCA across model eyes when the complete optical system was considered. These results provide a standards-compliant framework for chromatic validation of IOL test benches under physiologically relevant conditions.

1. Introduction

Intraocular lens (IOL) optical performance testing relies on model eyes that emulate the optical properties of the human eye. More broadly, the goal of such preclinical measurements is not only to characterize the optics of the IOL itself, but also to ensure that bench-derived image-quality metrics can be interpreted under physiologically meaningful conditions. Historically, most optical bench assessments were performed under narrowband illumination [1] (around 546 nm), which limited sensitivity to chromatic effects and decoupled IOL evaluation from wavelength-dependent optical performance.

In ISO standard 11979-2-2024, Annex C [2], optical characterization is now explicitly linked to clinically relevant outcomes, and preclinical assessments that include optical bench testing are required to be performed using the Annex B model eye modified to allow measurements in white light. This reflects the need to evaluate IOL performance under polychromatic conditions representative of real-world vision, typically defined over the visible spectrum and weighted by the photopic luminous efficiency function V(λ).

Polychromatic testing is particularly critical for diffractive and other simultaneous-vision IOL designs, whose optical performance depends explicitly on wavelength, on the redistribution of energy among diffraction orders, and, in some cases, on the intentional manipulation or partial compensation of ocular longitudinal chromatic aberration (LCA) [3–7]. Under such conditions, the chromatic properties of the model eye become an integral part of the measurement, and the model cornea must induce a physiological chromatic focal shift in order for metrics such as the modulation transfer function (MTF) to provide a clinically meaningful representation of in-vivo performance [2]. More generally, this means that under white-light testing the model eye is no longer a neutral support element, but part of the optical system that determines the measured image quality. In this context, physiological relevance should be understood at the level of the complete bench system rather than as a requirement that each isolated optical element reproduces the corresponding ocular component in a uniquely biomimetic manner.

Beyond chromatic aberration, model eyes are also expected to reproduce other key optical characteristics of the human eye, most notably corneal spherical aberration (SA) [8,9]. Although an average corneal SA value of approximately 0.27 µm is often quoted for a 6-mm entrance pupil diameter [10], corneal SA exhibits substantial inter-subject variability and depends on measurement conditions. In parallel, commercial IOL designs implement a wide range of SA correction strategies, from near-zero residual SA to partial or full compensation of the average corneal value. As a result, a single SA target is insufficient to support fair and clinically meaningful comparisons across different IOL platforms.

Model-eye testing therefore benefits from defining physiologically plausible levels of spherical aberration and implementing the corresponding corneal geometries. In the ISO model-eye configuration, this can be achieved using a conic model cornea whose conic constant is selected to produce the desired SA at the specified 5.15-mm beam diameter and image-plane location (25–28 mm), while preserving the standard geometry. This flexibility allows the ISO model eye to accommodate different clinically relevant SA targets, reflecting both inter-subject variability and the diversity of SA correction strategies employed in contemporary IOL designs.

The chromatic dispersion of the ocular media has been extensively characterized in the literature, notably by Thibos et al. [11] and by Atchison and Smith [12], providing a robust physiological basis for defining target values of LCA under polychromatic conditions relevant to clinical vision. In contrast to spherical aberration, the magnitude of longitudinal chromatic aberration is comparatively consistent across human eyes, with reported inter-subject variability on the order of ∼20% [13,14]. This relative invariance makes it reasonable to define a canonical chromatic physiological reference that a model eye should replicate.

Previous work in this area can be broadly divided into three categories: schematic and standards-oriented model eye designs for IOL testing [1,15,16], physiological studies of ocular chromatic dispersion and chromatic difference of refraction [11,12], and analyses of polychromatic image quality and its dependence on chromatic aberration [17]. While these studies provide the necessary optical and physiological background, they do not fully resolve how chromatic agreement between model eyes should be assessed when the complete bench geometry includes the cornea, cuvette windows, immersion medium, implanted IOL, and image-space propagation.

