The Aspheric Cornea, Spherical Aberration, and Intraocular Lenses: Considerations for Surgical Management

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By John Lloyd, MD, FRCSC, DABO, Reem Alnabulsi, MD, and Michael Wan, MD

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The cornea is the main refractive surface of the eye. The prolate shape of the cornea plays a role in maintaining the optimum total spherical aberration (SA) of the eye by neutralizing the negative SA of the lens. As we age the lenticular SA shifts in the positive direction while the corneal SA remains the same, making the total ocular SA more positive. SA of the eye is directly proportional to the Q ­coefficient that represents the corneal aspheric shape. In order to replace the natural lenticular SA after senile cataract surgery, aspheric lenses with different amounts of inherent SA have been developed. The evidence supporting the use and benefits of these lenses is controversial with many limitations. Despite limited evidence, most of the existing studies show that aspheric lenses give better contrast sensitivity and lower higher-order aberrations (HOAs) as well as SAs postoperatively. The outcomes are dependent on many factors such as the pre­operative HOAs and SAs, decentration/tilt, pupil size and the surgically induced HOAs. Superior outcomes were demonstrated when the preoperative HOAs and SAs were measured when choosing an aspheric intraocular lens (IOL) to target zero postoperative SA. This issue of Ophthalmology Rounds will review the SA of the eye, its relation to the image quality and how it changes with aging, IOL implantation, and corneal surgery. Furthermore, the theory behind developing aspheric IOLs and the evidence available to demonstrate their benefits over spheric lenses will be summarized.

 

The cornea is prolate in shape with flatter periphery and steeper centre.[1] The shape of the cornea is important as it influences the spherical aberration (SA) of the cornea and therefore the total SA of the optical apparatus.[1] Maintaining a balance between the lenticular and corneal SAs is important for optimal vision quality.[1] Changes in the shape of the cornea following laser-assisted in situ keratomileusis (LASIK) surgery or age-related changes in the lens can disturb the natural balance of the SA of the ocular system.[2-4] This can lead to halos, glare, starburst and other visual defects. SA may be an important consideration for customizing the implantation of an intraocular lens (IOL) following cataract extraction.[5-7]

 

Basic Optical Consideration: SA and Its Relation to Corneal Asphericity

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SA is a higher fourth-order aberration that is produced by a difference between the central and the peripheral power of a refracting surface so that light rays passing through the periphery (marginal rays) are bent differently than those passing through the paraxial area, which leads to rays focusing at more than one point.[1] SA is positive when the peripheral rays focus in front of the paraxial rays (Figure 1) while negative when the opposite happens.[1,8]

 

Figure 1: A diagram of positive spherical aberration.

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The aspheric shape of the cornea can be approximated as a conic section. In mathematics, conic sections are formed by the intersection of a plane with a cone (Figure 2). Conic sections are described by a number of coefficients, which are all different ways of describing the curvature of the conic section and can be converted mathematically. Table 1 describes the relationships.[1,9]

 

Figure 2: Conic sections

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Table 1: Relationships of conic section coefficients

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p defines how much curvature varies from a circle; Q represents asphericity,
Q=0 is a circle; e is eccentricity and e2 represents the index of asphericity.
Reproduced from Calossi A. J Refract Surg. 2007;23(5):505-514 with permission
of SLACK Incorporated.

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An ellipse is described by the equation x[2]/a[2]+y[2]/b[2]=1. If a>b then the ellipse has its major (longer) axis along the horizontal and is called prolate. Figure 3A shows the curvature decreasing as we move away from the apex. When b>a, the opposite occurs and this is termed oblate (Figure 3B). If we consider the visual axis to be the horizontal, then the cornea has a prolate configuration. The term “p” is defined as b[2]/a[2] and represents how much the curvature varies from a circle (in which a=b, and therefore p=1). The asphericity term “Q” is simply defined as p-1. Doing this adjusts the scale so that Q=0 describes a spherical (circular) surface. The result is that negative Q values are prolate and positive ones are oblate, with the special cases of Q=-1 being a parabola and Q<-1 being a hyperbola.

