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Simulations of Decentration and Tilt of a Supplementary Sulcus-Fixated Intraocular Lens in a Polypseudophakic Combination Using Ray-Tracing Software

Simulations of Decentration and Tilt of a Supplementary Sulcus-Fixated Intraocular Lens in a... hv photonics Article Simulations of Decentration and Tilt of a Supplementary Sulcus-Fixated Intraocular Lens in a Polypseudophakic Combination Using Ray-Tracing Software Grzegorz Łabuz *, Gerd U. Auffarth , Weijia Yan, Timur M. Yildirim and Ramin Khoramnia The David J Apple Center for Vision Research, Department of Ophthalmology, University Hospital Heidelberg, INF 400, 69120 Heidelberg, Germany; Gerd.Auffarth@med.uni-heidelberg.de (G.U.A.); Weijia.Yan@med.uni-heidelberg.de (W.Y.); Timur.Yildirim@med.uni-heidelberg.de (T.M.Y.); Ramin.Khoramnia@med.uni-heidelberg.de (R.K.) * Correspondence: Grzegorz.Labuz@med.uni-heidelberg.de Abstract: This study aimed to assess image quality after the tilt and decentration of supplementary intraocular lenses (IOLs) in a two-lens configuration. One was designed for sulcus fixation with a nominal power range of 1D–10D and was combined with a capsular fixation 20D IOL. The optical performance of a ray-tracing model was tested under IOL misalignment through the area under the modulation transfer function (MTFa) and wave aberrations. Tilting by 10 resulted in a 4% reduction of the MTFa for a 10D IOL as compared to 9% for the 20D lens. The two models demonstrated good tolerance to a 1 mm decentration; as for the 10D sulcus-fixated lens, the MTFa loss was 2%, and 4% for the capsular fixation lens. Coma and astigmatism increased three- and four-fold, respectively, after a 10 tilt compared to the aberration level induced by the 1 mm decentration. Both analyses showed a trend towards a lower MTF impact and fewer optical errors with decreasing nominal power. In conclusion, when misaligned, low-power sulcus-fixated IOLs might retain their good Citation: Łabuz, G.; Auffarth, G.U.; optical quality. An extreme tilt of 10 has a more detrimental effect on the IOL performance than Yan, W.; Yildirim, T.M.; Khoramnia, R. a 1 mm decentration. The proper alignment of a high-power capsular fixation lens is important in Simulations of Decentration and Tilt achieving a desirable postoperative outcome. of a Supplementary Sulcus-Fixated Intraocular Lens in a Keywords: supplementary IOLs; lens tilt and decentration; MTF; HOAs; polypseudophakia Polypseudophakic Combination Using Ray-Tracing Software. Photonics 2021, 8, 309. https:// doi.org/10.3390/photonics8080309 1. Introduction Received: 29 June 2021 Phacoemulsification with intraocular lens (IOL) implantation into a capsular bag is a Accepted: 29 July 2021 routine procedure for cataract treatment. Although cataract surgery is usually performed Published: 2 August 2021 in patients over 60 years of age, refractive lens exchange, which results in clear crystalline lens removal and IOL implantation, may be offered to younger patients who wish to be Publisher’s Note: MDPI stays neutral spectacle independent [1]. This shift from cataract to refractive surgery reinforces the need with regard to jurisdictional claims in for a continuous improvement of crystalline lens implants. Similarly, an accurate lens published maps and institutional affil- position is considered essential in obtaining satisfactory vision [2–14]. IOL performance is iations. optimal when the lens is placed in an on-axis position, but precise centration is difficult to achieve during surgery [2–14]. While the incidence of severe tilt and dislocation may compromise vision [15], clinical studies have indicated that if the extent of the IOL’s tilt and decentration is low, visual impairment might not be measurable [2]. Most of those Copyright: © 2021 by the authors. studies have, however, been performed on capsule fixation IOLs [2–4,9–11,13–15]. Still, Licensee MDPI, Basel, Switzerland. little is known about the tolerance to the misalignment of sulcus-fixated supplementary This article is an open access article IOLs, which are also offered in refractive surgery. distributed under the terms and Despite significant advances in biometry techniques and IOL power calculation, conditions of the Creative Commons postoperative refractive errors may still occur in pseudophakic eyes [16]. Gayton and Attribution (CC BY) license (https:// Sanders first described a piggyback technique in 1993 [17], which was initially used to creativecommons.org/licenses/by/ correct postoperative hyperopia in microphthalmia. In 1999, Gayton et al. applied the 4.0/). Photonics 2021, 8, 309. https://doi.org/10.3390/photonics8080309 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 309 2 of 9 same approach to correct myopia in normal and post-penetrating keratoplasty eyes [18]. However, the implantation of two IOLs into the capsular bag resulted in postoperative complications such as interlenticular opacification [19]. The use of sulcus-fixated IOLs that have purposely been designed to be implanted into the ciliary sulcus rather than the capsular bag is accepted as safe and efficacious when they are used in polypseudophakia to supplement or correct an iatrogenic refractive error arising from the implantation of the primary, capsular fixation lens [6–8,12]. Recently, the sulcus-fixated IOLs’ application range moved beyond refractive error correction to reversible multifocality (i.e., bifocality or trifocality) in pseudophakic eyes [6,8,20]. Clinical studies have reported the postoperative misalignment of sulcus-fixated IOLs [6,7,12] whose appearance might be exacerbated by their proximity to the pupil, which is often considered a reference. An off-axis position, which may coincide with the poor visual performance of unknown etiology, may prompt an early decision to explant the IOL. However, the impact of IOL misalignment on the optical quality of sulcus-implanted IOLs has rarely been studied. Decision making or explanations could be improved by a better understanding of the effects of misalignment. Though our group has recently shown that a 5 tilt and a 0.6 mm decentration of a trifocal sulcus-fixated IOL minimally impacts the image quality [8], we only assessed a zero-power model in that study, and we recognized the need for further research using a range of powers. Moreover, a close distance between sulcus-fixated and capsular-fixated IOLs poses a challenge in simulating the misalignment of only the former lens in bench-top measurements. This could be resolved by ray-tracing simulations in a numerical model. The purpose of this study was to evaluate the effect of the tilt and decentration of a sulcus-fixated IOL in simulated polypseudophakia. We applied a ray-tracing model and computed the eye’s higher-order aberrations (HOAs) as well as their impact on the modulation transfer function (MTF) to assess the potential effects of sulcus-fixated lens misalignment on patients’ vision. 2. Materials and Methods 2.1. Intraocular Lenses We performed the optical simulations of ten sulcus-fixated supplementary IOLs, Sulcoflex Aspheric, 653L, (Rayner Ltd., Worthing, UK) with the nominal power ranging from 1 D to 10 D (in 1 D increments). The IOLs were designed based on propriety data provided by Rayner Ltd. under a non-disclosure agreement. Each sulcus-fixated lens had an optic size of 6.5 mm and featured a convex anterior and a concave posterior surface. The lens featured a round edge to decrease the likelihood of pigmentary dispersion and secondary glaucoma. To mimic a polypseudophakic condition, we included a 20 D capsular fixation lens, the RayOne Aspheric, RAO600C, (Rayner Ltd., Worthing, UK) with a complete optical design provided by the manufacturer. The capsular fixation lens differed from the sulcus- fixated lens as it had a smaller optic (i.e., 6 mm), was biconvex, and had a sharp optic edge. However, the material characteristics were identical for both models, which were made of hydrophilic acrylic material (26% water content) with the refractive index and an Abbe number of 1.46 and 56, respectively. Both had an aspheric (‘aberration-neutral’) design to minimize each IOL’s spherical aberration and ensure diffraction-limited performance for a parallel beam. 2.2. Ray-Tracing Simulations A model eye was built in OpticStudio (Radiant Zemax LLC, Redmond, WA, USA) in accordance with the data published by Liou and Brennan [21]. According to this model, the front and back corneal surfaces have a 7.77 mm and 6.40 mm radius of curvature, with a 0.18 and 0.60 asphericity, respectively. The central corneal thickness was 0.50 mm. The anterior chamber depth was 3.16 mm, which was the distance between the back surface of the cornea and the pupil. The retina shape was modeled as an asphere with a 8.10 mm radius of curvature and a conic constant of 0.96. The refractive index and the Abbe number Photonics 2021, 8, 309 3 of 9 of the cornea were 1.376 and 55.48, respectively. Although the aqueous humor had a slightly higher dispersion (50.37) than the vitreous (51.30), both shared a refractive index of 1.336. Ocular media dispersion was derived from the Atchison and Smith study [22]. The crystalline lens was replaced with the RAO600C capsular fixation IOL, and a sulcus- fixated supplementary lens was placed anteriorly with a 0.5 mm separation between the two lenses [6]. The sulcus-fixated lens was located 1.59 mm behind the pupil. The optical simulations were performed in polychromatic light, with the spectrum weight corresponding with the CIE photopic luminosity function. To account for the power difference between the sulcus IOLs, the distance between the primary lens and the retina for each model was modified using a minimum root-mean-square (RMS) wavefront focus adjustment. The IOLs were compared according to their image quality metrics, which were evalu- ated utilizing a Huygens modulation transfer function (MTF) at a 3 mm pupil. The MTF was calculated for sagittal and tangential planes, and then averaged. The IOLs’ tolerance to decentration (up to 1 mm, with a 0.25 mm step) in the X (horizontal) and Y (vertical) directions with respect to the optical axis as well as IOL tolerance to tilt along a horizontal axis (up to 10 , with a 2.5 step) were both tested. The pupil was decentered by 0.5 mm off the axis, as proposed by Liou and Brennan [23]. The impact of tilt and decentration on the imaging performance of each supplementary IOL was assessed in a two-lens configuration with the capsular fixation lens. For comparison, the tolerance to misalignment of the RayOne Aspheric with a centrally aligned 10 D sulcus-fixated lens was also simulated. The IOLs were evaluated using a macro that computed and saved the MTF for each condition. MTF results were later analyzed with a dedicated MATLAB program (MathWorks Inc., Natick, MA, USA). Image deterioration was assessed by comparing the area under the MTF function (MTFa) [24], which was calculated based on the following formula: f =50/d MTFa = MTF( f d) (1) f =0 The maximum frequency (f ) used to calculate the MTF area was 50 lp/mm, and the frequency step was d = 1 lp/mm. The Huygen’s point-spread function (PSF) was calculated and compared. Furthermore, the change in monochromatic aberrations (555 nm) was quantified by Zernike coefficients expressed up to the 6th order. The RMS was calculated for all higher-order terms (above the 6th term—Noll’s notation). However, primary and secondary coma aberrations were only reported due to the low level of other higher-order aberrations (HOAs). Astigmatism induced due to IOL misalignment was calculated from the 5th and the 6th terms after power-vector conversion [25]. 3. Results Figure 1 shows the decrease of the MTFa as a function of tilt (A) and decentration (B). Tilt appears not to have an important impact on the optical quality up to 5 for all IOLs, except for the primary lens. Above this level, the 10 D sulcus-fixated lens’ MTFa decreased slightly, with a sharp decrease above 7.5 . However, the lower the nominal power of the sulcus-fixated supplementary IOL, the more robust the optical performance was against tilt. Nevertheless, the maximum reduction of the MTFa for the 10 D sulcus-fixated lens was 4%, as compared to 9% for the 20 D lens. A lens decentration of up to 1 mm had a less deleterious effect on the optical quality than a 10 tilt. The primary lens demonstrated a gradual decrease of the MTFa with decentration. The sulcus-fixated models were hardly affected by their off-axis position, with a 2% maximum MTFa reduction for the 10 D sample and virtually no effect for lower- power lenses. For the capsular fixation lens, decentration by 1 mm caused a mere 4% loss of image quality. Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Photonics 2021, 8, 309 4 of 9 Figure 1. The impact of isolated tilt (A) and decentration (B). The solid black lines refer to 10 sulcus-fixated IOLs, with the nominal power from 1 D (bottom line) to 10 D (top line). The dashed red line indicates the 20 D capsular fixation lens. Figure 1. The impact of isolated tilt (A) and decentration (B). The solid black lines refer to 10 sulcus-fixated IOLs, with the Figure 1. The impact of isolated tilt (A) and decentration (B). The solid black lines refer to 10 sulcus-fixated IOLs, with the nominal power from 1 D (bottom line) to 10 D (top line). The dashed red line indicates the 20 D capsular fixation lens. nominal power from 1 D (bottom line) to 10 D (top line). The dashed red line indicates the 20 D capsular fixation lens. Figure 2 shows representative images of the combined impact of IOL misalignment Figure 2 shows representative images of the combined impact of IOL misalignment on on the MTF val Figure 2 sho uesw . For t s reprh esent e 3 D lens ative im , no ages change of the combin s in opt ed ical impact qual o ity f can be obser IOL misalignmv ent ed. For the MTF values. For the 3 D lens, no changes in optical quality can be observed. For the 6 D, on the MTF values. For the 3 D lens, no changes in optical quality can be observed. For the 6 D, the effects of misalignment could only be noticed at the extreme ends of the sur- the effects of misalignment could only be noticed at the extreme ends of the surface plot. the 6 D, the effects of misalignment could only be noticed at the extreme ends of the sur- face plot. The MTFa of the 9 D IOL was only decreased at a higher tilt and X = Y = 1 mm The MTFa of the 9 D IOL was only decreased at a higher tilt and X = Y = 1 mm decentration. face plot. The MTFa of the 9 D IOL was only decreased at a higher tilt and X = Y = 1 mm decentration. The primary (20 D) lens results confirmed that tilt impacts the optical quality The primary (20 D) lens results confirmed that tilt impacts the optical quality more than decentration. The primary (20 D) lens results confirmed that tilt impacts the optical quality more than decentration, with the largest separation between the five surfaces. decentration, with the largest separation between the five surfaces. more than decentration, with the largest separation between the five surfaces. Figure 2. The effect of decentration and tilt on the optical quality of a 20 D capsular fixation IOL, as well as 3, 6, and 9 D Figure 2. The effect of decentration and tilt on the optical quality of a 20 D capsular fixation IOL, as well as 3, 6, and 9 D sulcus-fixated IOLs in polypseudophakia. The imaging performance was quantified with the area under the modulation sulcus-fixated IOLs in polypseudophakia. The imaging performance was quantified with the area under the modulation transfer function (MTFa). Each figure′s top and bottom surfaces correspond to a condition with zero and 10° tilt, respec- Figure 2. The effect of decentration and tilt on the optical quality of a 20 D capsular fixation IOL, as well as 3, 6, and 9 D tively. For the 20 D IOL, a 2.5° tilt increase resulted in a gradual degradation of the optical quality, creating five distinct transfer function (MTFa). Each figure’s top and bottom surfaces correspond to a condition with zero and 10 tilt, respectively. sulcus-fixated IOLs in polypseudophakia. The imaging performance was quantified with the area under the modulation surfaces of the MTFa change. For the 20 D IOL, a 2.5 tilt increase resulted in a gradual degradation of the optical quality, creating five distinct surfaces of transfer function (MTFa). Each figure′s top and bottom surfaces correspond to a condition with zero and 10° tilt, respec- the MTFa change. tively. For the 20 D IOL, a 2.5° tilt increase resulted in a gradual degradation of the optical quality, creating five distinct surfaces of the MTFa change. Photonics 2021, 8, 309 5 of 9 Photonics Photonics 2021, 8, x FO Photonics 2021 R P , 8, x FO EER 2021 RE R P , 8 VIEW , x FO EER Photonics RE R P VIEW EER 2021 RE , 8 VIEW , x FO R PEER REVIEW 5 of 11 5 of 11 5 of 11 5 of 11 PhotonicsPhotonics 2021, 8, x FO Photonics Photonics Photonics 2021 R P , 8, x FO EER Photonics Photonics Photonics 2021 2021 2021 RE R P , , , 8 8 8VIEW , x FO , x FO , x FO EER Photonics Photonics 2021 2021 2021 RE R P R P R P , , , 8 8 8 VIEW , x FO , x FO , x FO EER EER EER 2021 2021 RE RE RE R P R P R P , , 8 VIEW 8 VIEW VIEW , x FO EER , x FO EER EER RE RE RE R P R P VIEW VIEW VIEW EER EER RE RE VIEW VIEW 5 of 11 5 of 11 5 of 5 of 5 of 11 11 11 5 of 5 of 5 of 11 11 11 5 of 5 of 11 11 Photonics PhotonicsPhotonics Photonics 2021 2021, , 8 8, x FO , x FO 2021 2021 R P R P , , 8 8, x FO , x FO EER EER Photonics RE RE R P R P VIEW VIEW EER EER Photonics 2021 RE RE , 8 VIEW VIEW , x FO 2021 R P , 8, x FO EER RE R P VIEW EER RE VIEW 5 of 5 of 11 11 5 of 5 of 11 11 5 of 11 5 of 11 The PSF analysis presented in Table 1 confirms that the performance of the 3 D sulcus- The PSF The PSF analysis presented in T The PSF analysis presented in T The PSF analysis presented in T The PSF analysis presented in T able 1 c analysis presented in T o able nfirms that t 1 ca o ble nfirms that t 1 c h a o e perform ble nfirms that t 1 ch a oble e perform nfirms that t a 1 c nch e of the oe perform nfirms that t anc h 3 D sul- e of the e perform anch e of the 3 D sul- e perform ance of the 3 D sul- ance of the 3 D sul- 3 D sul- The PSF The PSF The PSF analysis presented in T The PSF The PSF The PSF analysis presented in T analysis presented in T The PSF The PSF The PSF analysis presented in T analysis presented in T analysis presented in T The PSF The PSF analysis presented in T analysis presented in T analysis presented in T able 1 c analysis presented in T analysis presented in T a a oble ble nfirms that t 1 c 1 c a a a o o ble ble ble nf nfirms that t irms that t 1 c 1 c 1 ch a a a o o oble e perform ble ble nf nf nfirms that t irms that t irms that t 1 c 1 c 1 c h h a o a o o e perform e perform ble ble nf nf nfirms that t irms that t irms that t a 1 c 1 c nc h h h e of the o o e perform e perform e perform nf nfirms that t a irms that t an nc c h h h e of the e of the 3 D sul- e perform e perform e perform a a an n nc c ch h e of the e of the e of the 3 D sul- 3 D sul- e perform e perform a a an n nc c ce of the e of the e of the 3 D sul- 3 D sul- 3 D sul- a an nc ce of the 3 D sul- e of the 3 D sul- 3 D sul- 3 D sul- 3 D sul- The PSF The PSF The PSF analysis presented in T analysis presented in T analysis presented in T The PSF a able ble 1 c 1 c analysis presented in T a o oble nf nfirms that t irms that t 1 confirms that t h he perform e perform h ae perform blea a 1 c n nc ce of the e of the onfirms that t ance of the 3 D sul- 3 D sul- h 3 D sul- e performance of the 3 D sul- Photonics 2021, 8, x FOR PEER REVIEW 5 of 10 fixated IOL does not substantially differ under various severities of misalignments. For the cus-fixacus-fix ted IOL does not substa a cus-fix ted IOa cus-fix L does not substa ted IOa L does not substa cus-fix ted I ntia Oa ll L does not substa ted I y di ntia ff Oer u L does not substa lly di ntia nder ffer u lly di vari ntia nder ff ous er u lly di vari seve ntia nder ff ous er u rities of misalign lly di vari seve nder ff ous er u rities of misalign vari seve nder ous rities of misalign vari m seve ents. ous rities of misalign seve ments. rities of misalign ments. ments. ments. cus-fixa cus-fix cus-fix ted IOa a cus-fix cus-fix cus-fix L does not substa ted I ted IO O a a a L does not substa cus-fix cus-fix cus-fix L does not substa ted I ted I ted IO O Oa a a L does not substa L does not substa L does not substa cus-fix cus-fix cus-fix ted I ted I ted I ntia O O Oa a L does not substa a L does not substa L does not substa llted I ted I ted I y di ntia ntia ff O O O er u ll L does not substa L does not substa ll L does not substa y di y di ntia ntia ntia nder ff ffer u er u ll ll lly di y di y di vari ntia ntia ntia n nder der ff ff ff ous er u er u er u ll ll lly di y di y di vari vari seve ntia ntia n n n ntia der der der ff ff ff ous ous er u er u er u rities of misalign ll ll lly di y di vari vari vari y di seve seve n n nder der der ff ff ff ous ous ous er u er u er u rities of misalign rities of misalign vari vari vari seve seve seve n n nder der der ous ous ous rities of misalign rities of misalign rities of misalign vari vari vari seve m seve seve ents. ous ous ous rities of misalign rities of misalign rities of misalign m seve m seve seve ents. ents. rities of misalign rities of misalign rities of misalign m m ments. ents. ents. m m ments. ents. ents. m m ments. ents. ents. cus-fix cus-fixa a cus-fix ted I ted IO Oa L does not substa L does not substa ted IOL does not substa ntia ntiall lly di y di ntia ff ffer u er u lly di n nder der ffer u vari vari nder ous ous vari seve seve ous rities of misalign rities of misalign severities of misalign m ments. ents. ments. 6 D IOL, a slight change in the PSF appearance could be observed at a 10 tilt, but for the For the 6 D IOL, a slight change in the PSF appearance could be observed at a 10° tilt, For the For t 6 D Ih O e L, 6 D I a slO ig For t L, ht c a s h h l ange e ig For t For t 6 D I ht c in t h h h O ange e e h L, 6 D I 6 D I e a s PSF in t lO O ig ap L, L, h ht e a s p a s c PSF e haran llange iig g ap ht htce cou c c pin t h e haran ange ange he ld b ce cou PSF in t in t e o ap h hb e e lserv d b p PSF PSF earan eed ap o ap bce cou at p serv pe e a aran aran 1 ed 0l° t d b ce cou ce cou at ilt a e, 1 o0 b ll° t d b d b serv ilt e e, o ed ob bserv at serv a 1 ed ed 0° t at ati a a lt, 1 10 0° t ° tiilt lt, , For t For t For th h he e e For t For t For t 6 D I 6 D I 6 D I h h h O O O e e e For t For t For t L, L, L, 6 D I 6 D I 6 D I a s a s a s h h h ll O O lO ii e e e ig g g For t L, L, For t For t L, 6 D I 6 D I 6 D I ht ht hta s a s c a s c ch h h h h h l l O O O lange ange ange i i e e i e g g g L, L, L, For t For t 6 D I 6 D I 6 D I ht ht hta s a s a s c c c in t in t in t h h h h h l l lO O O ange ange i i i ange e e g g g L, h L, L, h h ht 6 D I ht ht 6 D I e e e a s a s a s c c c PSF PSF PSF in t in t in t h h hll lO O ange ange ange ii ig g g ap ap ap h L, h L, h ht ht ht e e e a s c a s p c c p p PSF PSF PSF in t in t in t e h e e h haran l aran l aran ange ange ange iig g ap ap ap h h h ht ht e e e ce cou ce cou c ce cou p p c PSF PSF PSF p in t in t in t e e h e haran aran aran ange ange ap ap ap h h he e e ll ld b d b ce cou d b ce cou p p p ce cou PSF PSF PSF in t in t e e earan aran aran e e e o ap o ap o ap h hb e b e b l lld b d b ce cou ce cou ce cou serv d b p serv serv p p PSF PSF e e earan aran aran e e e o o ed ap ap o ed ed b b b l l ld b d b d b ce cou ce cou serv serv ce cou at p at serv p at e e a a a aran aran e e e 1 1 1 o o o ed ed ed 0 0 0 b b b ll l° t ° t ° t d b d b d b serv serv serv ce cou ce cou at at at ii i a a a lt lt lt e e e, 1 1 , , 1 o o o ed ed ed 0 0 0 b b b ll° t ° t ° t d b d b serv serv at serv at ati ii a a a lt lt lt e e 1 1 1 , , , o ed o ed ed 0 0 0 b b ° t ° t ° t serv at serv at ati i i a a a lt lt lt 1 , , , 1 1 ed ed 0 0 0° t ° t ° t at at ii i a a lt lt lt, 1 , , 10 0° t ° tiilt lt, , other conditions, differences from the centered PSF were not apparent. 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Both but for the ot but for the ot but for the ot but for the ot but for the ot but for the ot her condit her condit her condit but for the ot but for the ot her condit her condit her condit but for the ot but for the ot ion ion ions s sher condit her condit , d , d , d but for the ot but for the ot ii iion ion fference ion fference fference s s sher condit her condit , d , d , di iiion ion fference fference fference s s s from the cent from the cent from the cent s sher condit , d , d her condit i iion ion fference fference s s s from the cent from the cent from the cent s s, d , di iion ion fference fference s s ered P ered P ered P from the cent from the cent s s, d , diifference fference S S s S s ered P ered P ered P F F F from the cent from the cent wer wer were e e S S s s S ered P ered P not apparen not apparen not apparen F F F from the cent from the cent wer wer were e S S eered P ered P not apparen not apparen not apparen F F wer wert t t e e S . Both S . Both . Both ered P not apparen not apparen ered P F F wer wert tte e S . Both . Both S . Both not apparen not apparen F F wer wer t te e . Both . Both not apparen not apparen t t. Both . Both t t. Both . Both the 20 D IOLs proved to be minimally affected by a 0.5 mm decentration, but at 1 mm, an The PSF analysis presented in Table 1 confirms that the performance of the 3 D sul- the 9 Dthe 9 D and the 20 D and the 20 D IOLs proved to be IOLs proved to be minima mini lly af m fe act lly ed b affe yct a ed b 0.5 m y a m0. decent 5 mm decent ration, b rau titon, b ut the 9 D the 9 D and and the 20 D the 20 D the 9 D IOLs IOLs the 9 D and the 9 D the 20 D proved to be proved to be and the 9 D and the 9 D the 20 D the 20 D IOLs and andmini mini the 20 D the 20 D proved to be IOLs IOLs m ma all ll proved to be proved to be y y IOLs IOLs af aff fe emini ct ct proved to be proved to be ed b ed b my y a mini mini ll a a y 0. 0. af m 5 5 m f m m e a a mini mini ct ll ll m m y y ed b decent decent af af m m ffe y e a a ct ct ll ll a ed b y ed b y 0. ra ra af af 5t t m f f i iy e y on, b e on, b ct ct a m a ed b ed b 0. 0. decent 5 u u 5 m m t ty y m m a a 0. decent 0. ra decent 5 5 t m i m on, b m mra decent ra decent u ttt ii on, b on, b ra ra u u t ttt ii on, b on, bu ut t the 9 D the 9 Dthe 9 D and the 9 D and the 9 D the 20 D the 20 D the 9 D the 9 D and and and the 20 D the 20 D the 20 D IOLs IOLs and and the 9 D the 9 D the 20 D the 20 D proved to be proved to be IOLs IOLs IOLs the 9 D and the 9 D and the 20 D the 20 D proved to be proved to be proved to be IOLs IOLs and andmini mini the 20 D the 20 D proved to be proved to be IOLs IOLs m ma a mini mini mini ll ll proved to be proved to be y IOLs y IOLs af af m m m ffe e a a a mini mini ct ct ll ll ll proved to be proved to be y y ed b y ed b af af af m m f ffy e e a a y e mini mini ct ct ll ll ct a a y y ed b ed b ed b 0. 0. af af 5 m 5 m f m f m e e y y a y a mini mini ct ct ll ll m a a m a y y ed b ed b 0. 0. decent 0. decent af af 5 5 m m 5 m m f f m y y e e a act ct ll ll a a m m m y y ed b ed b 0. 0. decent decent ra decent ra af af 5 5tt m m f f iie y y e on, b on, b ct ct m m a a ed b ed b 0. 0. decent decent ra ra ra u 5 5 u t tt m m t i i tiy y on, b on, b on, b m a m a 0. 