Within the ANSI Z80.35 framework [15], the Physiological and Fluid Cell model eyes are specified as alternative physical implementations intended to reproduce the optical behavior of the human eye under white-light testing conditions. Although the standard does not prescribe an explicit chromatic target, their configuration implicitly assumes a chromatic response representative of the human cornea, motivating their use as reference model eyes for polychromatic IOL evaluation. However, recent results [16] shown that the two configurations have slightly different LCA values.

In this work, we investigate the design of a model eye for optical bench testing that aims to reproduce physiologically realistic levels of both spherical aberration and longitudinal chromatic aberration, while remaining compatible with standard ISO and ANSI geometries and preserving interchangeability with existing optical bench setups. The purpose is not merely to optimize a model eye to match a predefined chromatic target, but to evaluate whether an optical bench configuration reproduces a physiologically meaningful pseudophakic chromatic baseline when the complete optical system is considered. We then compare the proposed configuration in terms of chromatic behavior and polychromatic image quality against an accepted benchmark model eye and examine how residual differences in LCA affect the interpretation of bench-derived image-quality metrics.

2. Methods

The model cornea was implemented as a two-element doublet, with its three radii of curvature optimized in Zemax OpticStudio 2025 (Zemax LLC, Kirkland, WA, USA). The doublet thickness was kept fixed to satisfy the mechanical and dimensional constraints of the optical bench.

The optimization followed the ISO 11979-2 Annex B.3.1 configuration, corresponding to a model eye without an IOL and an image-space refractive index of 1.336 (Abbe number 56). Three optimization targets were imposed: (i) spherical aberration (SA) of 0.28 µm for a 5.15-mm aperture stop; (ii) working F-number matched to the ISO configuration for the corresponding SA value, in order to preserve image magnification and spatial-frequency scaling, and (iii) physiological longitudinal chromatic aberration (LCA). During optimization, LCA was expressed as a longitudinal focal shift, in metric units, relative to the paraxial image plane at 550 nm. This quantity was used exclusively as a tuning parameter and is not interpreted as a physical performance metric.

Chromatic performance was subsequently simulated using the complete model eye implanted with an IOL having dispersion properties equivalent to the crystalline lens. The IOL asphericity was adjusted at the reference wavelength to minimize residual monochromatic aberrations in each configuration. Exact ray tracing was performed for wavelengths between 400 and 700 nm, in 20-nm steps. LCA was then computed in diopters as the chromatic difference in paraxial defocus between 550 nm and the remaining wavelengths, derived from the exit-pupil wavefront of the complete model-eye system. This calculation explicitly accounts for the complete optical system, including the model cornea, IOL, immersion medium, cuvette windows and image-space propagation. The longitudinal focal-shift target in the Zemax merit function was iteratively adjusted until the resulting LCA computed at the exit-pupil matched the physiological target.

The final model cornea consists of a crown–flint doublet fabricated from glasses H-K9L and H-QF50, with spherical surfaces. Planar fused-silica windows (3-mm thickness) were placed before and after the IOL to represent the fluid-filled cuvette used in bench testing. A circular aperture stop of 5.15 mm diameter was positioned at the IOL plane, 2 mm behind the first window, in accordance with the ISO model-eye specification. This configuration ensures a beam diameter of 5.15 mm at a distance of 27.83 mm behind the paraxial image plane of the cornea. Different levels of corneal spherical aberration are realized by selecting distinct values for the posterior-surface conic constant of the corneal doublet (Q ≠ 0), thereby defining a family of corneal variants within the same bench geometry, following an approach similar to that adopted in the ISO model.

2.1. Reference phakic eye LCA and normalization across model eyes

The chromatic difference in defocus of the human eye is conventionally defined in diopters in object space, with reference to the spectacle plane. Accordingly, to enable a meaningful comparison between model-eye predictions and physiological longitudinal chromatic aberration, chromatic defocus must be expressed with respect to a physiological entrance pupil and propagated to the spectacle plane.