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Figure 3: Types of ellipses

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Knowing the corneal asphericity measurements in a population is helpful for customized laser ablation and contact lens fitting. Altering the corneal aspher­icity by targeting a more negative Q value may be useful in presbyLASIK.[10] Further elaboration on the calculation of the Q value and on eccentricity (e) are beyond the scope of this paper. Interested readers are referred to the excellent review article by Calossi.[1]

 

A spherical refracting surface has positive SA. When a surface is aspherized, giving a non-zero Q value, the change in Seidel SA at the aspheric surface is determined by an aspheric aberration contribution factor (k), which was defined by Hopkins and Welford (Table 2).[11] The total SA of the eye comes from the cornea, lens, and retina;[12] however, more than 95% arises from the anterior corneal surface as it is the main dioptric power of the eye.[13] The SA is  directly proportional to the Q value and is inversely proportional to the apical radius of curvature.[14]

 

Table 2: Hopkins and Welford definition of aspheric aberration contribution factor (κ)

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In the human cornea, a Q value of -0.53 would be predicted to give 0 SA,[1] which is sometimes referred to as a “perfect” prolate ellipsoid. Average corneal Q values have been found to be -0.26, predicting a positive SA of +0.19 µm; however, actual measured SA has been found to average around +0.27 µm.[15,16] This discrepancy arises because the true corneal shape is more complex than a simple radius of curvature and a Q value can predict.[17] Therefore, there is no easy way to convert from a Q value to the SA, and measurement of SA is best performed by a topo­grapher who has Zernicke analysis.

 

In a young eye, the measured SA of the crystalline lens is about -0.26 µm, which acts to neutralize the average corneal SA (+0.27 µm) over a corneal zone of 6 mm.18 As the eye ages, the corneal SA (anterior surface) remains almost the same or changes slightly,[4] while the negative SA of the crystalline lens shifts positively, as does the posterior cornea. These effects combine to create an overall positive change in the total SA of the eye.[2] This increased positive SA translates as poorer vision quality.[18] In order to restore the natural balance of the SA in the ocular system, wave front-adjusted IOLs with a SA that resembles that of the young crystalline lens have been developed.[19]

 

If the natural prolate shape of the cornea is lost in the case of refractive surgery, the total SA of the eye changes.[3,20] Studies have shown the Q value and consequently the SA change in the positive direction after myopic refractive surgery and in the negative direction after hyperopic ablation.[3,21] This means, theoretically, that the post-hyperopic LASIK group would benefit from a standard IOL (positive inherent SA) that will offset the surgically induced negative SA of the eye, while a post-myopic LASIK eye would benefit from a negative-SA aspheric lens that will offset the surgically induced positive SA.22 Bottos et al[3] reported a change in the Q value of up to +2 after myopic surgery and as much as -1.2 following hyperopic surgery. The same study measured an increase in SAs up to +0.82 µm following myopic refractive surgery and a reduction of up to -0.91 µm following hyperopic corrective surgery. The higher the refractive error, the more the Q value and the SA will change after surgery, which leads to worsening of visual quality despite 20/20 vision on the chart secondary to glare, ­starburst, and halos.[3,23,24] This makes refractive surgery less favourable in the presence of a high refractive error.[3]

 

The presence of some SA has been shown to improve the quality of the defocused image and can increase the depth of perception.[25-27] Furthermore, as the SA is rotationally symmetric, it can balance or offset other types of higher-order aberrations (HOAs).[28] Some studies claim that individuals with excellent visual performance (20/12) have an average of +0.2 µm of positive SA when measured over the 5.7-mm pupil diameter and thus SA is the only HOA that has non-zero mean value.[29-32] It has even been postulated in one report that the increase in positive SA over age is the natural way of the eyes to compensate for the lost accommodation that happens in presbyopia.[28] However, the subjects in these studies were aged 22–70 years while the best visual performance is known to be at age 19, making these conclusions debatable.[14,30,31] Holladay argued that near-zero SA around the age of 19 is the ideal SA for the eye, which should be the target SA postoperatively, especially in younger individuals.[14]

 

The optimum SA after senile cataract surgery for best image quality has yet to be determined.[3] Some simulation studies have concluded that the best visual performance was associated with variable degrees of residual SA in different eyes. In the majority, the ideal residual SA was found to be slightly negative, ranging from (0.0 to -0.1), assuming the second-order aberrations are fully corrected.[33-40] This can be especially true in pseudophakic presbyopic patients needing better near vision, which is helped by a residual negative SA as the pupil constricts during accommodation (stronger central power).[14] The available aspheric lenses (SA ranging from 0.00 to -0.27)[41] have been designed to neutralize the natural average amount of corneal SA present in the non-operated population.[42]