0. ra decent ra decent u u 5 5 u t t m m t t i iton, b on, b m m decent decent ra ra u ut tt ti i on, b on, b ra ra u u t tt t ii on, b on, bu ut t asymmetry of the PSF becomes visible, which is particularly pronounced at a 10 tilt. cus-fixated IOL does not substantially differ under various severities of misalignments. at 1 mm, ata 1 mm, n asymmetry of at 1 mm, an asymmetry of an asymmetry of the at 1 mm, PSFthe beco a PSF n mes vis asymmetry of the beco PSF mes vis ibl beco e, whi mes vis ibl the ch is pa e, PSF whi ibl beco c rticu e, h is pa whi lmes vis arcly pronou rticu h is pa lia bl rrticu ly pronou e, whi nced lar cly pronou h is pa at nced rticu atnced larly pronou at nced at at 1 mm, at 1 mm, an asymmetry of a a at t t 1 mm, 1 mm, 1 mm, an asymmetry of a a at t t 1 mm, 1 mm, 1 mm, a a an n n asymmetry of asymmetry of asymmetry of the a at t 1 mm, a PSF 1 mm, a an n n asymmetry of asymmetry of asymmetry of the beco PSF a an n mes vis asymmetry of the the the asymmetry of beco PSF PSF PSF mes vis ibl the the the beco beco beco e, PSF whi PSF PSF mes vis mes vis mes vis ibl the the beco beco c beco e, h is pa whi PSF PSF mes vis mes vis mes vis i i ibl bl bl c beco beco rticu e, e, e, h is pa whi whi whi l mes vis mes vis ii ia bl bl bl r c c crticu ly pronou h is pa e, h is pa h is pa e, e, whi whi whi li a ibl bl r c c c rticu rticu rticu ly pronou h is pa h is pa h is pa e, e, whi whi nced l l la a ar r rc c rticu rticu rticu ly pronou ly pronou ly pronou h is pa h is pa atnced ll la a ar r rrticu ly pronou ly pronou rticu ly pronou atnced nced nced lla ar rly pronou ly pronou a a at t tnced nced nced a a at t t nced nced a at t a att 1 mm, 1 mm, a att 1 mm, a 1 mm, an n asymmetry of asymmetry of a an n asymmetry of asymmetry of at 1 mm, the the at 1 mm, PSF PSF an asymmetry of the the beco beco PSF a PSF n mes vis mes vis asymmetry of beco becomes vis mes vis iibl bl the e, e, whi PSF whi iibl bl the c beco ch is pa e, h is pa e, whi PSF whi mes vis c beco c rticu rticu h is pa h is pa lmes vis li a a bl r rrticu ly pronou rticu ly pronou e, whi llia a bl r r cly pronou ly pronou e, h is pa whi nced nced crticu h is pa a attnced nced larrticu ly pronou a att larly pronou nced atnced at For the 6 D IOL, a slight change in the PSF appearance could be observed at a 10° tilt, a 10° tilt a 10 . ° tilt a 10 . ° tilt a 10 . ° tilt a 10 . ° tilt. a 10° tilt a 10 a 10 . ° ° ttiilt a 10 a 10 a 10 lt.. ° ° ° t t ti i ilt lt lt a 10 a 10 a 10 ... ° ° ° t t tii ilt lt lt a 10 a 10 ... ° ° t tiilt lt.. a 10 a 10° ° ttiilt lt a 10 .. ° tilt. a 10° tilt. Table 1. The point-spread function of the IOLs assessed at the on-axis position, with decentration but for the other conditions, differences from the centered PSF were not apparent. Both and tilt. Table 1. The point-spread function of the IOLs assessed at the on-axis position, with decentration and tilt. Table 1. Table 1. The po th int-spread fu e 9 D The p and oTable 1. int-spread fu tnction of he 2 Table 1. The p 0 Dnction of IOLs the IOLs a oint-spread fu The p pr the IOLs a o ov int-spread fu sse ed t sse nction of od a bsse et m the on-axis po sse nction of i the IOLs a nim d ata the on-axis po lly the IOLs a af sse f sition ect sse ed b d a , with sse sition ty the on-axis po sse a de 0. d a , with centration and t 5 m t the on-axis po m de decent centration and t sitionra , with ilt. tsition ion, b de , with centration and t u ilt. t decentration and t ilt. ilt. Table 1. Table 1. Table 1. Table 1. Table 1. Table 1. The p The p The po o oint-spread fu Table 1. Table 1. Table 1. int-spread fu int-spread fu The p The p The po o oTable 1. int-spread fu int-spread fu Table 1. Table 1. int-spread fu The p The p The p nction of nction of nction of o o oint-spread fu int-spread fu int-spread fu Table 1. Table 1. Table 1. The p The p The p nction of nction of nction of the IOLs a the IOLs a the IOLs a o o oint-spread fu int-spread fu int-spread fu The p The p The p nction of nction of nction of the IOLs a the IOLs a the IOLs a o o oint-spread fu int-spread fu int-spread fu sse sse ssesse sse sse nction of nction of nction of the IOLs a the IOLs a the IOLs a d a d a d a sse sse sse t t t the on-axis po the on-axis po the on-axis po sse sse sse nction of nction of nction of the IOLs a the IOLs a the IOLs a d a d a d a sse sse sse t tt the on-axis po the on-axis po the on-axis po sse sse sse the IOLs a the IOLs a the IOLs a d a d a d a sse sse sse sition sition sition t t t the on-axis po the on-axis po the on-axis po sse sse ssed a d a d a , with , with , with sse sse sse sition sition sition t t t the on-axis po the on-axis po the on-axis po sse sse sse de de de d a d a d a , with , with , with centration and t centration and t centration and t sition sition sition t tt the on-axis po the on-axis po the on-axis po de de de , with , with , with centration and t centration and t centration and t sition sition sition de de de , with , with , with centration and t centration and t centration and t ilt. ilt. ilt. sition sition sition de de de , with , with , with centration and t ilt. centration and t ilt. centration and t ilt. de de deilt. ilt. ilt. centration and t centration and t centration and t ilt. ilt. ilt. ilt. ilt. ilt. at 1 mm, an asymmetry of the PSF becomes visible, which is particularly pronounced at Decentration Tilt Decentration Tilt DecentraDectionen tration DecentDecrationen tration Tilt Tilt Tilt Tilt DecDeceennttDecraDecratitiononeenn ttDecDecDecraratitioneoneennn ttt DecDecDecrararatititionononeeennn tttDecraDecraraDectititionononeeennn tttrararatititiononon TiltTilt TiltTilt TiltTiltTilt TiltTiltTilt TiltTiltTilt DecentDecrationen tration Tilt Tilt a 10° tilt. IOL IOL Centere Ce d ntered 0.5 mm0. 5 mm 1.0 mm1. 0 mm 5° 5° 10° 10° IOL IOL IOL Ce Ce IOL nt ntere ere Ce d d IOL IOL ntere Ce d IOL IOL IOL ntere Ce Ce d 0. 0. nt nt 5 m 5 m ere ere m Centered m Ce Ce d d 0. nt nt 5 m ere ere m d d 0. 5 mm0.5 0. 0. 1. 1. 5 m 5 m 0 m 0 m mm m m m m 0. 0. 1. 5 m 5 m 0 mm m m 1.0 1. 0 m mm m1. 1. 0 m 0 m 5° 5°m m1. 1. 0 m 0 m 55° m m 5° 10 5° 10 5° 10 ° ° 10 5° 5° ° 10° 10 10° ° 10 10° ° IOL IOL IOL IOL Ce Ce IOL IOL nt ntere ere Ce Ce d d IOL IOL nt ntere ere Ce Ce d d IOL IOL nt ntere ere Ce Ce d d 0. 0. nt nt 5 m 5 m ere ere m Ce m Ce d d 0. 0. nt nt 5 m 5 m ere ere m m d d 0. 0. 5 m 5 mm m0. 0. 1. 1. 5 m 5 m 0 m 0 m m m m m 0. 0. 1. 1. 5 m 5 m 0 m 0 m m m m m 1. 1. 0 m 0 mm m1. 1. 0 m 0 m 5° 5° m m 1. 1. 0 m 0 m 5° 5° m m 5° 5° 10 5° 5° 10 ° ° 5° 10 5° 10 ° ° 10 10° ° 10 10° ° 10 10° ° Table 1. The point-spread function of the IOLs assessed at the on-axis position, with decentration and tilt. Decentration Tilt 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D IOL Centered 0.5 mm 1.0 mm 5° 10° 3 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 20 D 20 D 20 D 20 D 20 20 20 D D D 20 20 20 D D D 20 20 20 D D D 20 20 20 D D D 20 20 20 D D D 20 20 D D 20 D The coma The coma aberration abes rration ′ RMSs an′ Rd M ast S an igm d at ast ism igm are atism show are n in show Figu n in re F 3i, conf gure 3 irm , conf ing t irm hat ing that The coma The coma The coma abe aberration rration The coma The coma abes s rration The coma The coma The coma ′′ R RM M abe abe S S an an s rration rration The coma The coma ′ R d d M abe abe abe ast ast S an s s rration rration rration ii′′gm gm R R d M M abe abe at at ast S Sism ism an an s s s rration rration i′′′gm R R R d d are M are M M at ast ast S S S ism show show an an an s s i i′gm gm ′ R R d d d are M M at at ast ast ast n in n in S S ism ism show an an iiigm gm gm F F d d are are iiat at at gu gu ast ast n in ism ism ism show show re re iigm gm F 3 3 are are are ,,i conf at conf at gu n in n in ism show show ism show re F F 3 irm irm are are ,i i conf gu gu n in n in n in iin show n show re re g g t t F 3 3 F F irm h h ,,iii conf conf gu at at gu gu n in n in in re re re g t 3 irm 3 irm F 3 F h ,,,ii conf conf conf at gu gu i in nre re g g t t irm 3 irm irm 3 h h,,at at conf conf iiin n ng g g t t t irm irm h h hat at at iin ng g t th hat at The coma The coma The coma The coma abe aberration rration The coma abe abes s rration rration The coma ′′ R RM M abe S S an an s rration sThe coma The coma ′′ R R d d M M abe ast ast S S an s an rration ii′gm gm R d d M abe abe at at ast ast Sism ism an s rration rration ii′gm gm R d are are M at at ast S ism show ism show an s si′′gm R R d are M are M at ast n in n in S S ism show show an an igm F F d d are iiat gu ast gu ast n in n in ism show re re iigm gm 3 F 3 F are ,i,iat conf at conf gu gu n in ism ism show re re F 3 irm 3 irm are are ,i, conf gu conf n in iin show show n re g g t 3 t F irm irm h h ,i conf at gu at n in n in iin n re g g t F t 3 irm F h h ,ii conf at gu gu at inre re g t 3 3 irm h ,, conf at conf ing t irm irm hat iin ng g t th hat at The coma aberrations’ RMS and astigmatism are shown in Figure 3, confirming that The coma aberrations′ RMS and astigmatism are shown in Figure 3, confirming that the decrease the decrease of the decrease the opti of the decrease the opti cal q of u the decrease the opti alcal ity wi q of u the opti a th cal litmi y wi q of sal u the opti ath cal liignment results from ty wi mi qu sal ath cal liignment results from tmi y wi qu sal a th liignment results from tmi y wi sal th ithe combined effect o gnment results from misalithe combined effect o gnment results from the combined effect o the combined effect o f the combined effect o f f f f the decrease the decrease of the decrease the decrease the decrease the opti of the decrease the decrease the opti cal q of of of u the decrease the decrease the opti the opti the opti acal lity wi q of of u the opti the opti ath cal cal cal lity wi mi q q q of of u u u sal a a a the opti the opti th cal l l l cal ii i ignment results from t t ty wi mi y wi y wi q qu u sal a a th th th ll cal cal iiignment results from t tmi mi mi y wi y wi q qsal sal sal u ua a th th li i i lignment results from gnment results from gnment results from ittmi mi y wi y wi sal sal th th iithe combined effect o gnment results from gnment results from mi misal saliithe combined effect o gnment results from gnment results from the combined effect o the combined effect o the combined effect o the combined effect o the combined effect o f the combined effect o f the combined effect o f f f f f ff the decrease the decrease the decrease the decrease of of the opti the opti of of the decrease the opti the opti cal cal q qu u the decrease a al cal l cal iitty wi y wi q q of u u the opti a a th th lliittmi y wi mi y wi of sal sal the opti th th cal iignment results from gnment results from mi mi qsal u sal acal liiignment results from gnment results from ty wi quath litmi y wi sal th ithe combined effect o the combined effect o gnment results from misalithe combined effect o the combined effect o gnment results from the combined effect o ff the combined effect o ff f f the decrease of the optical quality with misalignment results from the combined effect of the decrease of the optical quality with misalignment results from the combined effect of these two a these two a berra these two a tions. An extreme ti berra these two a tions. An extreme ti berra these two a tions. An extreme ti berra lt of ti ons. An extreme ti b erra 10° y ltti of ions. An extreme ti elded h 10l° y t of ielded h i gher 10° y lt of RM ielded h i gher 10 S ° y lt an of iRM d ast elded h i gher 10S ° y ian gmat RM ielded h d ast igher S ism levels an igmat RM d ast igher S ism levels an igmat RM d ast S ism levels an igmat d ast ism levels igmat ism levels these two a these two a these two a berra these two a these two a these two a tions. An extreme ti b berra erra these two a these two a these two a ti tions. An extreme ti ons. An extreme ti b b berra erra erra these two a these two a these two a ti ti tions. An extreme ti ons. An extreme ti ons. An extreme ti b b berra erra erra ltti ti ti of ons. An extreme ti ons. An extreme ti ons. An extreme ti b b b erra erra 1 erra 0° y lltt of ti ti of tiions. An extreme ti ons. An extreme ti ons. An extreme ti elded h 1 10 0° y ll l° y t t t of of of iielded h elded h i gher 1 1 10 0 0° y ° y ° y llltt t of of of ii RM ielded h elded h elded h i i gher 1 gher 1 10 0 0 S ° y ° y ° y lllt tan t of of of RM iiiRM elded h elded h elded h d ast ii i gher gher gher 1 1 10 0 0 S S ° y ° y ° y an an igmat RM RM RM iiid ast elded h elded h d ast elded h iiigher gher gher S S S ism levels an an an iigmat gmat RM RM RM d ast d ast d ast iiigher gher gher S S S ism levels ism levels an an an ii igmat gmat gmat RM RM RM d ast d ast d ast S S S ism levels ism levels ism levels an ian iian gmat gmat gmat d ast d ast d ast ism levels ism levels ism levels iiigmat gmat gmat ism levels ism levels ism levels these two a these two a these two a b berra errati tions. An extreme ti ons. An extreme ti berrations. An extreme ti lltt of of 1 10 0° y ° y lt of iielded h elded h 10° yielded h iigher gher RM RM igher S S an an RM d ast d ast S an iigmat gmat d ast ism levels ism levels igmatism levels these two aberrations. An extreme tilt of 10 yielded higher RMS and astigmatism levels these two aberrations. An extreme tilt of 10° yielded higher RMS and astigmatism levels than a 1 mm decentration. However, a gradual increase in these optical errors with the than a 1 m than a m decent 1 mmrat decent thian a on. Howev rat t1 m han a ion m. e Howev decent 1 m r, a g mr rat decent ad er,iua a on g l . irat rHowev n ad crease iua onl . Howev ienr, icrease n a these opti gre ad r, in a ua these opti g l rica n ad crease l errors ual ica nicrease n l errors wi these opti th the inwi these opti th the cal errors cal errors with the with the ttth h han a an a an a 1 m tt1 m 1 m th h han a an a an a m m m decent decent decent ttt1 m 1 m 1 m h h han a an a an a m m m rat rat rat decent decent decent t1 m 1 m 1 m tth h hiian a ian a an a on on on m m m . . . rat rat Howev rat Howev Howev decent decent decent 1 m t1 m 1 m tth h hiiian a an a an a on on on m m m . . . rat rat rat Howev Howev decent e Howev decent e decent e1 m 1 m 1 m r, r, r,iii a a a on on on g m g m g m . . . r r rat r rat rat Howev Howev Howev e e decent decent ad e ad decent ad r, r, r,iii a a ua a ua on ua on on g g g l l l . . . r r ir irat Howev irat Howev Howev rat e e e n ad ad n n ad r, r, r, crease crease crease ii a a a iua ua ua on on on g g g l l l . . . r r riiiHowev Howev e Howev e e ad ad n ad n nr, r, r, iiicrease crease crease n n n a a a ua ua ua these opti these opti these opti g g g l l l r r r iiie n n ad n e ad ad er, r, iir, crease crease crease in n n a ua a ua ua a these opti these opti these opti g g g l l l r ir iir ca ca ca n n n ad ad ad iiicrease crease crease l errors n n n l errors l errors ua ua ua these opti these opti these opti l l l iica ca ica n n niiicrease crease crease n l errors l errors n n l errors wi wi wi these opti these opti these opti th the th the th the ca ca caiiil errors l errors l errors n n nwi wi wi these opti these opti these opti th the th the th the ca ca cal errors l errors l errors wi wi with the th the th the ca ca cal errors l errors l errors wi wi with the th the th the wi wi with the th the th the than a 1 mm decentration. However, a gradual increase in these optical errors with the than a 1 mm decentration. However, a gradual increase in these optical errors with the nominal power was observed in both types. nominal pow nominal pow enominal pow r was observ e nominal pow nominal pow r was observ ed i enominal pow r was observ nominal