Previous clinical studies and computational modeling have shown that the retinal image in the peripheral visual field differs in pseudophakic eyes than in phakic eyes.1–8 Recent studies found that the peripheral retinal image quality is degraded in pseudophakic patients and peripheral image degradation can affect visual function.1,9 Reduced contrast and image quality in the periphery of the visual field could also affect diagnostic and imaging procedures in pseudophakic eyes, such as wide-field retinal imaging or visual field testing.10 A design process for aspheric intraocular lenses (IOLs) that optimizes image quality over a field of view of ±10 degrees has been proposed previously.10 More recently, a meniscus IOL designed specifically to optimize retinal image quality in both the center and the periphery of the field has been developed, showing a significant reduction of peripheral defocus.2,8

The decrease in peripheral retinal image quality found in earlier studies when the crystalline lens is replaced with an IOL is most likely due to differences in the power, shape, and axial position of the IOLs compared with the crystalline lens.2,3 In particular, there can be large differences in power between the crystalline lens (typically around 24 diopters [D]) and the IOL depending on the preoperative refractive error.9–12 We can therefore expect that myopes or hyperopes who are implanted with lower or higher power IOLs will experience larger differences in peripheral performance after cataract surgery.

The factors contributing to the degradation in the peripheral image can be studied using computational pseudophakic eye models.2,3 One of the challenges of such models is that the design specifications of IOLs are generally not provided by IOL manufacturers. Another approach is to directly measure the peripheral image of IOLs using an optical test bench. Experimental studies on physical model eyes that incorporate IOLs can help validate simulations and study the peripheral behavior of lenses.5 A limitation of artificial eye models is that the peripheral behavior is determined by the combined contribution of the artificial cornea and the IOL. A more specific understanding of the impact of IOL design parameters such as lens shape and asphericity on peripheral optical performance can be gained by quantifying the peripheral behavior of the isolated IOL.

We previously developed an optical test bench combining a laser ray tracing aberrometer and an optical coherence tomography (LRT–OCT) system to quantify the peripheral defocus of isolated human lenses.13 The purpose of this study was to use the LRT–OCT system to characterize the peripheral defocus of IOLs and to compare the measurements with theoretical predictions.

METHODS

Measurements were acquired on 14 biconvex spherical IOLs made of poly(methyl methacrylate) (PMMA) (APPALENS 207, Appasamy Associates) and 14 aspheric hydrophobic acrylic IOLs (Acrysof SN60WF, Alcon Laboratories, Inc.). All IOLs were monofocal. APPALENS 207 powers were 17.5 D, 18 D, 18.5 D, 19 D, 19.5 D, 20 D, 20.5 D, 21 D, 22 D, 22.5 D, 23 D, 23.5 D, 24 D, and 24.5 D, and Acrysof SN60WF powers were 17 D, 17.5 D, 18 D, 19 D, 19.5 D, 20 D, 21.5 D, 22 D, 22.5 D, 23 D, 23.5 D, 24 D, 24.5 D, and 25 D. All IOLs had an optic diameter of 6.0 mm. The specified refractive index is 1.49 for the PMMA IOLs and 1.55 for the acrylic IOLs.

LRT–OCT System Description

The combined LRT and OCT system was previously described in detail.13 In summary, it consists of 4 subunits: a tissue chamber, a spectral domain OCT imaging system, a LRT aberrometer, and an off-axis positioning system (Figure 1, Left). In this study, the OCT system was used to precisely align and center the IOL with the beam delivery system of the LRT system. The LRT beam delivery system is mounted on a motorized rotation stage that allows measurements at different incidence angles, corresponding to different peripheral viewing angles. For this study, measurements were acquired with delivery angles ranging from −30 to +30 degrees in 5-degree increments about the lens optical axis.