 

As previously mentioned, studies of postoperative LASIK patients have shown that myopic ablation induces additional positive SA and hyperopic negative SA, with larger degrees of ametropia causing larger shifts.[3,43] With the target postoperative SA ranging from (0.00 to -0.10), only 20% of the patients who underwent refractive surgery in one study could achieve such a target with the current range of aspheric IOLs.[3] This suggests that measurement of post-LASIK SA may be necessary to determine the suitability of these patients for the current aspheric IOLs.[3] Since SA measurements are not readily available to many cataract surgeons, avoiding negative SA aspheric IOLs in post-hyperopic LASIK patients is the simplest way to take this fact into consideration.

 

Aspheric IOL Implantation

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Many factors can influence the clinical outcome of an aspheric IOL implantation.[44] These include decentration, tilt, preoperative corneal HOAs, surgically induced HOAs, inherent SA of the lens, postoperative defocus and astigmatism, and pupil size (senile miosis).[44,45] In addition, the time at which the patient is assessed postoperatively plays a role as the neural ­adaption of the brain to the new vision may take 3–12 months.[14,36,46]

 

Numerous papers compared the outcomes of aspheric and spherical lenses in terms of post­operative HOAs, visual acuity, and photopic and mesopic contrast sensitivities.[44] However, few of these studies assessed the preoperative corneal HOAs or the SA to optimize the postoperative SA, which is a significant limitation to the available evidence on the benefits of these lenses.[44] Moreover, many of the conclusions were based on computer simulation testing where the visual axis is at the center of the pupil, which is not the case in the human eye.[44]

 

In most of these clinical trials, no statistically significant difference in best-corrected visual acuity (BCVA) was found between spherical and aspheric IOLs.[35,37-39,44,47-52] Two studies, however, found significantly better BCVA outcomes with the aspheric lens.[33,36] When photopic and mesopic contrast sensitivity were evaluated, the results depended mostly on the spatial frequency at which the contrast sensitivities were analyzed.[44] Most of the studies found that aspheric lenses give better contrast sensitivity compared to spheric lenses, mainly in dim light and larger pupil size.[44] As well, the majority of studies that examined HOAs postoperatively found that HOAs are lower in eyes with aspheric lenses as compared to spherical ones, while all studies that examined SA postoperatively found the SA to be significantly lower in eyes implanted with aspheric lenses.[44] On the other hand, Negishi et al[53] found no statistical difference between pre- and postoperative SA or HOAs, which may be explained by the surgically induced HOAs. Packer, Chantra, and Lian targeted zero SA postoperatively through the measurement of the preoperative corneal topographic SA.[5-7] They were able to demonstrate the feasibility of this method and showed better outcomes compared to studies that did not consider the preoperative SA.

 

A recent large meta-analysis of all the available randomized, controlled trials comparing the HOAs postoperatively with aspheric versus spheric monofocal IOLs confirmed that aspheric IOLs did result in less HOAs particularly SA.[54] 

 

Conclusion

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The SAs of the lens and cornea balance each other in the natural young eye. When this balance is lost because of lenticular aging or cataract extraction with inappropriate IOL implantation, or when the SA of the cornea changes following refractive surgery, the vision quality drops as a result of halos, glare, and ­starburst formation despite 20/20 vision on visual acuity testing. For a cataract surgeon, it is important to keep in mind the preoperative SA of the eye and any history of refractive surgery when choosing a standard IOL versus an aspheric one, which will influence the postoperative vision quality.

 

Many factors other than the SA contribute to the vision quality postoperatively. These include lower order aberrations, pupil size, ­tilt/ ­decentration, the preoperative HOAs and the induction of new aberrations following surgery.[44,45] Based on the current available evidence, aspheric lenses are either better or at least similar to spherical lenses.[44,45]

 

As the rotationally symmetrical SA may balance other HOAs as the eye ages, this complex interaction needs further exploration, and should be considered in future studies when conclusions are drawn regarding the optimal SA.[54-61] Attempting to measure the preoperative corneal SA in order to implant a “matching” aspheric IOL appears in some studies to have merit, but the benefit is not so substantial that the general ophthalmologist need rush out to buy specialized instruments to do so.