However, different model eyes may exhibit different pupil magnifications—even when sharing the same physical stop position, due to differences in corneal power and in the cornea–IOL separation. As a result, identical chromatic defocus values referenced to the exit pupil do not, in general, correspond to the same effective defocus when referenced to the entrance pupil. To avoid this ambiguity, the vergence derived at the exit pupil is scaled to the entrance pupil of the ANSI Physiological eye and subsequently propagated to the spectacle plane, defined as 12 mm in front of the corneal apex.

Wavefront vergence as a function of wavelength is derived from the exit-pupil wavefront error by expanding the optical path difference in spherical Zernike polynomials up to 8^th order. From the resulting coefficients, the corresponding paraxial mean quadratic vergence is computed as [18]:

$$V_{\text{EP}}(\lambda )=\frac{-c_0^2(\lambda )\cdot 4\sqrt{3}+c_0^4(\lambda )\cdot 12\sqrt{5}-c_0^6(\lambda )\cdot 24\sqrt{7}+c_0^8(\lambda )\cdot 40\sqrt{9}}{r^2}$$

where $c_0^2$ is the Zernike defocus coefficient and $c_0^4,c_0^{6}and{c}_0^8$ are the 4^th, 6^th and 8^th Zernike spherical aberration coefficients, respectively. This formulation defines chromatic defocus from paraxial vergence and provides a well-defined reference in the presence of residual spherical aberration, rather than estimating it from the second-order term alone. The resulting paraxial vergence is scaled to a physiological entrance pupil by applying a paraxial pupil-scaling equivalence between the bench exit pupil and the physiological entrance pupil. This results in a scaling of vergence by the square of the pupil-diameter ratio:

$$V_{\text{EP}}(\lambda )=V_{\text{XP}}(\lambda ){\left(\frac{{\mathrm{\Phi }}_{\text{EP}\mathrm{\_}\text{ref}}}{{\mathrm{\Phi }}_{\text{XP}\mathrm{\_}\text{model}}}\right)}^2$$

Here, $V_{\text{XP}}$ is the vergence derived at the model’s exit pupil of diameter ${\mathrm{\Phi }}_{\text{XP}\mathrm{\_}\text{model}}$ , and ${\mathrm{\Phi }}_{\text{EP}\mathrm{\_}\text{ref}}$ is the entrance pupil diameter of the physiological reference eye. For the present configurations, ${\left(\frac{{\mathrm{\Phi }}_{\text{EP}\mathrm{\_}\text{ref}}}{{\mathrm{\Phi }}_{\text{XP}\mathrm{\_}\text{model}}}\right)}^2$ yields a scaling factor of ≈ ¾ across all tested model eyes.

The wavelength dependence of physiological ocular LCA was taken from the reference equation reported by Atchison and Smith [12], as recommended by ISO 11979-2 (Annex C.1) and also adopted in ANSI Z80.35-2018. In this framework, the chromatic difference of refraction is expressed in diopters at the spectacle plane as a function of wavelength λ (nm) and parameterized by a four-term Cauchy equation (Eq. 5a):

$$\text{LC}{\mathrm{A}}_{\text{phys}}(\lambda )=1.60911-\frac{6.70941\times {10}^{-1}}{{\lambda }^2}+\frac{5.55334\times {10}^{-2}}{{\lambda }^4}-\frac{5.59998\times {10}^{-3}}{{\lambda }^6},$$

Accordingly, all LCA values reported in this work are expressed in diopters at the spectacle plane and are compared against this physiological reference.

2.2. IOL selection and insertion

The longitudinal chromatic aberration expression referenced in ISO 11979-2 and ANSI Z80.35 corresponds to a phakic human eye and should therefore be interpreted as a physiological reference condition. It is not a quantity that must be reproduced by the model eye alone, nor by the model eye combined with an arbitrary intraocular lens. Rather, this reference defines the chromatic baseline that should be matched under crystalline-lens–equivalent conditions before any pseudophakic configuration is evaluated.

