Standard intraocular lenses (IOLs) have positive spherical aberration (SA), which, when added to the positive SA in the normal cornea, increases ocular SA. Aspheric IOLs have been designed to compensate for the positive SA of the cornea.^1–4 Several aspheric IOLs with different amounts of asphericity are available. These include the Tecnis (SA = −0.27 μm for a 6-mm pupil; Advanced Medical Optics, Inc, Santa Ana, California), AcrySof IQ (SA = −0.20 μm; Alcon Laboratories, Inc, Fort Worth, Texas), and SofPort AO (SA = 0.00 μm; Bausch & Lomb Inc, Rochester, New York). Large ranges of corneal SA in the population have been reported.⁵ Therefore, depending on an individual’s corneal SA and the SA of the IOL selected, a wide range of residual ocular SA is possible for an eye undergoing IOL implantation.

It is well known that other higher-order aberrations (HOAs) exist in human cornea and that HOAs vary widely among subjects.⁵ Applegate and colleagues⁶ have reported that aberrations in different Zernike terms interact to increase or decrease optical performance. It is unclear what the optimal amount of SA would be in eyes with various HOAs. The purpose of this study was to investigate, based on anterior corneal HOAs, the optimal amount of ocular SA needed to maximize optical quality.

• No previous ocular or corneal surgery
• No corneal pathology
• No contact lens wear or discontinuation of contact lens wear for 8 weeks for RGP lens, 4 weeks for toric soft lens, and 2 weeks for soft lens
• No missing data points within the central 7-mm zone on Humphrey Atlas corneal topographic maps (Carl Zeiss Meditec, Inc, Dublin, California)

In each eye, implantation of aspheric IOLs was simulated with different amounts of SA to produce residual ocular SA from −0.30 μm to +0.30 μm with intervals of 0.01 μm. The residual ocular wavefront aberrations were combined aberrations from the cornea and the aspheric IOLs. Thus, the residual ocular 4th-order SA ranged from −0.30 μm to +0.30 μm, and all other ocular HOAs equaled those in the anterior corneal surface.

• Modulation transfer function (MTF) volume up to 30 cycles/degree. This is a 3-D volume under the MTF curve up to 30 cycles/degree, equivalent to visual acuity of 20/20.
• MTF volume up to 15 cycles/degree: equivalent to visual acuity of 20/40.
• Strehl ratio: ratio of peak focal intensities in aberrated PSF and ideal PSF. The Strehl ratio is 1 for a perfect optical system and less than 1 for an aberrated optical system.
• Encircled energy (EE) at 2 arc minutes. The EE is a fractional energy within a given radius or field of view.
• EE at 4 arc minutes.

We selected the residual ocular SA at which the maximal image quality was achieved as “optimal SA” for that eye. For example, if an eye had maximal MTF volume up to 30 cycles/degree at SA of −0.13 μm, this value would be the optimal SA for this eye for this parameter.

The mean age of the 94 patients was 61 ± 12 years (range, 40–80 years). For a 6-mm pupil, the mean root-mean-square of the anterior corneal HOAs was 0.506 ± 0.130 μm (range, 0.234–0.857 μm), and 4th-order SA was +0.287 ± 0.090 μm (range, 0.076–0.544 μm).

For each parameter, optimal visual function was achieved for at least 25% of eyes at the following amounts of ocular SA: (1) MTF volume up to 30 cycles/degree: −0.05 μm and 0.00 μm (Figure 1); (2) MTF volume up to 15 cycles/degree: −0.05 μm (Figure 2); (3) Strehl ratio: −0.05 μm and 0.00 μm (Figure 3); (4) EE at 2 arc minutes: −0.05 μm and 0.00 μm (Figure 4); and (5) EE at 4 arc minutes: −0.10 μm and −0.05 μm (Figure 5).

FIGURE 1 Distribution of optimal ocular spherical aberration (SA, C40) to produce best image quality as evaluated by modulation transfer function volume up to 30 cycles/degree. The optimal SA was rounded to the nearest SA in 0.05-μm intervals. For example, (more ...)

FIGURE 2 Distribution of optimal ocular spherical aberration (SA, C40) to produce best image quality as evaluated by modulation transfer function volume up to 15 cycles/degree. The optimal SA was rounded to the nearest SA in 0.05-μm intervals. For example, (more ...)