 

Dr. Lloyd is a staff ophthalmologist at the Sunnybrook Health Sciences Centre and the Kensington Eye Institute, and is the medical director of the Downtown LasikMD surgicentre, Toronto, Ontario. Dr. Alnabulsi is a PGY3 resident, Department of Ophthalmology and Vision Sciences, University of Toronto, Toronto, Ontario. Dr. Wan is a staff pediatric ophthalmologist at The Hospital for Sick Children, Toronto, Ontario.

 

1. References:

2.  

3. Calossi A. Corneal asphericity and spherical aberration. J  Refract Surg. 2007;23(5):505-514.

4. Wang L, Santaella RM, Booth M, Koch DD. Higher-order aberrations from the internal optics of the eye. J Cataract Refract Surg. 2005;31(8):1512-1519.

5. Bottos KM, Leite MT, Aventura-Isidro M, et al. Corneal asphericity and spherical aberration after refractive surgery. J Cataract Refract Surg. 2011;37(6):1109-1115.

6. Guirao A, Gonzalez C, Redondo M, Geraghty E, Norrby S, Artal P. Average optical performance of the human eye as a function of age in a normal population. Invest Ophthalmol Vis Sci. 1999;40(1):203-213.

7. Packer M, Fine IH, Hoffman RS. Aspheric intraocular lens selection based on corneal wavefront. J Refract Surg. 2009;25(1):12-20.

8. Chantra S, Pachimkul P, Naripthaphan P. Wavefront and ocular spherical aberration after implantation of different types of aspheric intraocular lenses based on corneal spherical aberration. J Med Assoc Thai. 2011;94(Suppl 2):S71-S75.

9. Lian HF, Tang X, Song H. The influence of preoperative corneal spherical aberration on relatively personalized implantation of aspheric intraocular lens [Chinese]. Zhonghua Yan Ke Za Zhi. 2010;46(5):410-144.

10. Thibos LN, Applegate RA, Schwiegerling JT, Webb R. Standards for reporting the optical aberrations of eyes. J Refract Surg. 2002;18(5):S652-S660.

11. Ying J, Wang B, Shi M. Anterior corneal asphericity calculated by the tangential radius of curvature. J Biomed Opt. 2012;17(7):075005.

12. Pallikaris IG, Panagopoulou SI. PresbyLASIK approach for the correction of presbyopia. Curr Opin Ophthalmol. 2015;26(4):265-272.

13. Smith GA, Atchison DA. The Eye and Visual Optical Instruments. Cambridge (UK): Cambridge University Press; 1997.

14. Chang D (ed.). Mastering Refractive IOLs: The Art and Science. Thorofare (NJ): Slack Incorporated; 2008.

15. Barbero S, Marcos S, Merayo-Lloves J, Moreno-Barriuso E. Validation of the estimation of corneal aberrations from videokeratography in keratoconus. J Refract Surg. 2002; 18(3):263-270.

16. Holladay JT. Spherical aberration: the next frontier. Cataract and Refractive Surgery Today. 2006:95-102. Available at: http://crstoday.com/2006/11/CRST1106_18.php.

17. Holladay JT, Piers PA, Koranyi G, et al. A new intraocular lens design to reduce spherical aberration of pseudophakic eyes. J Refract Surg. 2002;18(6):683-691.

18. Wang L, Dai E, Koch DD, Nathoo A. Optical aberrations of the human anterior cornea. J Cataract Refract Surg. 2003;29(8):1514-1521.

19. Roberts C. Characterization of the inherent error in a spherically-biased corneal topography system in mapping a radially aspheric surface. J Refract Corneal Surg. 1994; 10(2):103-111; discussion 112-116.

20. Holladay JT. Quality of Vision: Essential Optics for the Cataract and Refractive Surgeon. 1st edition. Thorofare (NJ): Slack Incorporated; 2006.

21. Atchison DA. Design of aspheric intraocular lenses. Ophthalmic Physiol Opt. 1991;11(2):137-146.

22. Chen CC, Izadshenas A, Rana MA, Azar DT. Corneal asphericity after hyperopic laser in situ keratomileusis. J Cataract Refract Surg. 2002;28(9):1539-1545.

23. Holladay JT, Janes JA. Topographic changes in corneal asphericity and effective optical zone after laser in situ keratomileusis. J Cataract Refract Surg. 2002;28(6):942-947.

24. American Academy of Ophthalmology. How to choose an aspheric intraocular lens [database on the Internet]. 2010  [cited 25th August 2013]. Available from: http:// www.aao.org/publications/eyenet/201011/upload/ CUcatref- Nov-Dec-2010.pdf.