Figure 1.:

Left: Schematic diagram of the LRT–OCT system. Right: Tissue chamber with IOL placed on a nylon-sutured ring immersed in balanced salt solution. LRT = laser ray tracing

The IOL is positioned in the center of a custom lens holder which is comprised of a ring with nylon sutures oriented in a criss-cross pattern. The technical details of the lens holder can be found in a previous publication.14 The lens holder is placed in a tissue chamber within the LRT–OCT system (Figure 1, Right). The IOL is immersed in balanced salt solution (Alcon Laboratories, Inc.) during the experiment. To ensure that the IOL is located at the pivot point of the oblique delivery system, the delivery probe was rotated from the −30- to the +30-degree positions and the height of the tissue chamber was adjusted until the lens remained centered in the OCT scans when the rotation stage was moved. The images acquired between −15 degrees and +15 degrees were used for this alignment step (Figure 2). At larger angles, the IOL boundaries are not visible because of the decrease in backscattered signal returning from the OCT sample arm at high-incidence angles.

Figure 2.:

OCT images of an Alcon SN60WF (+17.5 D) used to center and align the IOL within the LRT–OCT system acquired at −15- to +15-degree delivery angles. The horizontal lines in the image at 0 degree correspond to multiple reflection artifacts from the cell window boundaries. LRT = laser ray tracing

The LRT system delivered narrow parallel beams in a raster scan pattern over the central 3 mm zone of the IOL, in 0.25 mm step increments (13 × 13 = 169 rays). The LRT system includes an image sensor mounted on an adjustable vertical positioning stage under the tissue chamber. The image sensor records the spot distribution for the 169 rays at 9 different axial positions in 1 mm increments. The spot images are used to reconstruct the path of the 169 rays after refraction by the IOL. The reconstructed rays are used to calculate the focal length and power of the IOL.

The focal length is defined as the distance from the back principal plane of the IOL to the axial position where the root mean square (RMS) spot size is minimized. The RMS spot size was calculated as the RMS of the distance of the 169 rays to the nodal ray. The IOL power was calculated using the formula 1.343/f, where 1.343 is the group refractive index of the hydration media at 880 nm and f is the focal length. The obliquity of the ray was taken into account in the calculation of lens power. The group refractive index of balanced salt solution at 880 nm was measured by filling the tissue cell with 7 different volumes of balanced salt solution. The window appears to shift backward because more balanced salt solution is added to the cell because balanced salt solution has a higher refractive index than the volume of air that it replaces. The group refractive index was calculated directly from the slope of a linear regression of the apparent window shift plotted vs the optical thickness of balanced salt solution.

The ray trace experiment was performed 3 times on each IOL. The IOL was repositioned before each experiment. The average of the 3 measurements was used for the statistical analysis. In a separate study, the LRT system was calibrated and validated using planoconvex glass lenses of known shape and power.

Statistical Analysis

The power measurements at 0 degree were compared with the nominal power, taking into account the effect of dispersion. The nominal power is defined for monochromatic visible light (589 nm), while the LRT–OCT system uses broadband near-infrared light (880 nm). Assuming that the IOLs are thin lenses, the formula for lens power predicts that there is a linear relation between the measured power at 880 nm and the nominal power at 589 nm:(1)P880=nIOL(880)−nAqueous(880)nIOL(589)−nAqueous(589)×P589At 589 nm, the refractive indices for aqueous, acrylic, and PMMA are n = 1.336, n = 1.55, and n = 1.49, respectively. At 880 nm, the group refractive index must be used. The group refractive index takes into account the contribution of the entire spectrum of the light source. The group refractive index of the IOLs was measured using the method of Uhlhorn et al.15 We found n = 1.496 for APPALENS 207 and n = 1.566 for SN60WF. With these values, and assuming an uncertainty of ±0.005 in the nominal and measured IOL refractive index values and ±0.003 in the aqueous index, we predict that the ratio of measured power to the nominal power is between 0.968 and 1.121 for the SN60WF IOLs and between 0.895 and 1.102 for the APPALENS 207 IOLs.

The relative peripheral defocus of the IOL, ΔP, in Diopters was calculated as the difference between the power at the respective delivery angle P(α) and the on-axis power P(0 degrees), where ΔP = P(α) − P(0 degrees).

The peripheral defocus was compared with the predictions from the Coddington equations.16,17 The Coddington equations predict that the tangential (PT) and sagittal (PS) powers of a thin lens of on-axis power P and refractive index nL immersed in a medium of refractive index n in the incidence angle θ are given by(2)PT=1cos2⁡θ×nL2−n2⁡sin2⁡θ−n⁡cos⁡θ(nL−n)×Pcos⁡θ(3)PS=nL2−n2⁡sin2⁡θ−n⁡cos⁡θ(nL−n)×Pcos⁡θ

Note that in these formulas, the incidence angle is the incidence angle in fluid, whereas the LRT incidence angles are specified for air (for instance, 21.9 degrees for 30-degree incidence angle in air), and the reference axis for measurement of distances is the optical axis.