pow n both types. e ed i er was observ r was observ n both types. ed i e er was observ r was observ n both types. ed i ed in n both types. both types. ed i ed in n both types. both types. nominal pow nominal pow nominal pow nominal pow nominal pow nominal pow e e enominal pow nominal pow r was observ r was observ r was observ e e enominal pow nominal pow r was observ r was observ r was observ ed i ed i ed i e enominal pow nominal pow r was observ r was observ n n n both types. both types. both types. ed i ed i ed i e er was observ r was observ n n n both types. both types. both types. ed i ed i e er was observ r was observ n n both types. both types. ed i ed in n both types. both types. ed i ed in n both types. both types. nominal power was observed in both types. nominal power was observed in both types. A) A) A) A) A) A) A) A) A) A) A) A) A) A) A) A) A) B) A) A) A) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) A) B) Figure 3. The root-mean-square (RMS) of the primary and secondary coma aberrations (A) and Figure 3. Figure 3. The root-mean-square (RMS) o Figure 3. The root-mean-square (RMS) o Figure 3. The root-mean-square (RMS) o Figure 3. The root-mean-square (RMS) o fThe r the primary and secondary coma oot-mean-square (RMS) o f the primary and secondary coma f the primary and secondary coma f the primary and secondary coma f the aberrations primary and secondary coma aberrations (A) and aberrations ( in- A) and aberrations (in- A) and aberrations (in- A) and (in- A) and in- Figure 3. Figure 3. Figure 3. The root-mean-square (RMS) o Figure 3. Figure 3. Figure 3. The r The root-mean-square (RMS) o oot-mean-square (RMS) o Figure 3. Figure 3. Figure 3. The r The r The root-mean-square (RMS) o oot-mean-square (RMS) o oot-mean-square (RMS) o Figure 3. Figure 3. Figure 3. The r The r The root-mean-square (RMS) o oot-mean-square (RMS) o oot-mean-square (RMS) o fThe r The r the The r primary and secondary coma oot-mean-square (RMS) o oot-mean-square (RMS) o oot-mean-square (RMS) o ff the the primary and secondary coma primary and secondary coma f f f the the the primary and secondary coma primary and secondary coma primary and secondary coma ff f the the the primary and secondary coma primary and secondary coma primary and secondary coma f ff the the the aberrations primary and secondary coma primary and secondary coma primary and secondary coma aberrations aberrations (A) and aberrations aberrations aberrations ((in- A A) and ) and aberrations aberrations aberrations ( ( (in- A A in- A) and ) and ) and aberrations aberrations aberrations (( (in- in- in- A A A) and ) and ) and ( (( in- in- in- A A A) and ) and ) and in- in- in- Figure 3. Figure 3. Figure 3. The r The root-mean-square (RMS) o oot-mean-square (RMS) o The root-mean-square (RMS) o ff the the primary and secondary coma primary and secondary coma f the primary and secondary coma aberrations aberrations aberrations ((A A) and ) and (in- in- A) and in- Figure 3. The root-mean-square (RMS) of the primary and secondary coma aberrations (A) and in- induced astigmatism (B) in the studied IOLs under isolated 10 tilt (black bars) and 1 mm decentration duced astigmatism (B) in the studied IOLs under isolated 10° tilt (black bars) and 1 mm decentration du duced a ced as s du tig tig ced a m ma at ti idu sm sm stig ced a ( ( m B B) ) a in the in the ts du idu sm tig ced a ced a m (B st st a)tu u in the is s sm du du d d tig tig ied ied ced a ced a ( m m B st IOL IOL a a ) in the t ti u is sm s sm d tig tig s sied u u ( ( m m n B n B st der i der i a ) IOL a ) in the in the t u ti id sm sm ied s s s u olate olate ( (B n st B st IOL der i ) ) in the u in the u d d d d s 10° 10° ied ied u solate n st tilt st tilt IOL der i IOL u u (b d (b d d s s 10° ied s ied u u lack lack olate n nder i tilt IOL der i IOL bars) bars) d (b 10° s s s s u u olate olate lack n and 1 n and 1 tilt der i der i bars) d d (b 10° 10° s s m m lack olate olate and 1 tilt m m tilt bars) de de d (b d (b 10° 10° ce ce lack m lack ntration ntration and 1 tilt m tilt bars) bars) de (b (b ce m lack lack and 1 ntration and 1 m de bars) bars) ce m m ntration and 1 and 1 m m de dece ce m m ntration ntration m m de dece centration ntration du duced a ced as du du s du tig tig ced a ced a ced a m ma at tiidu s s du sm s sm tig tig tig ced a ced a ( ( m m m B B a a ) a ) in the t t in the ti ii s s du du sm sm sm tig tig ced a ced a ( ( ( m m B B B st st a a ) ) ) in the t in the t u in the u i is s du sm sm du d d tig tig ied ied ced a ced a ( ( m m B B st st st IOL IOL a a ) ) in the in the t t u u u i is s sm sm d d d tig tig s s ied ied ied u u ( ( m m n n B B st st IOL IOL der i a IOL der i a ) ) in the in the t u t u i ism d d sm s s s ied ied s s u u u olate ( olate (n n B n B st st IOL IOL der i der i der i ) ) in the in the u u d d d d s 10° s 10° ied ied s s u u solate olate olate n n st st tilt tilt der i IOL der i IOL u u d d d (b d d (b 10° 10° s s 10° ied ied s s u u lack olate olate lack n n tilt tilt tilt IOL IOL der i der i bars) bars) d d (b (b (b 10° 10° s ss s u u lack lack olate lack olate n n and 1 and 1 tilt tilt der i der i bars) bars) bars) d d (b (b 10° 10° s s m m lack lack olate olate and 1 and 1 and 1 m tilt tilt m bars) bars) de de d d (b (b 10° 10° ce ce m m m lack lack ntration ntration and 1 and 1 m m tilt tilt m de de bars) bars) de (b (b ce ce ce m m lack lack ntration ntration ntration and 1 and 1 m m de de bars) bars) ce ce m m ntration ntration and 1 and 1 m m de dece ce m m ntration ntration m m de dece centration ntration duced astigmatism (B) in the studied IOLs under isolated 10° tilt (black bars) and 1 mm decentration (gray bars) at a 3 mm aperture. (gray bars) at a (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. 3 mm aperture. 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. 3 mm aperture. (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. Photonics 2021, 8, 309 6 of 9 4. Discussion We demonstrated that the tilt and decentration of the sulcus-fixated supplemen- tary IOLs in polypseudophakic configuration have minimal effect on the retinal image, expressed as MTFa. The capsular fixation lens appears to be less tolerant to tilt, but decentration alone did not substantially impact its imaging quality. The sulcus-fixated supplementary IOLs showed robust performance against tilt and decentration. However, the gradual increase of the optical errors along with the IOL power indicates that susceptibility to misalignment depends on the IOL’s refractive power. Another aspect is the asphericity level, as a higher nominal power yields a greater conic constant. These two factors may explain the smaller impact of IOL misalignment on the low-power supplementary IOLs in the sulcus as compared to the high-power capsular fixation lens. Fujikado and Saika studied the misalignment effect in aspheric IOLs with various spherical aberration corrections (i.e., 0.27 m, 0.17 m, and 0.04 m) [5]. They used a set of holders to simulate a 0.5 mm decentration and a 5 tilt, and subsequently measured the HOAs of IOLs using a Hartmann–Shack device [5]. Although they detected increased coma aberration in all misaligned IOLs, the lens with the highest conic constant demonstrated a higher coma compared to the other designs [5]. The IOL with the lowest spherical aberration correction proved to have a higher tolerance to misalignment [5]. In the current study, the IOLs’ optical performance did not substantially change despite a 1.0 mm decentration, which was also true for the capsular fixation lens. The good image quality retained by the high-power IOL might be due to its aberration-neutral design, which appears to be more robust against misalignment than that which corrects the positive spherical aberration of the cornea, as shown by Fujikado and Saika [5]. In subsequent studies, Tandogan et al. measured the impact of decentration up to 1.0 mm in another aberration-neutral lens using an optical-bench system. They found a slight change of the MTF at 50 lp/mm of 0.02 [14], which is in line with the results of the current study. Lee et al. demonstrated that the MTF of an extended depth-of-focus IOL with a 0.27 m spherical-aberration correction deteriorates under 0.75 mm decentration more than its aberration-neutral counterpart [9]. Eppig et al. performed a ray-tracing analysis and showed that a 5 tilt does not affect aberration-free IOLs [4], which was confirmed by our simulations. Although the performance of the capsular fixation lens presented only a 1% decrease of the MTFa under a 5 tilt, an extreme tilt of 10 may induce increased astigmatism and coma aberrations, thus potentially affecting patients’ visual quality. Fujikado and Saika also reported more coma aberration after tilting than after decen- tering the IOLs [5], which agrees with our findings, as we also obtained a higher RMS value following IOL tilt. In a clinical study by Taketani et al., 40 patients were implanted with spherical capsular fixation IOLs [13]. The level of IOL misalignment was quantified using a Scheimpflug topographer, and HOAs were assessed with a Hartmann–Shack aber- rometer [13]. They identified the mean (standard deviation), a 3.43 (1.55 ) tilt, and a 0.303 (0.168) mm decentration [13]. Taketani et al. reported a significant correlation of coma aberrations with tilt. However, no correlation was found between lens decentration and HOAs [13], which might have resulted from a smaller decentration range in their patients. In subsequent work, Oshika and co-workers applied a similar methodology to measure HOAs under the misalignment of sclera-sutured IOLs [10]. The level of tilt and decentration reported in that study was 4.43 (3.02 ) and 0.279 (0.162) mm, respectively. Thus, they confirmed Taketani’s findings on the significant correlation of tilt with coma aberrations, with a minimal impact of decentration in their cohort [10,13]. Of the 45 eyes assessed by the Oshika group, only one had tilt beyond the range of the current study (i.e., 10 ) [10]. In the Taketani et al. measurements, IOL tilt was found to be below 10 in all patients, with a maximum of approximately 7 and 0.7 mm of decentration [13]. A similar range of tilt in eyes implanted with either spherical or aspheric IOL was found by Baumeister et al. [2]. However, the mean value was lower, which was 2.85 for spherical IOLs and 2.89 for aspheric ones [2]. The mean decentration was 0.19 (0.12) mm for Photonics 2021, 8, 309 7 of 9 the former group and 0.27 (0.16) mm for the latter [2]. IOL misalignment observed by Baumeister et al. did not cause a significant reduction in the optical quality [2], indicating that moderate tilt and decentration have a low potential to affect the eye’s visual function, which is in line with the conclusions of our current study. The extent of IOL misalignment on the retinal image in pseudophakic eyes has been assessed in numerous studies [2–4,6,7,10–13]. Although in those publications, the average tilt typically did not exceed 4 [4], Phillips et al. reported the mean value of 7.8 [11]. Taketani et al., Oshika et al., and Baumeister et al. [2,10,13], discussed in detail in the preceding paragraph, provided evidence for improved tilt outcomes in modern cataract surgery, with mean values well below the level found by Phillips et al. Crnej et al. presented the results of their analysis of misalignment in eyes having plate-haptic IOLs, as well as one- and three-piece AcrySof lenses [3]. They used a Purkinje-image-based system to assess the lens position [3]. In the postoperative examination performed three months after the surgical procedure, tilt ranged from 1.9 (1.4 ) to 2.9 (0.9 ) in the plate-haptic group, 2.6 (4.1 ) to 5.3 (2.4 ) in the three-piece group, and 1.9 (0.3 ) to 2.2 (7.2 ) in the one-piece group, with a significant variability indicated by a high SD in this group [3]. In that study, decentration was within a 0.07 (0.28) mm and 0.34 (0.15) mm range after plate-haptic IOL implantation, from -0.08 (0.57) mm to 0.32 (0.48) mm with three-piece IOLs, and 0.08 (0.30) mm to 0.19 (0.20) mm with one-piece IOLs [3]. Decentration was generally within the 1.0–1.0 range, with only one case falling beyond this margin. The mean levels reported by Crnej et al. [3] were in agreement with the conclusions of Eppig et al. [4], who has also shown the populational variability of IOL decentration, with approximately 0.3 mm on average. The range observed in those publications helped select the lens displacement limits applied in this in vitro model to align our simulation with clinically relevant situations. Given that the secondary implantation of a sulcus-fixated lens is performed less frequently than standard capsular fixation implantation, the available data on the mis- alignment of sulcus-fixated supplementary IOL are limited. One of the first reports on tilt and decentration in sulcus IOLs was presented by Kahraman and Amon [7]. Although they did not present the average level of misalignment in their series, they found <0.5 mm decentration in one of their 12 cases, which did not compromise the visual function [7]. Prager et al. compared the decentration of capsular fixation and sulcus-fixated IOLs in a polypseudophakic configuration [12]. They found that the secondary (sulcus) IOLs yielded a smaller shift from the pupil center as compared to the primary (capsular fixation) IOLs (0.22  0.02 mm vs. 0.29  0.03 mm) in their population of 43 patients [12]. Gerten et al. recorded the largest off-axis deviation of 0.8 mm in one eye [6]. However, the decentration level was below the 0.5 mm threshold in 98.2% of their population [6]. The misalignment observed in that study did not affect the patients’ vision despite the lens being bifocal [6]. The impact of the misalignment of a trifocal sulcus-fixated IOL has recently been studied by our group [8]. We found that decentration of up to 0.6 mm did not affect the far-focus performance of a zero-power trifocal lens in that laboratory investigation [8]. A slight reduction of the MTF was observed at the intermediate and near focus, and the negligible impact of a 5 tilt [8]. That finding agrees with the current study’s results on monofocal technology, as we also observed virtually no change in the MTFa of sulcus-fixated IOLs up to 5 . Vega et al. studied the association of the MTFa with clinically measured visual acu- ity [24]. They set the MTFa reference level = 20, above which the IOL’s optical performance does not compromise visual acuity [24]. Given that the MTFa was above this level in all studied sulcus-fixated lenses, the expected impact of their misalignment on visual acuity is minimal. Although with a combined tilt and decentration, the bag-fixated lens demonstrated an MTFa = 31.6, which is still above the reference level. The increase in coma and astigmatism aberrations may affect the patients’ vision beyond the recognition of high-contrast letters. The presence of shadowing effects, reduced contrast sensitivity, or photic phenomena, typically associated with increased HOAs [26,27], might not be Photonics 2021, 8, 309 8 of 9 detected if only visual acuity is used in the postoperative assessment, as shown by our MTFa analysis. Another limitation of our model is that it may not reflect the variability in the popula- tion. For instance, in this study, the off-the-center position of the pupil was marked by a 0.5 mm decentration. However, studies have shown that besides intersubject variability, pupil dilation may further influence the pupillary center ’s shift [28]. This variability in the natural centration of the pupil may influence how the misaligned IOL affects optical performance, as both a slight improvement or a deterioration, more substantial than ob- served in the current study, might be expected depending on the direction and the extent of each element’s shift. In addition, we did not include corneal HOAs [29] or the dynamic behavior of the tear film [30]. However, further increasing the complexity of our model could introduce additional confounders, which would not necessarily improve the accuracy of our prediction as the complex interactions between each factor would then need to be studied in order to unmask the impact of IOL misalignment on optical quality. Including population data appears to be essential in the study of our results’ repeatability, which warrants further research. 