FIGURE 3 Distribution of optimal ocular spherical aberration (SA, C40) to produce best image quality as evaluated by Strehl ratio. The optimal SA was rounded to the nearest SA in 0.05-μm intervals. For example, the reported optimal SA of 0 μm included (more ...)

FIGURE 4 Distribution of optimal ocular spherical aberration (SA, C40) to produce best image quality as evaluated by encircled energy at 2 arc minutes. The optimal SA was rounded to the nearest SA in 0.05-μm intervals. For example, the reported optimal (more ...)

FIGURE 5 Distribution of optimal ocular spherical aberration (SA, C40) to produce best image quality as evaluated by encircled energy at 4 arc minutes. The optimal SA was rounded to the nearest SA in 0.05-μm intervals. For example, the reported optimal (more ...)

For MTF volume up to 15 cycles/degree, 8 Zernike terms predicted the optimal SA with a multiple correlation coefficient R of 0.889. The 8 predictors were the same 8 Zernike terms as in the model for MTF volume up to 30 cycles/degree, but with a slightly different order of importance (from most to least): Z₆⁰, Z₆², Z₄², Z₅³, Z₆⁴, Z₃⁻¹, Z₃³, and Z₃¹. The multiple regression equation for optimal SA was:

For Strehl ratio, 4 Zernike terms predicted the optimal SA with a lower multiple correlation coefficient (R = 0.611) compared with those for MTF volume. The order of importance of the 4 predictors to optimal SA from most to least was as follows: Z₄², Z₆⁰, Z₅¹, and Z₃¹. For EE at 2 arc minutes, 6 predictors significantly contributed to the model with R value of 0.563 (Z₆⁰, Z₄², Z₃⁻¹, Z₃³, Z₆⁻⁴, and Z₅⁵). For EE at 4 arc minutes, 3 predictors significantly contributed to the model with R value of 0.608 (Z₆⁰, Z₆⁶, and Z₆⁻²).

There are two primary reasons to customize the asphericity of the IOL for each eye: (1) There is a wide range of corneal SA in the population. (2) As shown in this study, other higher-order corneal aberrations interact variably with SA to increase or decrease optical performance. Applegate and colleagues⁶ investigated how pairs of Zernike modes interact to increase or decrease visual acuity. They found that acuity varied significantly, depending on the modes that were selected and the relative contribution of each mode. Two modes 2 radial orders apart and having the same sign and angular frequency combined to increase visual acuity, whereas 2 modes within the same radial order combined to decrease acuity. We are unaware of any studies investigating what the optimal amount of SA would be in eyes with various corneal HOAs.

In this study, we evaluated the optimal amount of ocular SA needed to maximize optical quality in patients in the cataract age range (40–80 years). To account for chromatic aberrations and the Stiles-Crawford effect in the human eye, the polychromatic PSF was calculated with Stiles-Crawford effect incorporated; the goal was to simulate the image quality a subject might experience in the white-light environment. Five parameters were used to quantify the optical image quality of the eye. Various metrics evaluating optical quality have been studied,^10–12 and controversy exists regarding which metric or combination of metrics best predicts quality of vision.

We found that most eyes did not have best image quality at SA of 0 μm and that the optimal SA varied widely among eyes. For 4 of the 5 parameters that were used to predict optical image quality of the eye (MTF volume up to 30 cycles/degree, MTF volume up to 15 cycles/degree, Strehl ratio, and EE at 2 arc minutes), the highest percentage of eyes had best image quality at residual ocular SA of −0.05 μm (34.4%–61.7%). With the EE at 4 arc minutes, the highest percentage of eyes had best image quality at residual ocular SA of −0.10 μm (45.5%).

Using the stepwise multiple regression analysis, we found that the amount of optimal SA could be predicted based on other HOAs of the cornea with a coefficient of multiple determination (R²) up to 79% for MTF volume up to 15 cycles/degree, indicating that 79% of the variation in the optimal SA is accounted for by the 8 Zernike terms included in the model. The R² values were 63% for MTF volume up to 30 cycles/degree, and 32% to 37% for Strehl ratio and EE at 2 and 4 arc minutes, respectively. Among the Zernike terms that significantly contributed to the optimal SA, 6th-order SA (Z₆⁰) made the greatest contribution for 4 of the 5 parameters evaluated in this study. This demonstrates aberration interactions among Zernike terms as reported by Applegate and colleagues.⁶