RESULTS

As predicted by Equation (1), we found a linear relation between the measured and nominal power, with a slope of 1.090 ± 0.026 for the Appasamy APPALENS 207 IOLs and 0.978 ± 0.017 for the Alcon SN60WF IOLs (Figure 3). The values are within the predicted range (0.895 to 1.102 for the Appasamy APPALENS 207 and 0.968 to 1.121 for the Alcon SN60WF).

Figure 3.:

Scatterplot shows the nominal power vs measured power for the Appasamy APPALENS 207 (orange) and Alcon SN60WF (purple) IOLs.

For all IOLs, IOL power and relative peripheral defocus increase significantly as the incidence angle increases as predicted from theory (Eqs. 2 and 3; Figure 4, A and B). In other words, the position of the best focus moves closer to the IOL as the incidence angle increases. For the Appasamy APPALENS 207 IOLs, relative peripheral defocus at 30-degree incidence angle increases from 5.8 D for the 17.5 D IOL to 8.2 D for the 24 D IOL. For the Alcon SN60WF IOLs, relative peripheral defocus at 30 degrees increases from 4.9 D for the 17 D IOL to 7.2 D for the 24.5 D IOL (Supplemental Tables 1 and 2, available at https://links.lww.com/JRS/B129 and https://links.lww.com/JRS/B130 and Figure 4, C and D). We find that the peripheral defocus is slightly larger for the APPALENS 207 IOLs than for the Alcon SN60WF IOLs, with a difference that is independent of lens power. The difference between the relative peripheral defocus of APPALENS 207 and SN60WF IOLs, calculated as the average of the values at the positive and negative angle over all IOL powers, is −0.03 ± 0.05 D at 5 degrees, 0.07 ± 0.09 D at 10 degrees, 0.15 ± 0.13 D at 15 degrees, 0.30 ± 0.15 D at 20 degrees, 0.60 ± 0.22 D at 25 degrees, and 0.96 ± 0.21 D at 30 degrees. The difference may reflect a difference in lens shape (ratio of anterior to posterior radius of curvature). A ray-tracing simulation of a 1 mm thick IOL made of PMMA showed that the peripheral defocus increases by 0.9 D when the ratio of posterior to anterior radius of curvature is changed from −1 (symmetric biconvex) to −4 (the posterior surface is 4 times flatter than the anterior surface).

Figure 4.:

Scatterplot shows the (A, B) measured power and (C, D) relative peripheral defocus (difference between off-axis and on-axis power) for each IOL as a function of the delivery angle for (A, C) Appasamy APPALENS 207 and (B, D) Alcon SN60WF IOLs. For clarity, error bars are not shown. The range (maximum minus minimum) of repeated measurements was within 1.5 D for the Alcon SN60WF and within 0.8 D for the Appasamy APPALENS 207, except for the 20-degree measurement of the 21.5 D Appasamy APPALENS 207 IOL, where the range was 3.0 D.

A comparison with the predictions from the Coddington equations showed that the measured peripheral defocus closely matches the predicted tangential focus (Figure 5). The mean difference between the measured and predicted tangential power at ±30 degrees is 0.56 ± 0.16 D for the Appasamy APPALENS 207 IOLs and −0.41 D ± 0.10 D for the Alcon SN60WF IOLs, independent of the IOL power (P = .15). The small bias is within the expected precision of the measurements. The theoretical analysis shows that the IOLs suffer from a significant amount of oblique astigmatism. When defined as the difference between the tangential and sagittal power, predicted oblique astigmatism at 30 degrees is equal for both Appasamy APPALENS 207 and Alcon SN60WF IOLs, with values ranging from 3.1 D for the 17.5 D IOL to 4.3 D for the 24.5 D IOL.

Figure 5.:

The measured defocus, predicted tangential, and sagittal defocus at 30 degrees, 20 degrees, and 10 degrees plotted against the IOL power for Appasamy APPALENS 207 and Alcon SN60WF IOLs. For the measured values, the average of the measurements recorded at ±30 degrees, ±20 degrees, and ±10 degrees was used.

