Advances in intraocular lens (IOL) design have increased expectations from cataract surgery beyond merely providing good visual acuity. Among these designs, aspheric IOLs are supposed to offer visual quality advantages over spherical IOLs.1 An aspheric IOL is usually implanted to partially or totally reduce corneal spherical aberration, which could potentially improve contrast sensitivity in the aging eye.2 Other types of aspheric IOLs, such as aberration-free IOLs with zero spherical aberration, reduce the occurrence of other higher-order aberrations caused by slight decentration of the IOL.2 In addition, some IOL models introduce extra spherical aberration, resulting in an eye with a relatively high spherical aberration, which may increase the depth of focus and thus improve near vision.3
The desired impact on the visual quality of an aspheric IOL with a certain amount of spherical aberration could be diminished if its intraocular displacement is significant. The cause of such a negative effect has been described4 and is a consequence of the aberrations induced by tilt or decentration, mainly coma and astigmatism (Figure 1). Clinical studies in the literature1,4,5 assessing the amount of decentration that can be tolerated with a 6.0 mm pupil diameter found a value of approximately 0.4 mm. This report will show that a similar value can be obtained by a simple theoretic approach. Moreover, our results will indicate that the value will be independent of the asphericity of the IOL; rather, it depends linearly on the patient’s pupil size.
This can be shown using Zernike polynomials in Cartesian coordinates (x, y), for example, after vertical decentration (Δy) of an IOL with a certain amount of spherical aberration a(4,0), the following amounts of astigmatism a(2,2), coma a(3,−1), and defocus a(2,0) are being introduced6:
where r is the pupil radius. Assuming that the value of the spherical aberration introduced by the IOL compensates for the value from the cornea, the variance of the aberration (root mean square [RMS]) generated after decentration will be the same as the one pretended to be corrected when
Using the equations 1 to 4, we can obtain
From equation 5, we can calculate the maximum decentration for any given pupil radius, which will limit the benefit of the correction in terms of the RMS. If the generated defocus (equation 3) and astigmatism (equation 1) were corrected with a spectacle lens, the residual RMS after the correction will be created just by the coma (equation 2) and the resulting in the maximum displacement will be
The calculations have been done for a vertical decentration; however, given the rotational symmetry of the spherical aberration, a similar result will be found for the decentration in any other direction.
For a 5.0 mm pupil, equations 5 and 6 (equation 6 in Figure 2) gives a maximum displacement of 0.363 (= 0.145 × 2.5) and 0.395 mm (= 0.158 × 2.5), respectively, which is in good agreement with previously cited empirical results.1,4,5 Small differences can be the result of the fact that it is known that not all coefficients of the Zernike polynomial result in equivalent losses of visual quality.7 However, besides the explanation of the empirical results, equation 6 shows an interesting result: The decentration value only depends on pupil size, so it is independent of the value of the spherical aberration to be corrected. This is good news for surgeons because for small pupils, the decentration of an aspheric IOL will not be of great importance because the absolute value of the aberrations generated is small (small pupil); while for large pupils, the tolerance to decentration is larger, as indicated by equation 6.
1. Holladay JT, Piers PA, Koranyi G, van der Mooren M, Norrby NES. A new intraocular lens design to reduce spherical aberration of pseudophakic eyes. J Refract Surg
2. Shentu X, Tang X, Yao K. Spherical aberration, visual performance and pseudoaccommodation of eyes implanted with different aspheric intraocular lens. Clin Exp Ophthalmol
3. Amigo A, Bonaque S, López-Gil N, Thibos L. Simulated effect of corneal asphericity increase (Q-factor) as a refractive therapy for presbyopia. J Refract Surg
4. Altmann GE, Nichamin LD, Lane SS, Pepose JS. Optical performance of 3 intraocular lens designs in the presence of decentration. J Cataract Refract Surg
5. Wang L, Koch DD. Effect of decentration of wavefront-corrected intraocular lenses on the higher-order aberrations of the eye. Arch Ophthalmol. 123, 2005, p. 1226-1230, Available at: http://archopht.jamanetwork.com/data/Journals/OPHTH/9945/els50006.pdf
. Accessed January 31, 2015.
6. Lundström L, Unsbo P. Transformation of Zernike coefficients: scaled, translated, and rotated wavefronts with circular and elliptical pupils. J Opt Soc Am A Opt Image Sci Vis
7. Applegate RA, Sarver EJ, Khemsara V. Are all aberrations equal? J Refract Surg