To establish a physiological chromatic baseline, we first used the ANSI Physiological model eye in a “crystalline-lens–equivalent” condition by implanting an IOL whose dispersion matched that of the human crystalline lens. The target dispersion was defined as the mean crystalline-lens dispersive properties of the Le Grand and Navarro [19] model eyes, as compiled by Atchison and Smith (2005) [12]. Under this condition, the resulting LCA of the ANSI Physiological model eye is consistent with the physiological reference (Figure 1) recommended in ISO 11979-2 and adopted in ANSI Z80.35 through its normative reference to ISO 11979-2. In the present work, this condition is therefore used to establish a physiological chromatic baseline for the complete bench system prior to any pseudophakic comparison. Our claim is therefore that the proposed model is chromatically equivalent to this accepted benchmark when the complete optical system is considered, rather than that it provides a fully independent clinical validation of each internal chromatic-aberration component.

Fig. 1.

Left panel: Paraxial chromatic difference in defocus, defined at the spectacle plane, 12 mm in front of the anterior corneal apex, for the ANSI Physiological implanted with an IOL with the same chromatic properties as the human crystalline lens (right panel). The reference dotted values are taken from Atchison and Smith (2005) equation 5a [12].

Because the total LCA of the system depends on the dispersion of the implanted IOL, any modification of IOL material properties leads to a corresponding change in system LCA. Meaningful comparisons between model eyes must therefore be performed in the pseudophakic configuration and must account for the complete bench geometry, including the immersion medium (saline solution), cuvette windows, and image-space propagation.

To assess the influence of IOL material dispersion, two representative IOL materials spanning the range encountered in contemporary intraocular lenses were considered. The first corresponds to a low-dispersion acrylic with refractive index $n_d=1.460$ and Abbe number $V_d=58$ , representative of high-Abbe hydrophilic acrylic. The second corresponds to a high-dispersion acrylic with $n_d=1.555$ and $V_d=38$ , representative of high-index hydrophobic acrylic IOLs. In both cases, the wavelength dependence of the refractive index was explicitly included in the ray-tracing calculations. All IOLs had a paraxial spherical power of 20 D at 550 nm in saline.

Polychromatic MTFs were computed by weighting the monochromatic MTF at each wavelength by the CIE photopic luminous efficiency function $V(\lambda )$ , thereby implementing the ISO-recommendation “white-light with visual sensitivity” condition. A total of 16 wavelengths, uniformly sampled between 400 and 700 nm in 20-nm steps, were used in the calculation [17].

To enable a direct comparison between different model-eye configurations, the spatial-frequency axis was normalized by the diffraction-limited cutoff frequency at the reference wavelength, which ranged from 627 to 638 cycles/mm across the tested configurations. This normalization compensates for small variations in effective F-number or numerical aperture between models, ensuring that residual differences in the polychromatic MTF reflect only chromatic effects.

Following normalization and refocusing at the reference wavelength, any remaining differences in polychromatic MTF can be attributed primarily to longitudinal chromatic aberration. This is because the IOL surface asphericity was adjusted in each configuration to guarantee diffraction-limited performance at the reference wavelength, using the optimized geometrical parameters summarized in Table 1.

Table 1. Geometrical and aspheric parameters of the optimized IOL designs used in each model-eye configuration. The IOL material had refractive index Nd = 1.460 and Abbe number Vd = 58. For all configurations, the anterior surface was aspherical and optimized to achieve diffraction-limited performance at the reference wavelength, while the posterior surface remained spherical. The tabulated parameters include spherical aberration (SA) at a 5.15-mm aperture, anterior and posterior radii of curvature (R _ANT, R _POST), central thickness (CT), anterior conic constant (Q_ANT), and higher-order aspheric coefficients (A⁴_ANT, A⁶_ANT).

IOL material [Nd = 1.460; Vd = 58] | Anterior Aspherical | Posterior Spherical
Model Eye	$c_0^4$ [µm]	RANT [mm]	RPOST [mm]	CT [mm]	QANT	A4ANT	A6ANT
ANSI Physio	0.199	10.919	−14.762	0.686	−1.076	−6.49E-04	−8.48E-06
ANSI FCell	0.216	10.919	−14.762	0.686	−1.102	−8.03E-04	−1.02E-05
WME	0.280	10.919	−14.762	0.686	−0.997	−8.77E-04	−1.56E-05
TRI1	0.218	10.919	−14.762	0.686	−1.033	−6.78E-04	−9.40E-06
TRI2	0.282	10.919	−14.762	0.686	−1.120	−7.67E-04	−1.63E-05
ISO	0.280	10.919	−14.762	0.686	−1.112	−7.92E-04	−1.35E-05