DISCUSSION

This study presents measurements of peripheral defocus and its power dependence for 2 types of IOLs using a custom-built LRT aberrometer. The results show that IOLs exhibit significant myopic peripheral defocus in the periphery and that the peripheral defocus increases significantly as the lens power increases. Our analysis also shows that the IOL peripheral defocus can be closely predicted using optical theory (Coddington equations for thin lenses).

These results imply that the peripheral image quality will vary significantly across individuals, depending on the IOL power. Lower power IOLs implanted in myopic patients will introduce significantly less myopic peripheral defocus than the higher power IOLs implanted in hyperopic patients. This outcome is generally consistent with the finding that spectacle lenses with more negative power, which reduce the overall ocular dioptric power, result in more hyperopic (ie, less myopic) peripheral defocus.18 However, the overall ocular peripheral defocus will also depend on corneal shape, retinal shape, and ocular distances. The variation of the ocular components and retinal curvature with refractive error could partially compensate for the variability in peripheral defocus introduced by the difference in IOL power. In particular, emmetropes tend to have oblate retinas (ie, steeper in the periphery than in the center of the retina) and myopes tend to have less oblate retinas than emmetropes. The retina becomes less oblate as the amount of myopia increases.19 Hence, the fact that the lower power IOLs implanted in myopes have less relative myopic peripheral defocus could help compensate for the increased peripheral flattening of the retina in myopic eyes.

The close agreement between our measurements and theoretical predictions further validates our experimental approach. We find that the measured peripheral defocus profile is close (within 1 D at 30-degree incidence angle) to the tangential image plane predicted by the Coddington equations for thin lenses, as opposed to the sagittal focus (Eqs. 2 and 3). This result is inherent to the design of our experimental setup. The rotation of the stage which produces the −30- to +30-degree variation of the field angle is along the tangential meridian of the IOL. The field angle in the sagittal direction is 0 degree because the entrance beams are parallel to the meridional plane and centered with the IOL. By this design, we therefore expect that the experimental system will measure the tangential image plane. To further confirm this finding, we conducted an additional analysis on 4 Appasamy APPALENS 207 (18 D, 19.5 D, 23 D, and 24 D) and 4 Alcon SN60WF IOLs (17 D, 18 D, 23 D, and 24 D) using only the 13 rays contained in either the tangential meridian or the sagittal meridian instead of the 169 rays covering the entire 3 × 3 mm central zone of the lens. This analysis provides a more direct correspondence to the tangential and sagittal foci. The power was calculated from plots of ray slope vs ray height along the single meridians (tangential or sagittal) using the method of Maceo Heilman et al.20 There was good agreement between measured and theoretical tangential focus with a mean difference of −0.34 D (range, −0.06 to −0.75 D) for the 4 Alcon SN60WF IOLs and 1.56 D (range, 1.21 to 1.73 D) for the 4 Appasamy APPALENS 207 IOLs. Again, as discussed earlier, the larger difference for the Appasamy APPALENS 207 may reflect a difference in lens shape (ratio of anterior to posterior radius of curvature).

The Coddington formulas of Equations (2) and (3) are valid for a thin lens with spherical surfaces when the aperture stop (ie, the pupil) is located in the plane of the lens. In this case, we find that the main factor in determining the peripheral defocus is the on-axis paraxial power, independent of the IOL shape. In other words, with the thin lens model, the peripheral defocus of the isolated thin IOL will be the same for a planoconvex or symmetric biconvex IOL, or any other spherical shape. On the other hand, an error analysis shows that the material refractive index has minimal influence on the peripheral defocus predicted by Equations (2) and (3). In real-world IOLs, the IOL shape has some influence on the peripheral defocus. Ray-tracing simulations show that the 0.9 D difference in peripheral refraction measured between the 2 IOL types at the 30-degree angle can be accounted for if the IOL shape changes from symmetric-biconvex to a design where the posterior surface is 4 times flatter than the anterior surface. The position of the IOL relative to the pupil is another factor that may influence the contribution of the IOL to ocular peripheral defocus in a real eye. In a pseudophakic eye, the IOL is located posterior to the pupil. The distance from the pupil to the IOL can exceed 1 mm. The effect of the pupil shift on peripheral defocus depends on the lens shape. A simulation using ray-tracing shows that a 1 mm pupil shift is expected to change the relative peripheral defocus for 30-degree incidence angle by less than 1 D.