5. Conclusions Ray-tracing simulations showed good imaging quality in a two-lens configuration. Decentration of up to 1 mm and tilt up to 7.5 did not affect the optical performance of low-power sulcus-fixated IOLs in this simulated eye model. Although greater tilt (above 7.5 ) resulted in a more substantial MTFa loss, its impact on visual performance might be limited. One would expect a similar effect in a pseudophakic eye. The precise alignment of a high-power capsular-bag-fixation lens appears to be essential in both standard single-lens implantation and the two-lens configuration. Author Contributions: Conceptualization, G.Ł., G.U.A. and R.K.; methodology, G.Ł.; software, G.Ł.; validation, G.Ł., G.U.A. and R.K.; investigation, G.Ł., G.U.A., W.Y., T.M.Y. and R.K.; data analysis, G.Ł., W.Y. and T.M.Y.; resources, G.U.A. and R.K.; writing—original draft preparation, G.Ł., W.Y. and T.M.Y.; writing—review and editing, G.Ł., G.U.A. and R.K.; supervision, G.Ł., G.U.A. and R.K.; project administration, G.Ł., G.U.A. and R.K.; funding acquisition, G.U.A. and R.K. All authors have read and agreed to the published version of the manuscript. Funding: This study was funded by unrestricted research grants from the Klaus Tschira Stiftung and Rayner Ltd. The sponsors had no role in the design, execution, interpretation, or writing of the study. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The datasets used and analyzed for the present study are available from the corresponding author upon request. Acknowledgments: Donald J. Munro contributed to the review of the manuscript. Conflicts of Interest: G.U.A. reports grants, personal fees, non-financial support, and consulting fees from Johnson & Johnson and Alcon; grants, personal fees, and non-financial support from Carl Zeiss Meditec, Hoya, Kowa, Oculentis/Teleon, Rayner, Santen, Sifi, and Ursapharm; grants and personal fees from Biotech, Oculus, and EyeYon; grants from Acufocus, Anew, Contamac, Glaukos, Physiol, and Rheacell, outside the submitted work. R.K. reports grants, personal fees, and non-financial support from Alcon, Johnson & Johnson, Hoya, Physiol, and Rayner; personal fees and non-financial support from Kowa, Ophtec, Oculentis/Teleon, Santen, and Acufocus, outside the submitted work. G.Ł., W.Y., and T.M.Y. have nothing to disclose. 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Laboratory assessment of the image quality of extended-depth-of-focus intraocular lens models in polychromatic light. J. Cataract. Refract. Surg. 2020, 46, 108–115. [CrossRef] 10. Oshika, T.; Sugita, G.; Miyata, K.; Tokunaga, T.; Samejima, T.; Okamoto, C.; Ishii, Y. Influence of tilt and decentration of scleral-sutured intraocular lens on ocular higher-order wavefront aberration. Br. J. Ophthalmol. 2007, 91, 185–188. [CrossRef] 11. Phillips, P.; Rosskothen, H.D.; Pérez-Emmanuelli, J.; Koester, C.J. Measurement of intraocular lens decentration and tilt in vivo. J. Cataract. Refract. Surg. 1988, 14, 129–135. [CrossRef] 12. Prager, F.; Amon, M.; Wiesinger, J.; Wetzel, B.; Kahraman, G. Capsular bag–fixated and ciliary sulcus-fixated intraocular lens centration after supplementary intraocular lens implantation in the same eye. J. Cataract. Refract. Surg. 2017, 43, 643–647. [CrossRef] 13. Taketani, F.; Matuura, T.; Yukawa, E.; Hara, Y. 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Simulations of Decentration and Tilt of a Supplementary Sulcus-Fixated Intraocular Lens in a Polypseudophakic Combination Using Ray-Tracing Software

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hv photonics Article Simulations of Decentration and Tilt of a Supplementary Sulcus-Fixated Intraocular Lens in a Polypseudophakic Combination Using Ray-Tracing Software Grzegorz Łabuz *, Gerd U. Auffarth , Weijia Yan, Timur M. Yildirim and Ramin Khoramnia The David J Apple Center for Vision Research, Department of Ophthalmology, University Hospital Heidelberg, INF 400, 69120 Heidelberg, Germany; Gerd.Auffarth@med.uni-heidelberg.de (G.U.A.); Weijia.Yan@med.uni-heidelberg.de (W.Y.); Timur.Yildirim@med.uni-heidelberg.de (T.M.Y.); Ramin.Khoramnia@med.uni-heidelberg.de (R.K.) * Correspondence: Grzegorz.Labuz@med.uni-heidelberg.de Abstract: This study aimed to assess image quality after the tilt and decentration of supplementary intraocular lenses (IOLs) in a two-lens configuration. One was designed for sulcus fixation with a nominal power range of 1D–10D and was combined with a capsular fixation 20D IOL. The optical performance of a ray-tracing model was tested under IOL misalignment through the area under the modulation transfer function (MTFa) and wave aberrations. Tilting by 10 resulted in a 4% reduction of the MTFa for a 10D IOL as compared to 9% for the 20D lens. The two models demonstrated good tolerance to a 1 mm decentration; as for the 10D sulcus-fixated lens, the MTFa loss was 2%, and 4% for the capsular fixation lens. Coma and astigmatism increased three- and four-fold, respectively, after a 10 tilt compared to the aberration level induced by the 1 mm decentration. Both analyses showed a trend towards a lower MTF impact and fewer optical errors with decreasing nominal power. In conclusion, when misaligned, low-power sulcus-fixated IOLs might retain their good Citation: Łabuz, G.; Auffarth, G.U.; optical quality. An extreme tilt of 10 has a more detrimental effect on the IOL performance than Yan, W.; Yildirim, T.M.; Khoramnia, R. a 1 mm decentration. The proper alignment of a high-power capsular fixation lens is important in Simulations of Decentration and Tilt achieving a desirable postoperative outcome. of a Supplementary Sulcus-Fixated Intraocular Lens in a Keywords: supplementary IOLs; lens tilt and decentration; MTF; HOAs; polypseudophakia Polypseudophakic Combination Using Ray-Tracing Software. Photonics 2021, 8, 309. https:// doi.org/10.3390/photonics8080309 1. Introduction Received: 29 June 2021 Phacoemulsification with intraocular lens (IOL) implantation into a capsular bag is a Accepted: 29 July 2021 routine procedure for cataract treatment. Although cataract surgery is usually performed Published: 2 August 2021 in patients over 60 years of age, refractive lens exchange, which results in clear crystalline lens removal and IOL implantation, may be offered to younger patients who wish to be Publisher’s Note: MDPI stays neutral spectacle independent [1]. This shift from cataract to refractive surgery reinforces the need with regard to jurisdictional claims in for a continuous improvement of crystalline lens implants. Similarly, an accurate lens published maps and institutional affil- position is considered essential in obtaining satisfactory vision [2–14]. IOL performance is iations. optimal when the lens is placed in an on-axis position, but precise centration is difficult to achieve during surgery [2–14]. While the incidence of severe tilt and dislocation may compromise vision [15], clinical studies have indicated that if the extent of the IOL’s tilt and decentration is low, visual impairment might not be measurable [2]. Most of those Copyright: © 2021 by the authors. studies have, however, been performed on capsule fixation IOLs [2–4,9–11,13–15]. Still, Licensee MDPI, Basel, Switzerland. little is known about the tolerance to the misalignment of sulcus-fixated supplementary This article is an open access article IOLs, which are also offered in refractive surgery. distributed under the terms and Despite significant advances in biometry techniques and IOL power calculation, conditions of the Creative Commons postoperative refractive errors may still occur in pseudophakic eyes [16]. Gayton and Attribution (CC BY) license (https:// Sanders first described a piggyback technique in 1993 [17], which was initially used to creativecommons.org/licenses/by/ correct postoperative hyperopia in microphthalmia. In 1999, Gayton et al. applied the 4.0/). Photonics 2021, 8, 309. https://doi.org/10.3390/photonics8080309 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 309 2 of 9 same approach to correct myopia in normal and post-penetrating keratoplasty eyes [18]. However, the implantation of two IOLs into the capsular bag resulted in postoperative complications such as interlenticular opacification [19]. The use of sulcus-fixated IOLs that have purposely been designed to be implanted into the ciliary sulcus rather than the capsular bag is accepted as safe and efficacious when they are used in polypseudophakia to supplement or correct an iatrogenic refractive error arising from the implantation of the primary, capsular fixation lens [6–8,12]. Recently, the sulcus-fixated IOLs’ application range moved beyond refractive error correction to reversible multifocality (i.e., bifocality or trifocality) in pseudophakic eyes [6,8,20]. Clinical studies have reported the postoperative misalignment of sulcus-fixated IOLs [6,7,12] whose appearance might be exacerbated by their proximity to the pupil, which is often considered a reference. An off-axis position, which may coincide with the poor visual performance of unknown etiology, may prompt an early decision to explant the IOL. However, the impact of IOL misalignment on the optical quality of sulcus-implanted IOLs has rarely been studied. Decision making or explanations could be improved by a better understanding of the effects of misalignment. Though our group has recently shown that a 5 tilt and a 0.6 mm decentration of a trifocal sulcus-fixated IOL minimally impacts the image quality [8], we only assessed a zero-power model in that study, and we recognized the need for further research using a range of powers. Moreover, a close distance between sulcus-fixated and capsular-fixated IOLs poses a challenge in simulating the misalignment of only the former lens in bench-top measurements. This could be resolved by ray-tracing simulations in a numerical model. The purpose of this study was to evaluate the effect of the tilt and decentration of a sulcus-fixated IOL in simulated polypseudophakia. We applied a ray-tracing model and computed the eye’s higher-order aberrations (HOAs) as well as their impact on the modulation transfer function (MTF) to assess the potential effects of sulcus-fixated lens misalignment on patients’ vision. 