3. Results

3.1. Longitudinal chromatic aberration

The new model eye full configuration (denoted WME) is illustrated in Figure 2. Tables 2 and 3 summarize the parameters of the new physiologically chromatic model eye. The asphericity, Q, of the back surface of the cornea determines the target level of 4^th order spherical aberration and can therefore be used to define a set of fixed corneal variants for standardized bench testing. The relationship between Q and the level of 4^th order spherical aberration can be approximated by the following second-order expression: $Q=-3.2124\cdot {(c_0^4)}^2+10.1592\cdot (c_0^4)-2.5935$ .

Fig. 2.

On-axis ray trace on the proposed WME optical-bench model eye. The system comprises the corneal crown–flint doublet (left), the planar fused-silica cuvette windows placed before and after the IOL, and an aperture stop located at the IOL plane (5.15-mm diameter, shown in red). Rays are propagated through the complete bench geometry to the image plane (right), illustrating the ISO/ANSI-compatible layout used for subsequent monochromatic and polychromatic analyses.

Table 2. Parameters of the physiologically accurate chromatic model eyes (R = radius of curvature; t = distance; ct = central thickness).

Glass	Index Nd	Abbe Vd	R (mm)	t (mm)
H-K9L	1.5168	64.20	46.56	4.00
H-QF50	1.5814	40.89	−13.90	2.90
AIR	1.0000	89.20	−21.46	5.00
FUSED SILICA	1.4585	67.79	inf	3.00
SALINE	1.3347	55.98	inf	2.00
IOL MATERIAL	−	-	Ra	ct
SALINE	1.3347	55.98	Rp	3-ct
FUSED SILICA	1.4585	67.79	inf	3.00
AIR	1.0000	89.20	inf	—

Table 3. Posterior corneal-surface conic constant $Q$ (back surface) required to achieve the target primary 4^th order spherical aberration coefficient ( $c_0^4)$ of 0.00, 0.10, 0.20, and 0.28 µm, respectively, for a 5.15-mm aperture stop ( $Q=-3.2124\cdot {(c_0^4)}^2+10.1592\cdot (c_0^4)-2.5935$ ) .

Q	−2.556	−1.603	−0.686	0.00
$c_0^4$	0.000 $\mathrm{\mu }m$	0.100 $\mathrm{\mu }m$	0.200 $\mathrm{\mu }m$	0.280 $\mathrm{\mu }m$

The resulting chromatic focal shift curves for this model, computed from 400 nm to 700 nm, are shown in Figure 3 alongside with the ANSI Z80.35 reference models (Physiological and Fluid Cell), the ISO model (ISO 11979-2:2024 Annex C) and the two recent models from Ruprecht et al. (TRI1 and TRI2) [16]. The longitudinal chromatic aberration is plotted as the paraxial defocus in diopters at the spectacle plane as a function of wavelength (where 550 nm is the zero-defocus reference).

Fig. 3.

Paraxial chromatic difference in defocus at the spectacle plane as a function of wavelength, for an IOL with high Abbe number (left panel, N_d = 1.480; V_d = 58) and for an IOL with low Abbe number IOL (N_d = 1.555; V_d = 38). TRI1 and TRI2 correspond to the model eyes proposed by Ruprecht et al (2025).

Our optimized doublet-cornea model eye exhibits an LCA curve that that differs only minimally from the ANSI Physiological reference across the visible spectrum. Quantitatively, the total LCA (400–700 nm) in our model eye differs by less than 0.02 D from the reference for the high-Abbe IOL and by less than 0.06 D for the low-Abbe IOL (see Table 2). This confirms that the achromatic doublet cornea successfully reproduces the baseline of the ANSI Physiological benchmark across the tested IOL dispersion range. The zero-SA configuration was included to verify that corneal spherical aberration does not meaningfully affect LCA.