We compared our results on IOLs with data acquired on isolated human lenses using the same LRT–OCT system. The average on-axis power of the isolated older human lens (50 to 61 years) was 24.1 ± 3.2 D.11 Relative peripheral defocus was 5.1 D at ±30 degrees and 1.8 D at ±20 degrees (average values from measurements at the positive and negative angles). The corresponding values for the 24 D IOLs were 8.2 D and 3.2 D for the Appasamy APPALENS 207 and 7.2 D and 2.9 D for the Alcon SN60WF. This comparison shows that the relative peripheral defocus of the human lens is significantly smaller than that of IOLs of the same power. The difference could be due to differences in lens shape (asphericity and thickness) and to the presence of the gradient in the crystalline lens. Optical analyses show that a retinal image field that more closely mimics the peripheral defocus profile of the phakic eye with its crystalline lens can be achieved by using a concave convex meniscus lens instead of the traditional biconvex lens design.2,8,10

The higher myopic peripheral defocus of IOLs compared with the crystalline lens could be a factor that contributes to the reduced peripheral visual performance observed in pseudophakic eyes. The finding suggests that the aphakic eye has hyperopic peripheral defocus relative to the retina that is compensated at least partially by the myopic relative peripheral defocus of the crystalline lens. Implantation of an IOL would then cause the eye to have more relatively myopic peripheral defocus than the phakic eye.

The LRT–OCT system measures defocus of the IOL relative to a flat image plane. In the human eye, the concave retinal curvature will compensate for the myopic peripheral defocus of the IOL. Another difference is that the experimental setup delivers a set of parallel rays (zero vergence), whereas in the human eye, the rays incident on the IOL are focused by the cornea (positive vergence). One can show that for a thin lens, the relative peripheral defocus predicted by the Coddington equation is independent of the ray vergence. In other words, the relative peripheral defocus will be the same for zero vergence (parallel incident beam) and for positive vergence (conditions in the eye).

The difference found between the measured and nominal on-axis power is due to dispersion effects (the variation of refractive index with wavelength). The LRT system uses a broadband near-infrared light source, while the IOL power is specified for visible light. Since the LRT system uses a broadband source which has a range of wavelengths, the refractive index relevant to the current measurements is the group refractive index, which takes into account the dispersion within the infrared beam itself. For a thin lens such as the IOLs used in this study, the measured power is expected to be proportional to the nominal power with a proportionality factor that depends on the refractive indices of the material and of the surrounding medium (see Eq. 1). Our experimental results follow this trend: The measured power is proportional to the nominal power, with a proportionality factor that is close to the value calculated using the material refractive indices. The dispersion effect was also taken into account when comparing the theoretical and measured peripheral defocus. We used the measured power at 880 nm in Equations (2) and (3) so that the theoretical predictions correspond to our experimental conditions.

To summarize, we find that IOLs have a significant myopic peripheral defocus. The relative peripheral defocus of the IOLs varies considerably with IOL power, which could affect the quality of vision and visual function. At equal powers, the IOL peripheral defocus is also significantly larger than that of the crystalline lens.WHAT WAS KNOWN Previous studies have shown that the retinal image quality in the periphery of the visual field is worse in pseudophakic eyes than in phakic eyes. This image degradation can affect visual function.

WHAT THIS PAPER ADDS IOLs have a significant myopic relative peripheral defocus that varies with IOL power and design. The relative peripheral defocus of IOLs is larger than that of natural human lenses of the same power. Acknowledgments

The authors thank Mr. Kannan Umadevi Venkataraju for providing the spherical IOLs, Ms. Sheetal for providing the aspheric lenses for the experimental purpose, and Ms. Sushma Nandyala for assisting with the experiments.