25. Chalita MR, Krueger RR. Correlation of aberrations with visual acuity and symptoms. Ophthalmol Clin North Am. 2004;17(2):135-42, v-vi.

26. Chalita MR, Xu M, Krueger RR. Correlation of aberrations with visual symptoms using wavefront analysis in eyes after laser in situ keratomileusis. J Refract Surg.  2003; 19(6):S682-S686.

27. Nio YK, Jansonius NM, Fidler V, Geraghty E, Norrby S, Kooijman AC. Spherical and irregular aberrations are important for the optimal performance of the human eye. Ophthalmic Physiol Opt. 2002;22(2):103-112.

28. Nio YK, Jansonius NM, Geraghty E, Norrby S, Kooijman AC. Effect of intraocular lens implantation on visual acuity, contrast sensitivity, and depth of focus. J Cataract Refract Surg. 2003;29(11):2073-2081.

29. Altmann GE, Edwards KH. The Aberration-free IOL: Advanced Optical Performance Independent of Patient Profile. 2004. Available at: ­http://www.biokorp.si/admin/dokumenti/inbox/Aberration_Free_IOL_strokovni_ clanek.pdf. Accessed on August 18, 2016.

30. Altmann GE, Edwards KH. The Aberration-free IOL: Advanced Optical Performance Independent of Patient Profile. December 2009. Available at: http://www.bausch. com/Portals/109/-/m/BL/United%20States/Files/Downloads/ ECP/Surgical/Altmann-Whitepaper.pdf. Accessed on November 20, 2015.

31. Porter J, Guirao A, Cox IG, Williams DR. Monochromatic aberrations of the human eye in a large population. J Opt Soc Am A Opt Image Sci Vis. 2001;18(8):1793-1803.

32. Thibos LN, Hong X, Bradley A, Cheng X. Statistical variation of aberration structure and image quality in a normal population of healthy eyes. J Opt Soc Am A Opt Image Sci Vis. 2002;19(12):2329-2348.

33. Wang L, Koch DD. Ocular higher-order aberrations in individuals screened for refractive surgery. J Cataract Refract Surg. 2003;29(10):1896-1903.

34. Levy Y, Segal O, Avni I, Zadok D. Ocular higher-order aberrations in eyes with supernormal vision. Am J Ophthalmol. 2005;139(2):225-228.

35. Bellucci R, Scialdone A, Buratto L, et al. Visual acuity and contrast sensitivity comparison between Tecnis and AcrySof SA60AT intraocular lenses: A multicenter randomized study. J Cataract Refract Surg. 2005;31(4):712-717.

36. Franchini A. Comparative assessment of contrast with spherical and aspherical intraocular lenses. J Cataract Refract Surg. 2006;32(8):1307-1319.

37. Kershner RM. Retinal image contrast and functional visual performance with aspheric, silicone, and acrylic intraocular lenses: prospective evaluation. J Cataract Refract Surg. 2003;29(9): 1684-1694.

38. Mester U, Dillinger P, Anterist N. Impact of a modified optic design on visual function: clinical comparative study. J  Cataract Refract Surg. 2003;29(4):652-660.

39. Munoz G, Albarran-Diego C, Montes-Mico R, Rodriguez-Galietero A, Alio JL. Spherical aberration and contrast sensitivity after cataract surgery with the Tecnis Z9000 intraocular lens. J Cataract Refract Surg. 2006;32(8):1320-7.

40. Packer M, Fine IH, Hoffman RS, Piers PA. Improved functional vision with a modified prolate intraocular lens. J Cataract Refract Surg. 2004;30(5):986-992.

41. Packer M, Fine IH, Hoffman RS, Piers PA. Prospective randomized trial of an anterior surface modified prolate intraocular lens. J Refract Surg. 2002;18(6):692-696.

42. Wang L, Koch DD. Custom optimization of intraocular lens asphericity. J Cataract Refract Surg. 2007;33(10):1713-1720.

43. Wang L, Pitcher JD, Weikert MP, Koch DD. Custom selection of aspheric intraocular lenses after wavefront-guided myopic photorefractive keratectomy. J Cataract Refract Surg. 2010;36(1): 73-81.

44. Holladay JT, Piers PA, Koranyi G, van der Mooren M, Norrby NE. A new intraocular lens design to reduce spherical aberration of pseudophakic eyes. J Refract Surg. 2002; 18(6):683-691.