By contrast, the ANSI Fluid Cell model showed a moderate increase in LCA relative to the ANSI Physiological reference, with a maximum difference of 0.36 D. The TRI2 model showed a similar behavior, with a maximum difference of 0.32 D, whereas the TRI1 model remained closer to the reference, with a maximum difference of 0.14 D. The ISO model showed the largest deviation, reaching 0.85 D.

3.2. Polychromatic MTF performance

Differences in longitudinal chromatic aberration translate directly into differences in polychromatic MTF, although their impact is partially attenuated by the V(λ) spectral weighting, which strongly reduces the contribution of wavelengths at the extremes of the visible spectrum. As illustrated in Figure 4, increasing total LCA (Figure 3 and Table 4) is accompanied by a progressively stronger loss of polychromatic modulation transfer. Relative to the ANSI Physiological reference, the ANSI Fluid Cell and TRI2 models—whose LCA is moderately higher (≈14–23%)—show a consistent reduction in polychromatic MTF, most evident at low to mid spatial frequencies. The ISO model, characterized by the highest LCA among the tested configurations, represents the upper end of this same trend and shows the largest reduction in polychromatic MTF across the spatial-frequency range.

Fig. 4.

Monochromatic (overlapped dashed curves) and Polychromatic (continuous curves) MTF for all model eyes. IOL surface asphericity was adjusted so that each model eye + IOL combination yielded a diffraction-limited focal spot for green light, ensuring that any MTF degradation in white light is due to chromatic aberration rather than residual monochromatic aberration. Spatial frequency was normalized by the cut off value to ensure that monochromatic curves overlap in spite of differences in working F-numbers. The IOL material used for the simulations as an N_d of 1.460 and an Abbe number of 58.

Table 4. Paraxial chromatic difference in defocus at the spectacle plane between 400 nm and 700 nm and the reference wavelength (550 nm), with an IOL with high Abbe number and an IOL with low abbe number. TRI1 and TRI2 are the model eyes proposed by Ruprecht et al (2025).

		IOL material [Nd = 1.460; Vd = 58]			IOL material [Nd =1.555; Vd = 38]
Model Eye	$c_0^4$ [µm]	V [D] λ0 = 400nm	V [D] λ0 = 700nm	LCA [D]	V [D] λ0 = 400nm	V [D] λ0 = 700nm	LCA [D]
ANSI Physiological	0.199	−1.090	0.470	1.560	−1.550	0.710	2.260
ANSI Fluid Cell	0.216	−1.370	0.550	1.920	−1.840	0.780	2.620
WME000	0.000	−1.063	0.480	1.543	−1.539	0.719	2.258
WME280	0.280	−1.092	0.493	1.585	−1.582	0.740	2.321
TRI1	0.218	−1.180	0.500	1.680	−1.660	0.740	2.400
TRI2	0.282	−1.300	0.550	1.850	−1.780	0.800	2.580
ISO	0.280	−1.710	0.700	2.400	−2.170	0.940	3.110

For quantitative comparison, the spatial-frequency axis in Figure 4 is normalized by the diffraction cutoff frequency $f_c$ . For the present configuration, spatial frequencies of 25, 50, and 100 cycles/mm correspond to normalized frequencies of $f/f_c\approx 0.04$ , 0.08, and 0.16, respectively. At 50 cycles/mm ( $f/f_c\approx 0.08$ ), the ANSI Physiological model yields an MTF of approximately 0.50, while the ANSI Fluid Cell and TRI2 models decrease to 0.41 and 0.44, respectively; the ISO2 model shows a larger drop to approximately 0.33. A similar ordering is observed at 100 cycles/mm ( $f/f_c\approx 0.16$ ), where the ANSI Physiological model maintains an MTF of 0.26, compared to 0.21 for the Fluid Cell, 0.22 for TRI2, and 0.17 for ISO.

By contrast, the proposed WME model remained close to the ANSI Physiological reference at both 50 and 100 cycles/mm (MTF ≈ 0.49–0.50 and ≈ 0.25, respectively), consistent with the close-matching LCA values in Table 4. These residual differences are within expected experimental variability and would be indiscernible in standard optical bench measurements.