Both in the laboratory by using adaptive optics³ and in clinical studies, aspheric IOLs have been shown to reduce ocular SAs, improve contrast sensitivity, and improve night driving performance.^2,4 However, 2 recent studies^13,14 reported no differences between aspheric and spherical IOLs in low-contrast visual acuity, high-contrast visual acuity, and contrast sensitivity. Although multiple factors may contribute to these conflicting findings, lack of optimization of residual ocular SA might play a role. In the subjects included in this study, the corneal 4th-order SA ranged from 0.076 μm to 0.544 μm. Assuming implantation of Tecnis lens, AcrySof IQ lens, SofPort AO lens, and standard IOL with positive SA (SA = +0.18 μm) in these eyes, the residual ocular SA would range from −0.194 to 0.274 μm, −0.124 to 0.344 μm, 0.076 to 0.544 μm, and 0.256 to 0.724 μm, respectively. This spectrum of SA data may explain, at least in part, variations in studies’ results.

Limitations of the study included the following:

• This was a theoretical study, not a clinical study.
• We assumed that the 2nd-order aberrations (defocus and astigmatism) were fully corrected by some means, such as spectacles, following cataract surgery; the optimal SA would differ as a function of residual defocus or/and astigmatism.
• Calculations were made for a 6-mm pupil; the impact of residual SA will be less with a smaller pupil, and the optimal value for each eye might change as pupil size changes.
• This study assumed that the aspheric IOLs were well centered and not tilted; decentration of aspheric IOLs induces coma,^7,15 which may affect the amount of optimal SA for that eye.
• This study did not evaluate the effect of optimization of SA on depth of focus.
• This study ignored the neuroadaptive response. Using an adaptive optics system, Artal and colleagues¹⁶ found that the stimulus seen with the subject’s own aberrations was always sharper than when seen through the rotated version, but that subjects were capable of readapting to new HOAs; the magnitude and timing of this response is under study. Webster and associates¹⁷ reported that neural adaptation could also profoundly affect the actual perception of image focus.

In summary, the results of this study demonstrated that the optimal SA producing best image quality varied widely among subjects and could be predicted based on other HOAs. Customization of IOL selection should be based on the full spectrum of preexisting corneal HOAs and not on 4th-order SA alone. Further theoretical and clinical studies are desirable to address issues such as decentration, tilt, depth of focus, and, of course, clinical assessment of quality of vision.

Aspheric intraocular lenses have been developed, whereby the aspheric design of the implant can offset the SA of the cornea, attempting to mimic the crystalline lens of youth for improved image quality. However, current aspheric implants are available in a standard “one size fits all” approach. As the authors imply from their study, customized implants would need to be produced to compensate a variety of corneal HOAs. This begs the question, Is this practical for implant manufacturers? It has also been shown that the resultant wavefront aberrations after cataract surgery are affected by implant decentration, tilt, and rotation as well as the effect of corneal incision size, location, and wound healing.² These factors, which may only be assessed postoperatively, may offset the benefit of wavefront modified implants, which have been selected on the basis of preoperative corneal HOA. Ultimately, customized corneal refractive surgery may be used following the cataract surgery to correct the induced or residual optical aberrations of the eye. This could be additive to the benefits of customized, HOA-correcting implants. Also intriguing is the possibility of using light-adjustable lenses, which can be treated postoperatively to correct the residual HOAs. This technique was reported at last year’s AOS meeting.³

The authors rightfully point out that their study is limited as a theoretical study. Clinical studies are necessary to assess the effect of optical aberrations on image quality after cataract surgery. The authors are to be congratulated for the design and execution of their study. The information reported is incremental to our understanding of the complex nature of how aberrations of the eye affect visual outcomes from cataract surgery.

Financial Disclosures: None.

Funding/Support: Supported in part by an unrestricted grant from Research to Prevent Blindness.

Financial Disclosures: Dr Koch is a consultant for Advanced Medical Optics, Inc, Alcon Surgical, Inc, and Calhoun Vision, Inc. Dr Wang has reported no relevant financial interests.

Author Contributions: Design and conduct of the study (D.D.K., L.W.); Collection, management, analysis, and interpretation of the data (D.D.K., L.W.); Preparation, review, and approval of the manuscript (D.D.K., L.W.).