2. Materials and Methods 2.1. Intraocular Lenses We performed the optical simulations of ten sulcus-fixated supplementary IOLs, Sulcoflex Aspheric, 653L, (Rayner Ltd., Worthing, UK) with the nominal power ranging from 1 D to 10 D (in 1 D increments). The IOLs were designed based on propriety data provided by Rayner Ltd. under a non-disclosure agreement. Each sulcus-fixated lens had an optic size of 6.5 mm and featured a convex anterior and a concave posterior surface. The lens featured a round edge to decrease the likelihood of pigmentary dispersion and secondary glaucoma. To mimic a polypseudophakic condition, we included a 20 D capsular fixation lens, the RayOne Aspheric, RAO600C, (Rayner Ltd., Worthing, UK) with a complete optical design provided by the manufacturer. The capsular fixation lens differed from the sulcus- fixated lens as it had a smaller optic (i.e., 6 mm), was biconvex, and had a sharp optic edge. However, the material characteristics were identical for both models, which were made of hydrophilic acrylic material (26% water content) with the refractive index and an Abbe number of 1.46 and 56, respectively. Both had an aspheric (‘aberration-neutral’) design to minimize each IOL’s spherical aberration and ensure diffraction-limited performance for a parallel beam. 2.2. Ray-Tracing Simulations A model eye was built in OpticStudio (Radiant Zemax LLC, Redmond, WA, USA) in accordance with the data published by Liou and Brennan [21]. According to this model, the front and back corneal surfaces have a 7.77 mm and 6.40 mm radius of curvature, with a 0.18 and 0.60 asphericity, respectively. The central corneal thickness was 0.50 mm. The anterior chamber depth was 3.16 mm, which was the distance between the back surface of the cornea and the pupil. The retina shape was modeled as an asphere with a 8.10 mm radius of curvature and a conic constant of 0.96. The refractive index and the Abbe number Photonics 2021, 8, 309 3 of 9 of the cornea were 1.376 and 55.48, respectively. Although the aqueous humor had a slightly higher dispersion (50.37) than the vitreous (51.30), both shared a refractive index of 1.336. Ocular media dispersion was derived from the Atchison and Smith study [22]. The crystalline lens was replaced with the RAO600C capsular fixation IOL, and a sulcus- fixated supplementary lens was placed anteriorly with a 0.5 mm separation between the two lenses [6]. The sulcus-fixated lens was located 1.59 mm behind the pupil. The optical simulations were performed in polychromatic light, with the spectrum weight corresponding with the CIE photopic luminosity function. To account for the power difference between the sulcus IOLs, the distance between the primary lens and the retina for each model was modified using a minimum root-mean-square (RMS) wavefront focus adjustment. The IOLs were compared according to their image quality metrics, which were evalu- ated utilizing a Huygens modulation transfer function (MTF) at a 3 mm pupil. The MTF was calculated for sagittal and tangential planes, and then averaged. The IOLs’ tolerance to decentration (up to 1 mm, with a 0.25 mm step) in the X (horizontal) and Y (vertical) directions with respect to the optical axis as well as IOL tolerance to tilt along a horizontal axis (up to 10 , with a 2.5 step) were both tested. The pupil was decentered by 0.5 mm off the axis, as proposed by Liou and Brennan [23]. The impact of tilt and decentration on the imaging performance of each supplementary IOL was assessed in a two-lens configuration with the capsular fixation lens. For comparison, the tolerance to misalignment of the RayOne Aspheric with a centrally aligned 10 D sulcus-fixated lens was also simulated. The IOLs were evaluated using a macro that computed and saved the MTF for each condition. MTF results were later analyzed with a dedicated MATLAB program (MathWorks Inc., Natick, MA, USA). Image deterioration was assessed by comparing the area under the MTF function (MTFa) [24], which was calculated based on the following formula: f =50/d MTFa = MTF( f d) (1) f =0 The maximum frequency (f ) used to calculate the MTF area was 50 lp/mm, and the frequency step was d = 1 lp/mm. The Huygen’s point-spread function (PSF) was calculated and compared. Furthermore, the change in monochromatic aberrations (555 nm) was quantified by Zernike coefficients expressed up to the 6th order. The RMS was calculated for all higher-order terms (above the 6th term—Noll’s notation). However, primary and secondary coma aberrations were only reported due to the low level of other higher-order aberrations (HOAs). Astigmatism induced due to IOL misalignment was calculated from the 5th and the 6th terms after power-vector conversion [25]. 3. Results Figure 1 shows the decrease of the MTFa as a function of tilt (A) and decentration (B). Tilt appears not to have an important impact on the optical quality up to 5 for all IOLs, except for the primary lens. Above this level, the 10 D sulcus-fixated lens’ MTFa decreased slightly, with a sharp decrease above 7.5 . However, the lower the nominal power of the sulcus-fixated supplementary IOL, the more robust the optical performance was against tilt. Nevertheless, the maximum reduction of the MTFa for the 10 D sulcus-fixated lens was 4%, as compared to 9% for the 20 D lens. A lens decentration of up to 1 mm had a less deleterious effect on the optical quality than a 10 tilt. The primary lens demonstrated a gradual decrease of the MTFa with decentration. The sulcus-fixated models were hardly affected by their off-axis position, with a 2% maximum MTFa reduction for the 10 D sample and virtually no effect for lower- power lenses. For the capsular fixation lens, decentration by 1 mm caused a mere 4% loss of image quality. Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Photonics 2021, 8, x FOR PEER REVIEW 4 of 10 Photonics 2021, 8, 309 4 of 9 Figure 1. The impact of isolated tilt (A) and decentration (B). The solid black lines refer to 10 sulcus-fixated IOLs, with the nominal power from 1 D (bottom line) to 10 D (top line). The dashed red line indicates the 20 D capsular fixation lens. Figure 1. The impact of isolated tilt (A) and decentration (B). The solid black lines refer to 10 sulcus-fixated IOLs, with the Figure 1. The impact of isolated tilt (A) and decentration (B). The solid black lines refer to 10 sulcus-fixated IOLs, with the nominal power from 1 D (bottom line) to 10 D (top line). The dashed red line indicates the 20 D capsular fixation lens. nominal power from 1 D (bottom line) to 10 D (top line). The dashed red line indicates the 20 D capsular fixation lens. Figure 2 shows representative images of the combined impact of IOL misalignment Figure 2 shows representative images of the combined impact of IOL misalignment on on the MTF val Figure 2 sho uesw . For t s reprh esent e 3 D lens ative im , no ages change of the combin s in opt ed ical impact qual o ity f can be obser IOL misalignmv ent ed. For the MTF values. For the 3 D lens, no changes in optical quality can be observed. For the 6 D, on the MTF values. For the 3 D lens, no changes in optical quality can be observed. For the 6 D, the effects of misalignment could only be noticed at the extreme ends of the sur- the effects of misalignment could only be noticed at the extreme ends of the surface plot. the 6 D, the effects of misalignment could only be noticed at the extreme ends of the sur- face plot. The MTFa of the 9 D IOL was only decreased at a higher tilt and X = Y = 1 mm The MTFa of the 9 D IOL was only decreased at a higher tilt and X = Y = 1 mm decentration. face plot. The MTFa of the 9 D IOL was only decreased at a higher tilt and X = Y = 1 mm decentration. The primary (20 D) lens results confirmed that tilt impacts the optical quality The primary (20 D) lens results confirmed that tilt impacts the optical quality more than decentration. The primary (20 D) lens results confirmed that tilt impacts the optical quality more than decentration, with the largest separation between the five surfaces. decentration, with the largest separation between the five surfaces. more than decentration, with the largest separation between the five surfaces. Figure 2. The effect of decentration and tilt on the optical quality of a 20 D capsular fixation IOL, as well as 3, 6, and 9 D Figure 2. The effect of decentration and tilt on the optical quality of a 20 D capsular fixation IOL, as well as 3, 6, and 9 D sulcus-fixated IOLs in polypseudophakia. The imaging performance was quantified with the area under the modulation sulcus-fixated IOLs in polypseudophakia. The imaging performance was quantified with the area under the modulation transfer function (MTFa). Each figure′s top and bottom surfaces correspond to a condition with zero and 10° tilt, respec- Figure 2. The effect of decentration and tilt on the optical quality of a 20 D capsular fixation IOL, as well as 3, 6, and 9 D tively. For the 20 D IOL, a 2.5° tilt increase resulted in a gradual degradation of the optical quality, creating five distinct transfer function (MTFa). Each figure’s top and bottom surfaces correspond to a condition with zero and 10 tilt, respectively. sulcus-fixated IOLs in polypseudophakia. The imaging performance was quantified with the area under the modulation surfaces of the MTFa change. For the 20 D IOL, a 2.5 tilt increase resulted in a gradual degradation of the optical quality, creating five distinct surfaces of transfer function (MTFa). Each figure′s top and bottom surfaces correspond to a condition with zero and 10° tilt, respec- the MTFa change. tively. For the 20 D IOL, a 2.5° tilt increase resulted in a gradual degradation of the optical quality, creating five distinct surfaces of the MTFa change. Photonics 2021, 8, 309 5 of 9 Photonics Photonics 2021, 8, x FO Photonics 2021 R P , 8, x FO EER 2021 RE R P , 8 VIEW , x FO EER Photonics RE R P VIEW EER 2021 RE , 8 VIEW , x FO R PEER REVIEW 5 of 11 5 of 11 5 of 11 5 of 11 PhotonicsPhotonics 2021, 8, x FO Photonics Photonics Photonics 2021 R P , 8, x FO EER Photonics Photonics Photonics 2021 2021 2021 RE R P , , , 8 8 8VIEW , x FO , x FO , x FO EER Photonics Photonics 2021 2021 2021 RE R P R P R P , , , 8 8 8 VIEW , x FO , x FO , x FO EER EER EER 2021 2021 RE RE RE R P R P R P , , 8 VIEW 8 VIEW VIEW , x FO EER , x FO EER EER RE RE RE R P R P VIEW VIEW VIEW EER EER RE RE VIEW VIEW 5 of 11 5 of 11 5 of 5 of 5 of 11 11 11 5 of 5 of 5 of 11 11 11 5 of 5 of 11 11 Photonics PhotonicsPhotonics Photonics 2021 2021, , 8 8, x FO , x FO 2021 2021 R P R P , , 8 8, x FO , x FO EER EER Photonics RE RE R P R P VIEW VIEW EER EER Photonics 2021 RE RE , 8 VIEW VIEW , x FO 2021 R P , 8, x FO EER RE R P VIEW EER RE VIEW 5 of 5 of 11 11 5 of 5 of 11 11 5 of 11 5 of 11 The PSF analysis presented in Table 1 confirms that the performance of the 3 D sulcus- The PSF The PSF analysis presented in T The PSF analysis presented in T The PSF analysis presented in T The PSF analysis presented in T able 1 c analysis presented in T o able nfirms that t 1 ca o ble nfirms that t 1 c h a o e perform ble nfirms that t 1 ch a oble e perform nfirms that t a 1 c nch e of the oe perform nfirms that t anc h 3 D sul- e of the e perform anch e of the 3 D sul- e perform ance of the 3 D sul- ance of the 3 D sul- 3 D sul- The PSF The PSF The PSF analysis presented in T The PSF The PSF The PSF analysis presented in T analysis presented in T The PSF The PSF The PSF analysis presented in T analysis presented in T analysis presented in T The PSF The PSF analysis presented in T analysis presented in T analysis presented in T able 1 c analysis presented in T analysis presented in T a a oble ble nfirms that t 1 c 1 c a a a o o ble ble ble nf nfirms that t irms that t 1 c 1 c 1 ch a a a o o oble e perform ble ble nf nf nfirms that t irms that t irms that t 1 c 1 c 1 c h h a o a o o e perform e perform ble ble nf nf nfirms that t irms that t irms that t a 1 c 1 c nc h h h e of the o o e perform e perform e perform nf nfirms that t a irms that t an nc c h h h e of the e of the 3 D sul- e perform e perform e perform a a an n nc c ch h e of the e of the e of the 3 D sul- 3 D sul- e perform e perform a a an n nc c ce of the e of the e of the 3 D sul- 3 D sul- 3 D sul- a an nc ce of the 3 D sul- e of the 3 D sul- 3 D sul- 3 D sul- 3 D sul- The PSF The PSF The PSF analysis presented in T analysis presented in T analysis presented in T The PSF a able ble 1 c 1 c analysis presented in T a o oble nf nfirms that t irms that t 1 confirms that t h he perform e perform h ae perform blea a 1 c n nc ce of the e of the onfirms that t ance of the 3 D sul- 3 D sul- h 3 D sul- e performance of the 3 D sul- Photonics 2021, 8, x FOR PEER REVIEW 5 of 10 fixated IOL does not substantially differ under various severities of misalignments. For the cus-fixacus-fix ted IOL does not substa a cus-fix ted IOa cus-fix L does not substa ted IOa L does not substa cus-fix ted I ntia Oa ll L does not substa ted I y di ntia ff Oer u L does not substa lly di ntia nder ffer u lly di vari ntia nder ff ous er u lly di vari seve ntia nder ff ous er u rities of misalign lly di vari seve nder ff ous er u rities of misalign vari seve nder ous rities of misalign vari m seve ents. ous rities of misalign seve ments. rities of misalign ments. ments. ments. cus-fixa cus-fix cus-fix ted IOa a cus-fix cus-fix cus-fix L does not substa ted I ted IO O a a a L does not substa cus-fix cus-fix cus-fix L does not substa ted I ted I ted IO O Oa a a L does not substa L does not substa L does not substa cus-fix cus-fix cus-fix ted I ted I ted I ntia O O Oa a L does not substa a L does not substa L does not substa llted I ted I ted I y di ntia ntia ff O O O er u ll L does not substa L does not substa ll L does not substa y di y di ntia ntia ntia nder ff ffer u er u ll ll lly di y di y di vari ntia ntia ntia n nder der ff ff ff ous er u er u er u ll ll lly di y di y di vari vari seve ntia ntia n n n ntia der der der ff ff ff ous ous er u er u er u rities of misalign ll ll lly di y di vari vari vari y di seve seve n n nder der der ff ff ff ous ous ous er u er u er u rities of misalign rities of misalign vari vari vari seve seve seve n n nder der der ous ous ous rities of misalign rities of misalign rities of misalign vari vari vari seve m seve seve ents. ous ous ous rities of misalign rities of misalign rities of misalign m seve m seve seve ents. ents. rities of misalign rities of misalign rities of misalign m m ments. ents. ents. m m ments. ents. ents. m m ments. ents. ents. cus-fix cus-fixa a cus-fix ted I ted IO Oa L does not substa L does not substa ted IOL does not substa ntia ntiall lly di y di ntia ff ffer u er u lly di n nder der ffer u vari vari nder ous ous vari seve seve ous rities of misalign rities of misalign severities of misalign m ments. ents. ments. 6 D IOL, a slight change in the PSF appearance could be observed at a 10 tilt, but for the For the 6 D IOL, a slight change in the PSF appearance could be observed at a 10° tilt, For the For t 6 D Ih O e L, 6 D I a slO ig For t L, ht c a s h h l ange e ig For t For t 6 D I ht c in t h h h O ange e e h L, 6 D I 6 D I e a s PSF in t lO O ig ap L, L, h ht e a s p a s c PSF e haran llange iig g ap ht htce cou c c pin t h e haran ange ange he ld b ce cou PSF in t in t e o ap h hb e e lserv d b p PSF PSF earan eed ap o ap bce cou at p serv pe e a aran aran 1 ed 0l° t d b ce cou ce cou at ilt a e, 1 o0 b ll° t d b d b serv ilt e e, o ed ob bserv at serv a 1 ed ed 0° t at ati a a lt, 1 10 0° t ° tiilt lt, , For t For t For th h he e e For t For t For t 6 D I 6 D I 6 D I h h h O O O e e e For t For t For t L, L, L, 6 D I 6 D I 6 D I a s a s a s h h h ll O O lO ii e e e ig g g For t L, L, For t For t L, 6 D I 6 D I 6 D I ht ht hta s a s c a s c ch h h h h h l l O O O lange ange ange i i e e i e g g g L, L, L, For t For t 6 D I 6 D I 6 D I ht ht hta s a s a s c c c in t in t in t h h h h h l l lO O O ange ange i i i ange e e g g g L, h L, L, h h ht 6 D I ht ht 6 D I e e e a s a s a s c c c PSF PSF PSF in t in t in t h h hll lO O ange ange ange ii ig g g ap ap ap h L, h L, h ht ht ht e e e a s c a s p c c p p PSF PSF PSF in t in t in t e h e e h haran l aran l aran ange ange ange iig g ap ap ap h h h ht ht e e e ce cou ce cou c ce cou p p c PSF PSF PSF p in t in t in t e e h e haran aran aran ange ange ap ap ap h h he e e ll ld b d b ce cou d b ce cou p p p ce cou PSF PSF PSF in t in t e e earan aran aran e e e o ap o ap o ap h hb e b e b l lld b d b ce cou ce cou ce cou serv d b p serv serv p p PSF PSF e e earan aran aran e e e o o ed ap ap o ed ed b b b l l ld b d b d b ce cou ce cou serv serv ce cou at p at serv p at e e a a a aran aran e e e 1 1 1 o o o ed ed ed 0 0 0 b b b ll l° t ° t ° t d b d b d b serv serv serv ce cou ce cou at at at ii i a a a lt lt lt e e e, 1 1 , , 1 o o o ed ed ed 0 0 0 b b b ll° t ° t ° t d b d b serv serv at serv at ati ii a a a lt lt lt e e 1 1 1 , , , o ed o ed ed 0 0 0 b b ° t ° t ° t serv at serv at ati i i a a a lt lt lt 1 , , , 1 1 ed ed 0 0 0° t ° t ° t at at ii i a a lt lt lt, 1 , , 10 0° t ° tiilt lt, , other conditions, differences from the centered PSF were not apparent. 