4. Discussion

The results confirm that the proposed model eye can reproduce physiological chromatic aberration levels without compromising other key optical properties. The WME model eye yields longitudinal chromatic aberration values that closely match those of the ANSI Physiological benchmark in pseudophakic conditions, across the tested range of IOL material dispersions. This is a desirable characteristic for standardized optical bench testing, as it enables fair comparison of different IOL designs under realistic white-light conditions while ensuring that the baseline chromatic aberration remains physiologically representative. Within the present comparison framework, this agreement suggests that the non-IOL contribution to the system chromatic aberration is also closely matched.

The present results also clarify an important methodological limitation in recent model-eye analyses. In particular, the study by Ruprecht et al. [16] evaluated longitudinal chromatic aberration assuming an effectively infinite image space, such that the image forms entirely within the immersion liquid of the model eye. Under this assumption, light propagation through the second cuvette window and within the image-space region is neglected. As a consequence, the reported chromatic focal shifts are only proportional to the true system LCA if all compared model eyes share identical cuvette geometries, which is not the case for all the designs analyzed in that work.

Using the present full-system definition of LCA, the ANSI Fluid Cell model shows slightly higher LCA than the ANSI Physiological model, although both are accepted as physiologically representative benchmark configurations under ISO 11979-2:2024 and ANSI Z80.35. The polychromatic MTF results in Figure 4 are consistent with this difference: model eyes with higher LCA show lower modulation transfer, even after attenuation by the V(λ) spectral weighting at the ends of the visible spectrum. This agreement should be understood as a physically consistent cross-check of the LCA assessment, not as an independent validation by itself. More importantly, the comparison shows that the contribution of the present work is not limited to matching a target LCA curve. It also concerns how LCA should be defined when comparing model eyes with different post-IOL optical paths. In such cases, evaluating chromatic focal shift without accounting for the complete optical system may lead to incorrect LCA estimates.

In the ISO model-eye configuration, different physiological levels of spherical aberration are obtained by selecting corneal geometries with the appropriate conic constant to produce the desired SA at the specified 5.15-mm beam diameter, while preserving the standard geometry. The present work extends this concept by showing that a doublet cornea can be designed to reproduce not only physiological levels of corneal spherical aberration, but also the chromatic behavior required for white-light testing. Accordingly, different SA targets are realized through corresponding fixed values of the posterior-surface conic constant, while preserving interchangeability and compatibility with existing optical bench setups. This flexibility is particularly important for modern IOL characterization, where both monochromatic and chromatic aberrations must be representative of the physiological eye.

Finally, it should be noted that the LCA of the proposed model eye is a property of the entire bench optical system—including the corneal doublet, cuvette windows and immersion solution. Changes in cuvette geometry and/or the dispersive properties of the immersion solution can alter the system LCA and thus requires dedicated re-validation (and, if needed, re-design) to ensure that physiological behavior is preserved.

5. Conclusion

In this work, we demonstrate that physiologically accurate chromatic model eyes for intraocular lens characterization require full-system optical analysis and a careful definition of longitudinal chromatic aberration. By employing a doublet cornea, the proposed WME model successfully reproduced the chromatic behavior of the ANSI Physiological benchmark in pseudophakic conditions across different spherical aberration targets and IOL material dispersions.

Although white-light optical testing has only been introduced relatively recently in ISO 11979-2 and ANSI Z80.35, the current standards do not provide a sufficiently complete or unambiguous description of how optical benches should be validated with respect to chromatic aberration. This lack of methodological detail can lead to inconsistent interpretations and, in some cases, misleading LCA assessments.

By explicitly showing the limitations of evaluating LCA without considering the complete bench system, and by providing a method to assess whether a bench configuration reproduces the physiological LCA reference adopted in current standards, this work contributes to a more rigorous and physically meaningful framework for chromatic validation of IOL test benches.

Disclosures

The authors declare no conflicts of interest.

Data availability

The simulation outputs developed for this study are available from the authors upon reasonable request.