REFERENCES 1. Venkataraman AP, Rosén R, Heredia AA, Piers P, Vidal CC, Lundström L. Peripheral vision and hazard detection with average phakic and pseudophakic optical errors. Biomed Opt Express 2021;12:3082–3090 2. Artal P, Ginis H, Christaras D, Villegas EA, Tabernero J, Prieto PM. Inverted meniscus intraocular lens as a better optical surrogate of the crystalline lens. Biomed Opt Express 2023;14:2129–2137 3. van Vught L, Luyten GPM, Beenakker JWM. Peripheral visual field shifts after intraocular lens implantation. J Cataract Refract Surg 2023;49:1270 4. Tabernero J, Ohlendorf A, Fischer MD, Bruckmann AR, Schiefer U, Schaeffel F. Peripheral refraction in pseudophakic eyes measured by infrared scanning photoretinoscopy. J Cataract Refract Surg 2012;38:807–815 5. Togka KA, Livir-Rallatos A, Christaras D, Tsoukalas S, Papasyfakis N, Artal P, Ginis H. Peripheral image quality in pseudophakic eyes. Biomed Opt Express 2020;11:1892–1900 6. Smith G, Lu CW. Peripheral power errors and astigmatism of eyes corrected with intraocular lenses. Optom Vis Sci 1991;68:12–21 7. Jaeken B, Mirabet S, Marín JM, Artal P. Comparison of the optical image quality in the periphery of phakic and pseudophakic eyes. Invest Ophthalmol Vis Sci 2013;54:3594–3599 8. Villegas EA, Marín JM, Ginis H, Robles C, Alcón E, Hervella L, Prieto PM, Taña-Rivero P, Artal P. Peripheral refraction and contrast detection sensitivity in pseudophakic patients implanted with a new meniscus intraocular lens. J Refract Surg 2022;38:229–234 9. Ortiz-Peregrina S, Casares-López M, Castro-Torres JJ, Anera RG, Artal P. Effect of peripheral refractive errors on driving performance. Biomed Opt Express 2022;13:5533–5550 10. Barbero S, Marcos S, Montejo J, Dorronsoro C. Design of isoplanatic aspheric monofocal intraocular lenses. Opt Express 2011;19:6215–6230 11. Maceo Heilman B, Mohamed A, Ruggeri M, Williams S, Ho A, Parel JM, Manns F. Age-dependence of the peripheral defocus of the isolated human crystalline lens. Invest Ophthalmol Vis Sci 2021;62:15 12. Hernandez VM, Cabot F, Ruggeri M, de Freitas C, Ho A, Yoo S, Manns F. Calculation of crystalline lens power using a modification of the Bennett method. Biomed Opt Express 2015;6:4501–4515 13. Ruggeri M, Williams S, Heilman BM, Yao Y, Chang YC, Mohamed A, Sravani NG, Durkee H, Rowaan C, Gonzalez A, Ho A, Parel JM, Manns F. System for on- and off-axis volumetric OCT imaging and ray tracing aberrometry of the crystalline lens. Biomed Opt Express 2018;9:3834–3851 14. Martinez-Enriquez E, de Castro A, Mohamed A, Sravani NG, Ruggeri M, Manns F, Marcos S. Age-related changes to the three-dimensional full shape of the isolated human crystalline lens. Invest Ophthalmol Vis Sci 2020;61:11 15. Uhlhorn SR, Borja D, Manns F, Parel JM. Refractive index measurement of the isolated crystalline lens using optical coherence tomography. Vision Res 2008;48:2732–2738 16. Smith WJ. Chapter A: raytracing and aberration calculation. In: Modern Optical Engineering: The Design of Optical Systems. 4th ed. Singapore: McGraw-Hill; 2008 17. Jenkins FA, White HE. Fundamentals of Optics. 4th ed. New York: McGraw-Hill; 1976 18. Berntsen DA, Barr CD, Mutti DO, Zadnik K. Peripheral defocus and myopia progression in myopic children randomly assigned to wear single vision and progressive addition lenses. Invest Ophthalmol Vis Sci 2013;54:5761–5770 19. Atchison DA, Pritchard N, Schmid KL, Scott DH, Jones CE, Pope JM. Shape of the retinal surface in emmetropia and myopia. Invest Ophthalmol Vis Sci 2005;46:2698–2707 20. Maceo Heilman B, Manns F, de Castro A, Durkee H, Arrieta E, Marcos S, Parel JM. Changes in monkey crystalline lens spherical aberration during simulated accommodation in a lens stretcher. Invest Ophthalmol Vis Sci 2015;56:1743–1750