45. Chen CC, Izadshenas A, Rana MAA, Azar DT. Corneal asphericity after hyperopic laser in situ keratomileusis. J Cataract Refract Surg. 2002;28(9):1539-1545.

46. Montes-Mico R, Ferrer-Blasco T, Cervino A. Analysis of the possible benefits of aspheric intraocular lenses: review of the literature. J Cataract Refract Surg. 2009;35(1):172-181.

47. Bellucci R, Morselli S. Optimizing higher-order aberrations with intraocular lens technology. Curr Opin Ophthalmol. 2007; 18(1):67-73.

48. Artal P, Chen L, Fernandez EJ, Singer B, Manzanera S, Williams DR. Neural compensation for the eye’s optical aberrations. J Vis. 2004;4(4):281-287.

49. Bellucci R, Morselli S, Piers P. Comparison of wavefront aberrations and optical quality of eyes implanted with five different intraocular lenses. J Refract Surg. 2004;20(4):297-306.

50. Kasper T, Buhren J, Kohnen T. Intraindividual comparison of higher-order aberrations after implantation of aspherical and spherical intraocular lenses as a function of pupil diameter. J Cataract Refract Surg. 2006;32(1):78-84.

51. Rocha KM, Soriano ES, Chalita MR, et al. Wavefront analysis and contrast sensitivity of aspheric and spherical intraocular lenses: a randomized prospective study. Am J Ophthalmol. 2006;142(5): 750-756.

52. Kasper T, Buhren J, Kohnen T. Visual performance of aspherical and spherical intraocular lenses: intraindividual comparison of visual acuity, contrast sensitivity, and higher-order aberrations. J Cataract Refract Surg. 2006;32 (12):2022-2029.

53. Denoyer A, Le Lez ML, Majzoub S, Pisella PJ. Quality of vision after cataract surgery after Tecnis Z9000 intraocular lens implantation: effect of contrast sensitivity and wavefront aberration improvements on the quality of daily vision. J Cataract Refract Surg. 2007;33(2):210-216.

54. Tzelikis PF, Akaishi L, Trindade FC, Boteon JE. Spherical aberration and contrast sensitivity in eyes implanted with aspheric and spherical intraocular lenses: a comparative study. Am J Ophthalmol. 2008;145(5):827-833.

55. Negishi K, Kodama C, Yamaguchi T, Torii H, Saiki M, Dogru M, et al. Predictability of ocular spherical aberration after cataract surgery determined using preoperative corneal spherical aberration. J Cataract Refract Surg. 2010;36(5): 756-761.

56. Schuster AK, Tesarz J, Vossmerbaeumer U.  Ocular wavefront analysis of aspheric compared with spherical monofocal intraocular lenses in cataract surgery: Systematic review with meta-analysis. J Cataract Refract Surg. 2015;41(5):1088-1097.

57. Charman WN. The Charles F. Prentice Award Lecture 2005: optics of the human eye: progress and problems. Optom Vis Sci. 2006;83(6):335-345.

58. Chen L, Singer B, Guirao A, Porter J, Williams DR. Image metrics for predicting subjective image quality. Optom Vis Sci. 2005;82(5):358-369.

59. Marsack JD, Thibos LN, Applegate RA. Metrics of optical quality derived from wave aberrations predict visual performance. J Vis. 2004;4(4):322-328.

60. Cheng X, Bradley A, Thibos LN. Predicting subjective judgment of best focus with objective image quality metrics. J  Vis. 2004;4(4):310-321.

61. McLellan JS, Marcos S, Prieto PM, Burns SA. Imperfect optics may be the eye’s defence against chromatic blur. Nature. 2002; 417(6885):174-176.

62. Cheng X, Thibos LN, Bradley A. Estimating visual quality from wavefront aberration measurements. J Refract Surg. 2003; 19(5):S579-S584.

63. Huber C. Planned myopic astigmatism as a substitute for accommodation in pseudophakia. J Am Intraocul Implant Soc. 1981;7(3):244-249.

64. Sawusch MR, Guyton DL. Optimal astigmatism to enhance depth of focus after cataract surgery. Ophthalmology. 1991;98(7):1025-1029.

 

The authors have no any commercial interest in any of the discussed materials in this article. The authors did not receive any financial support from any public or private organization.

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