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Both but for the ot but for the ot but for the ot but for the ot but for the ot but for the ot her condit her condit her condit but for the ot but for the ot her condit her condit her condit but for the ot but for the ot ion ion ions s sher condit her condit , d , d , d but for the ot but for the ot ii iion ion fference ion fference fference s s sher condit her condit , d , d , di iiion ion fference fference fference s s s from the cent from the cent from the cent s sher condit , d , d her condit i iion ion fference fference s s s from the cent from the cent from the cent s s, d , di iion ion fference fference s s ered P ered P ered P from the cent from the cent s s, d , diifference fference S S s S s ered P ered P ered P F F F from the cent from the cent wer wer were e e S S s s S ered P ered P not apparen not apparen not apparen F F F from the cent from the cent wer wer were e S S eered P ered P not apparen not apparen not apparen F F wer wert t t e e S . Both S . Both . Both ered P not apparen not apparen ered P F F wer wert tte e S . Both . Both S . Both not apparen not apparen F F wer wer t te e . Both . Both not apparen not apparen t t. Both . Both t t. Both . Both the 20 D IOLs proved to be minimally affected by a 0.5 mm decentration, but at 1 mm, an The PSF analysis presented in Table 1 confirms that the performance of the 3 D sul- the 9 Dthe 9 D and the 20 D and the 20 D IOLs proved to be IOLs proved to be minima mini lly af m fe act lly ed b affe yct a ed b 0.5 m y a m0. decent 5 mm decent ration, b rau titon, b ut the 9 D the 9 D and and the 20 D the 20 D the 9 D IOLs IOLs the 9 D and the 9 D the 20 D proved to be proved to be and the 9 D and the 9 D the 20 D the 20 D IOLs and andmini mini the 20 D the 20 D proved to be IOLs IOLs m ma all ll proved to be proved to be y y IOLs IOLs af aff fe emini ct ct proved to be proved to be ed b ed b my y a mini mini ll a a y 0. 0. af m 5 5 m f m m e a a mini mini ct ll ll m m y y ed b decent decent af af m m ffe y e a a ct ct ll ll a ed b y ed b y 0. ra ra af af 5t t m f f i iy e y on, b e on, b ct ct a m a ed b ed b 0. 0. decent 5 u u 5 m m t ty y m m a a 0. decent 0. ra decent 5 5 t m i m on, b m mra decent ra decent u ttt ii on, b on, b ra ra u u t ttt ii on, b on, bu ut t the 9 D the 9 Dthe 9 D and the 9 D and the 9 D the 20 D the 20 D the 9 D the 9 D and and and the 20 D the 20 D the 20 D IOLs IOLs and and the 9 D the 9 D the 20 D the 20 D proved to be proved to be IOLs IOLs IOLs the 9 D and the 9 D and the 20 D the 20 D proved to be proved to be proved to be IOLs IOLs and andmini mini the 20 D the 20 D proved to be proved to be IOLs IOLs m ma a mini mini mini ll ll proved to be proved to be y IOLs y IOLs af af m m m ffe e a a a mini mini ct ct ll ll ll proved to be proved to be y y ed b y ed b af af af m m f ffy e e a a y e mini mini ct ct ll ll ct a a y y ed b ed b ed b 0. 0. af af 5 m 5 m f m f m e e y y a y a mini mini ct ct ll ll m a a m a y y ed b ed b 0. 0. decent 0. decent af af 5 5 m m 5 m m f f m y y e e a act ct ll ll a a m m m y y ed b ed b 0. 0. decent decent ra decent ra af af 5 5tt m m f f iie y y e on, b on, b ct ct m m a a ed b ed b 0. 0. decent decent ra ra ra u 5 5 u t tt m m t i i tiy y on, b on, b on, b m a m a 0. 0. ra decent ra decent u u 5 5 u t t m m t t i iton, b on, b m m decent decent ra ra u ut tt ti i on, b on, b ra ra u u t tt t ii on, b on, bu ut t asymmetry of the PSF becomes visible, which is particularly pronounced at a 10 tilt. cus-fixated IOL does not substantially differ under various severities of misalignments. at 1 mm, ata 1 mm, n asymmetry of at 1 mm, an asymmetry of an asymmetry of the at 1 mm, PSFthe beco a PSF n mes vis asymmetry of the beco PSF mes vis ibl beco e, whi mes vis ibl the ch is pa e, PSF whi ibl beco c rticu e, h is pa whi lmes vis arcly pronou rticu h is pa lia bl rrticu ly pronou e, whi nced lar cly pronou h is pa at nced rticu atnced larly pronou at nced at at 1 mm, at 1 mm, an asymmetry of a a at t t 1 mm, 1 mm, 1 mm, an asymmetry of a a at t t 1 mm, 1 mm, 1 mm, a a an n n asymmetry of asymmetry of asymmetry of the a at t 1 mm, a PSF 1 mm, a an n n asymmetry of asymmetry of asymmetry of the beco PSF a an n mes vis asymmetry of the the the asymmetry of beco PSF PSF PSF mes vis ibl the the the beco beco beco e, PSF whi PSF PSF mes vis mes vis mes vis ibl the the beco beco c beco e, h is pa whi PSF PSF mes vis mes vis mes vis i i ibl bl bl c beco beco rticu e, e, e, h is pa whi whi whi l mes vis mes vis ii ia bl bl bl r c c crticu ly pronou h is pa e, h is pa h is pa e, e, whi whi whi li a ibl bl r c c c rticu rticu rticu ly pronou h is pa h is pa h is pa e, e, whi whi nced l l la a ar r rc c rticu rticu rticu ly pronou ly pronou ly pronou h is pa h is pa atnced ll la a ar r rrticu ly pronou ly pronou rticu ly pronou atnced nced nced lla ar rly pronou ly pronou a a at t tnced nced nced a a at t t nced nced a at t a att 1 mm, 1 mm, a att 1 mm, a 1 mm, an n asymmetry of asymmetry of a an n asymmetry of asymmetry of at 1 mm, the the at 1 mm, PSF PSF an asymmetry of the the beco beco PSF a PSF n mes vis mes vis asymmetry of beco becomes vis mes vis iibl bl the e, e, whi PSF whi iibl bl the c beco ch is pa e, h is pa e, whi PSF whi mes vis c beco c rticu rticu h is pa h is pa lmes vis li a a bl r rrticu ly pronou rticu ly pronou e, whi llia a bl r r cly pronou ly pronou e, h is pa whi nced nced crticu h is pa a attnced nced larrticu ly pronou a att larly pronou nced atnced at For the 6 D IOL, a slight change in the PSF appearance could be observed at a 10° tilt, a 10° tilt a 10 . ° tilt a 10 . ° tilt a 10 . ° tilt a 10 . ° tilt. a 10° tilt a 10 a 10 . ° ° ttiilt a 10 a 10 a 10 lt.. ° ° ° t t ti i ilt lt lt a 10 a 10 a 10 ... ° ° ° t t tii ilt lt lt a 10 a 10 ... ° ° t tiilt lt.. a 10 a 10° ° ttiilt lt a 10 .. ° tilt. a 10° tilt. Table 1. The point-spread function of the IOLs assessed at the on-axis position, with decentration but for the other conditions, differences from the centered PSF were not apparent. Both and tilt. Table 1. The point-spread function of the IOLs assessed at the on-axis position, with decentration and tilt. Table 1. Table 1. The po th int-spread fu e 9 D The p and oTable 1. int-spread fu tnction of he 2 Table 1. The p 0 Dnction of IOLs the IOLs a oint-spread fu The p pr the IOLs a o ov int-spread fu sse ed t sse nction of od a bsse et m the on-axis po sse nction of i the IOLs a nim d ata the on-axis po lly the IOLs a af sse f sition ect sse ed b d a , with sse sition ty the on-axis po sse a de 0. d a , with centration and t 5 m t the on-axis po m de decent centration and t sitionra , with ilt. tsition ion, b de , with centration and t u ilt. t decentration and t ilt. ilt. Table 1. Table 1. Table 1. Table 1. Table 1. Table 1. The p The p The po o oint-spread fu Table 1. Table 1. Table 1. int-spread fu int-spread fu The p The p The po o oTable 1. int-spread fu int-spread fu Table 1. Table 1. int-spread fu The p The p The p nction of nction of nction of o o oint-spread fu int-spread fu int-spread fu Table 1. Table 1. Table 1. The p The p The p nction of nction of nction of the IOLs a the IOLs a the IOLs a o o oint-spread fu int-spread fu int-spread fu The p The p The p nction of nction of nction of the IOLs a the IOLs a the IOLs a o o oint-spread fu int-spread fu int-spread fu sse sse ssesse sse sse nction of nction of nction of the IOLs a the IOLs a the IOLs a d a d a d a sse sse sse t t t the on-axis po the on-axis po the on-axis po sse sse sse nction of nction of nction of the IOLs a the IOLs a the IOLs a d a d a d a sse sse sse t tt the on-axis po the on-axis po the on-axis po sse sse sse the IOLs a the IOLs a the IOLs a d a d a d a sse sse sse sition sition sition t t t the on-axis po the on-axis po the on-axis po sse sse ssed a d a d a , with , with , with sse sse sse sition sition sition t t t the on-axis po the on-axis po the on-axis po sse sse sse de de de d a d a d a , with , with , with centration and t centration and t centration and t sition sition sition t tt the on-axis po the on-axis po the on-axis po de de de , with , with , with centration and t centration and t centration and t sition sition sition de de de , with , with , with centration and t centration and t centration and t ilt. ilt. ilt. sition sition sition de de de , with , with , with centration and t ilt. centration and t ilt. centration and t ilt. de de deilt. ilt. ilt. centration and t centration and t centration and t ilt. ilt. ilt. ilt. ilt. ilt. at 1 mm, an asymmetry of the PSF becomes visible, which is particularly pronounced at Decentration Tilt Decentration Tilt DecentraDectionen tration DecentDecrationen tration Tilt Tilt Tilt Tilt DecDeceennttDecraDecratitiononeenn ttDecDecDecraratitioneoneennn ttt DecDecDecrararatititionononeeennn tttDecraDecraraDectititionononeeennn tttrararatititiononon TiltTilt TiltTilt TiltTiltTilt TiltTiltTilt TiltTiltTilt DecentDecrationen tration Tilt Tilt a 10° tilt. IOL IOL Centere Ce d ntered 0.5 mm0. 5 mm 1.0 mm1. 0 mm 5° 5° 10° 10° IOL IOL IOL Ce Ce IOL nt ntere ere Ce d d IOL IOL ntere Ce d IOL IOL IOL ntere Ce Ce d 0. 0. nt nt 5 m 5 m ere ere m Centered m Ce Ce d d 0. nt nt 5 m ere ere m d d 0. 5 mm0.5 0. 0. 1. 1. 5 m 5 m 0 m 0 m mm m m m m 0. 0. 1. 5 m 5 m 0 mm m m 1.0 1. 0 m mm m1. 1. 0 m 0 m 5° 5°m m1. 1. 0 m 0 m 55° m m 5° 10 5° 10 5° 10 ° ° 10 5° 5° ° 10° 10 10° ° 10 10° ° IOL IOL IOL IOL Ce Ce IOL IOL nt ntere ere Ce Ce d d IOL IOL nt ntere ere Ce Ce d d IOL IOL nt ntere ere Ce Ce d d 0. 0. nt nt 5 m 5 m ere ere m Ce m Ce d d 0. 0. nt nt 5 m 5 m ere ere m m d d 0. 0. 5 m 5 mm m0. 0. 1. 1. 5 m 5 m 0 m 0 m m m m m 0. 0. 1. 1. 5 m 5 m 0 m 0 m m m m m 1. 1. 0 m 0 mm m1. 1. 0 m 0 m 5° 5° m m 1. 1. 0 m 0 m 5° 5° m m 5° 5° 10 5° 5° 10 ° ° 5° 10 5° 10 ° ° 10 10° ° 10 10° ° 10 10° ° Table 1. The point-spread function of the IOLs assessed at the on-axis position, with decentration and tilt. Decentration Tilt 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D 3 D IOL Centered 0.5 mm 1.0 mm 5° 10° 3 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 6 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 9 D 20 D 20 D 20 D 20 D 20 20 20 D D D 20 20 20 D D D 20 20 20 D D D 20 20 20 D D D 20 20 20 D D D 20 20 D D 20 D The coma The coma aberration abes rration ′ RMSs an′ Rd M ast S an igm d at ast ism igm are atism show are n in show Figu n in re F 3i, conf gure 3 irm , conf ing t irm hat ing that The coma The coma The coma abe aberration rration The coma The coma abes s rration The coma The coma The coma ′′ R RM M abe abe S S an an s rration rration The coma The coma ′ R d d M abe abe abe ast ast S an s s rration rration rration ii′′gm gm R R d M M abe abe at at ast S Sism ism an an s s s rration rration i′′′gm R R R d d are M are M M at ast ast S S S ism show show an an an s s i i′gm gm ′ R R d d d are M M at at ast ast ast n in n in S S ism ism show an an iiigm gm gm F F d d are are iiat at at gu gu ast ast n in ism ism ism show show re re iigm gm F 3 3 are are are ,,i conf at conf at gu n in n in ism show show ism show re F F 3 irm irm are are ,i i conf gu gu n in n in n in iin show n show re re g g t t F 3 3 F F irm h h ,,iii conf conf gu at at gu gu n in n in in re re re g t 3 irm 3 irm F 3 F h ,,,ii conf conf conf at gu gu i in nre re g g t t irm 3 irm irm 3 h h,,at at conf conf iiin n ng g g t t t irm irm h h hat at at iin ng g t th hat at The coma The coma The coma The coma abe aberration rration The coma abe abes s rration rration The coma ′′ R RM M abe S S an an s rration sThe coma The coma ′′ R R d d M M abe ast ast S S an s an rration ii′gm gm R d d M abe abe at at ast ast Sism ism an s rration rration ii′gm gm R d are are M at at ast S ism show ism show an s si′′gm R R d are M are M at ast n in n in S S ism show show an an igm F F d d are iiat gu ast gu ast n in n in ism show re re iigm gm 3 F 3 F are ,i,iat conf at conf gu gu n in ism ism show re re F 3 irm 3 irm are are ,i, conf gu conf n in iin show show n re g g t 3 t F irm irm h h ,i conf at gu at n in n in iin n re g g t F t 3 irm F h h ,ii conf at gu gu at inre re g t 3 3 irm h ,, conf at conf ing t irm irm hat iin ng g t th hat at The coma aberrations’ RMS and astigmatism are shown in Figure 3, confirming that The coma aberrations′ RMS and astigmatism are shown in Figure 3, confirming that the decrease the decrease of the decrease the opti of the decrease the opti cal q of u the decrease the opti alcal ity wi q of u the opti a th cal litmi y wi q of sal u the opti ath cal liignment results from ty wi mi qu sal ath cal liignment results from tmi y wi qu sal a th liignment results from tmi y wi sal th ithe combined effect o gnment results from misalithe combined effect o gnment results from the combined effect o the combined effect o f the combined effect o f f f f the decrease the decrease of the decrease the decrease the decrease the opti of the decrease the decrease the opti cal q of of of u the decrease the decrease the opti the opti the opti acal lity wi q of of u the opti the opti ath cal cal cal lity wi mi q q q of of u u u sal a a a the opti the opti th cal l l l cal ii i ignment results from t t ty wi mi y wi y wi q qu u sal a a th th th ll cal cal iiignment results from t tmi mi mi y wi y wi q qsal sal sal u ua a th th li i i lignment results from gnment results from gnment results from ittmi mi y wi y wi sal sal th th iithe combined effect o gnment results from gnment results from mi misal saliithe combined effect o gnment results from gnment results from the combined effect o the combined effect o the combined effect o the combined effect o the combined effect o f the combined effect o f the combined effect o f f f f f ff the decrease the decrease the decrease the decrease of of the opti the opti of of the decrease the opti the opti cal cal q qu u the decrease a al cal l cal iitty wi y wi q q of u u the opti a a th th lliittmi y wi mi y wi of sal sal the opti th th cal iignment results from gnment results from mi mi qsal u sal acal liiignment results from gnment results from ty wi quath litmi y wi sal th ithe combined effect o the combined effect o gnment results from misalithe combined effect o the combined effect o gnment results from the combined effect o ff the combined effect o ff f f the decrease of the optical quality with misalignment results from the combined effect of the decrease of the optical quality with misalignment results from the combined effect of these two a these two a berra these two a tions. An extreme ti berra these two a tions. An extreme ti berra these two a tions. An extreme ti berra lt of ti ons. An extreme ti b erra 10° y ltti of ions. An extreme ti elded h 10l° y t of ielded h i gher 10° y lt of RM ielded h i gher 10 S ° y lt an of iRM d ast elded h i gher 10S ° y ian gmat RM ielded h d ast igher S ism levels an igmat RM d ast igher S ism levels an igmat RM d ast S ism levels an igmat d ast ism levels igmat ism levels these two a these two a these two a berra these two a these two a these two a tions. An extreme ti b berra erra these two a these two a these two a ti tions. An extreme ti ons. An extreme ti b b berra erra erra these two a these two a these two a ti ti tions. An extreme ti ons. An extreme ti ons. An extreme ti b b berra erra erra ltti ti ti of ons. An extreme ti ons. An extreme ti ons. An extreme ti b b b erra erra 1 erra 0° y lltt of ti ti of tiions. An extreme ti ons. An extreme ti ons. An extreme ti elded h 1 10 0° y ll l° y t t t of of of iielded h elded h i gher 1 1 10 0 0° y ° y ° y llltt t of of of ii RM ielded h elded h elded h i i gher 1 gher 1 10 0 0 S ° y ° y ° y lllt tan t of of of RM iiiRM elded h elded h elded h d ast ii i gher gher gher 1 1 10 0 0 S S ° y ° y ° y an an igmat RM RM RM iiid ast elded h elded h d ast elded h iiigher gher gher S S S ism levels an an an iigmat gmat RM RM RM d ast d ast d ast iiigher gher gher S S S ism levels ism levels an an an ii igmat gmat gmat RM RM RM d ast d ast d ast S S S ism levels ism levels ism levels an ian iian gmat gmat gmat d ast d ast d ast ism levels ism levels ism levels iiigmat gmat gmat ism levels ism levels ism levels these two a these two a these two a b berra errati tions. An extreme ti ons. An extreme ti berrations. An extreme ti lltt of of 1 10 0° y ° y lt of iielded h elded h 10° yielded h iigher gher RM RM igher S S an an RM d ast d ast S an iigmat gmat d ast ism levels ism levels igmatism levels these two aberrations. An extreme tilt of 10 yielded higher RMS and astigmatism levels these two aberrations. An extreme tilt of 10° yielded higher RMS and astigmatism levels than a 1 mm decentration. However, a gradual increase in these optical errors with the than a 1 m than a m decent 1 mmrat decent thian a on. Howev rat t1 m han a ion m. e Howev decent 1 m r, a g mr rat decent ad er,iua a on g l . irat rHowev n ad crease iua onl . Howev ienr, icrease n a these opti gre ad r, in a ua these opti g l rica n ad crease l errors ual ica nicrease n l errors wi these opti th the inwi these opti th the cal errors cal errors with the with the ttth h han a an a an a 1 m tt1 m 1 m th h han a an a an a m m m decent decent decent ttt1 m 1 m 1 m h h han a an a an a m m m rat rat rat decent decent decent t1 m 1 m 1 m tth h hiian a ian a an a on on on m m m . . . rat rat Howev rat Howev Howev decent decent decent 1 m t1 m 1 m tth h hiiian a an a an a on on on m m m . . . rat rat rat Howev Howev decent e Howev decent e decent e1 m 1 m 1 m r, r, r,iii a a a on on on g m g m g m . . . r r rat r rat rat Howev Howev Howev e e decent decent ad e ad decent ad r, r, r,iii a a ua a ua on ua on on g g g l l l . . . r r ir irat Howev irat Howev Howev rat e e e n ad ad n n ad r, r, r, crease crease crease ii a a a iua ua ua on on on g g g l l l . . . r r riiiHowev Howev e Howev e e ad ad n ad n nr, r, r, iiicrease crease crease n n n a a a ua ua ua these opti these opti these opti g g g l l l r r r iiie n n ad n e ad ad er, r, iir, crease crease crease in n n a ua a ua ua a these opti these opti these opti g g g l l l r ir iir ca ca ca n n n ad ad ad iiicrease crease crease l errors n n n l errors l errors ua ua ua these opti these opti these opti l l l iica ca ica n n niiicrease crease crease n l errors l errors n n l errors wi wi wi these opti these opti these opti th the th the th the ca ca caiiil errors l errors l errors n n nwi wi wi these opti these opti these opti th the th the th the ca ca cal errors l errors l errors wi wi with the th the th the ca ca cal errors l errors l errors wi wi with the th the th the wi wi with the th the th the than a 1 mm decentration. However, a gradual increase in these optical errors with the than a 1 mm decentration. However, a gradual increase in these optical errors with the nominal power was observed in both types. nominal pow nominal pow enominal pow r was observ e nominal pow nominal pow r was observ ed i enominal pow r was observ nominal pow n both types. e ed i er was observ r was observ n both types. ed i e er was observ r was observ n both types. ed i ed in n both types. both types. ed i ed in n both types. both types. nominal pow nominal pow nominal pow nominal pow nominal pow nominal pow e e enominal pow nominal pow r was observ r was observ r was observ e e enominal pow nominal pow r was observ r was observ r was observ ed i ed i ed i e enominal pow nominal pow r was observ r was observ n n n both types. both types. both types. ed i ed i ed i e er was observ r was observ n n n both types. both types. both types. ed i ed i e er was observ r was observ n n both types. both types. ed i ed in n both types. both types. ed i ed in n both types. both types. nominal power was observed in both types. nominal power was observed in both types. A) A) A) A) A) A) A) A) A) A) A) A) A) A) A) A) A) B) A) A) A) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) B) A) B) Figure 3. The root-mean-square (RMS) of the primary and secondary coma aberrations (A) and Figure 3. Figure 3. The root-mean-square (RMS) o Figure 3. The root-mean-square (RMS) o Figure 3. The root-mean-square (RMS) o Figure 3. The root-mean-square (RMS) o fThe r the primary and secondary coma oot-mean-square (RMS) o f the primary and secondary coma f the primary and secondary coma f the primary and secondary coma f the aberrations primary and secondary coma aberrations (A) and aberrations ( in- A) and aberrations (in- A) and aberrations (in- A) and (in- A) and in- Figure 3. Figure 3. Figure 3. The root-mean-square (RMS) o Figure 3. Figure 3. Figure 3. The r The root-mean-square (RMS) o oot-mean-square (RMS) o Figure 3. Figure 3. Figure 3. The r The r The root-mean-square (RMS) o oot-mean-square (RMS) o oot-mean-square (RMS) o Figure 3. Figure 3. Figure 3. The r The r The root-mean-square (RMS) o oot-mean-square (RMS) o oot-mean-square (RMS) o fThe r The r the The r primary and secondary coma oot-mean-square (RMS) o oot-mean-square (RMS) o oot-mean-square (RMS) o ff the the primary and secondary coma primary and secondary coma f f f the the the primary and secondary coma primary and secondary coma primary and secondary coma ff f the the the primary and secondary coma primary and secondary coma primary and secondary coma f ff the the the aberrations primary and secondary coma primary and secondary coma primary and secondary coma aberrations aberrations (A) and aberrations aberrations aberrations ((in- A A) and ) and aberrations aberrations aberrations ( ( (in- A A in- A) and ) and ) and aberrations aberrations aberrations (( (in- in- in- A A A) and ) and ) and ( (( in- in- in- A A A) and ) and ) and in- in- in- Figure 3. Figure 3. Figure 3. The r The root-mean-square (RMS) o oot-mean-square (RMS) o The root-mean-square (RMS) o ff the the primary and secondary coma primary and secondary coma f the primary and secondary coma aberrations aberrations aberrations ((A A) and ) and (in- in- A) and in- Figure 3. The root-mean-square (RMS) of the primary and secondary coma aberrations (A) and in- induced astigmatism (B) in the studied IOLs under isolated 10 tilt (black bars) and 1 mm decentration duced astigmatism (B) in the studied IOLs under isolated 10° tilt (black bars) and 1 mm decentration du duced a ced as s du tig tig ced a m ma at ti idu sm sm stig ced a ( ( m B B) ) a in the in the ts du idu sm tig ced a ced a m (B st st a)tu u in the is s sm du du d d tig tig ied ied ced a ced a ( m m B st IOL IOL a a ) in the t ti u is sm s sm d tig tig s sied u u ( ( m m n B n B st der i der i a ) IOL a ) in the in the t u ti id sm sm ied s s s u olate olate ( (B n st B st IOL der i ) ) in the u in the u d d d d s 10° 10° ied ied u solate n st tilt st tilt IOL der i IOL u u (b d (b d d s s 10° ied s ied u u lack lack olate n nder i tilt IOL der i IOL bars) bars) d (b 10° s s s s u u olate olate lack n and 1 n and 1 tilt der i der i bars) d d (b 10° 10° s s m m lack olate olate and 1 tilt m m tilt bars) de de d (b d (b 10° 10° ce ce lack m lack ntration ntration and 1 tilt m tilt bars) bars) de (b (b ce m lack lack and 1 ntration and 1 m de bars) bars) ce m m ntration and 1 and 1 m m de dece ce m m ntration ntration m m de dece centration ntration du duced a ced as du du s du tig tig ced a ced a ced a m ma at tiidu s s du sm s sm tig tig tig ced a ced a ( ( m m m B B a a ) a ) in the t t in the ti ii s s du du sm sm sm tig tig ced a ced a ( ( ( m m B B B st st a a ) ) ) in the t in the t u in the u i is s du sm sm du d d tig tig ied ied ced a ced a ( ( m m B B st st st IOL IOL a a ) ) in the in the t t u u u i is s sm sm d d d tig tig s s ied ied ied u u ( ( m m n n B B st st IOL IOL der i a IOL der i a ) ) in the in the t u t u i ism d d sm s s s ied ied s s u u u olate ( olate (n n B n B st st IOL IOL der i der i der i ) ) in the in the u u d d d d s 10° s 10° ied ied s s u u solate olate olate n n st st tilt tilt der i IOL der i IOL u u d d d (b d d (b 10° 10° s s 10° ied ied s s u u lack olate olate lack n n tilt tilt tilt IOL IOL der i der i bars) bars) d d (b (b (b 10° 10° s ss s u u lack lack olate lack olate n n and 1 and 1 tilt tilt der i der i bars) bars) bars) d d (b (b 10° 10° s s m m lack lack olate olate and 1 and 1 and 1 m tilt tilt m bars) bars) de de d d (b (b 10° 10° ce ce m m m lack lack ntration ntration and 1 and 1 m m tilt tilt m de de bars) bars) de (b (b ce ce ce m m lack lack ntration ntration ntration and 1 and 1 m m de de bars) bars) ce ce m m ntration ntration and 1 and 1 m m de dece ce m m ntration ntration m m de dece centration ntration duced astigmatism (B) in the studied IOLs under isolated 10° tilt (black bars) and 1 mm decentration (gray bars) at a 3 mm aperture. (gray bars) at a (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. 3 mm aperture. 3 mm aperture. 3 mm aperture. (gray bars) at a (gray bars) at a (gray bars) at a 3 mm aperture. 3 mm aperture. 3 mm aperture. (gray bars) at a 3 mm aperture. (gray bars) at a 3 mm aperture. Photonics 2021, 8, 309 6 of 9 4. Discussion We demonstrated that the tilt and decentration of the sulcus-fixated supplemen- tary IOLs in polypseudophakic configuration have minimal effect on the retinal image, expressed as MTFa. The capsular fixation lens appears to be less tolerant to tilt, but decentration alone did not substantially impact its imaging quality. The sulcus-fixated supplementary IOLs showed robust performance against tilt and decentration. However, the gradual increase of the optical errors along with the IOL power indicates that susceptibility to misalignment depends on the IOL’s refractive power. Another aspect is the asphericity level, as a higher nominal power yields a greater conic constant. These two factors may explain the smaller impact of IOL misalignment on the low-power supplementary IOLs in the sulcus as compared to the high-power capsular fixation lens. Fujikado and Saika studied the misalignment effect in aspheric IOLs with various spherical aberration corrections (i.e., 0.27 m, 0.17 m, and 0.04 m) [5]. They used a set of holders to simulate a 0.5 mm decentration and a 5 tilt, and subsequently measured the HOAs of IOLs using a Hartmann–Shack device [5]. Although they detected increased coma aberration in all misaligned IOLs, the lens with the highest conic constant demonstrated a higher coma compared to the other designs [5]. The IOL with the lowest spherical aberration correction proved to have a higher tolerance to misalignment [5]. In the current study, the IOLs’ optical performance did not substantially change despite a 1.0 mm decentration, which was also true for the capsular fixation lens. The good image quality retained by the high-power IOL might be due to its aberration-neutral design, which appears to be more robust against misalignment than that which corrects the positive spherical aberration of the cornea, as shown by Fujikado and Saika [5]. In subsequent studies, Tandogan et al. measured the impact of decentration up to 1.0 mm in another aberration-neutral lens using an optical-bench system. They found a slight change of the MTF at 50 lp/mm of 0.02 [14], which is in line with the results of the current study. Lee et al. demonstrated that the MTF of an extended depth-of-focus IOL with a 0.27 m spherical-aberration correction deteriorates under 0.75 mm decentration more than its aberration-neutral counterpart [9]. Eppig et al. performed a ray-tracing analysis and showed that a 5 tilt does not affect aberration-free IOLs [4], which was confirmed by our simulations. Although the performance of the capsular fixation lens presented only a 1% decrease of the MTFa under a 5 tilt, an extreme tilt of 10 may induce increased astigmatism and coma aberrations, thus potentially affecting patients’ visual quality. Fujikado and Saika also reported more coma aberration after tilting than after decen- tering the IOLs [5], which agrees with our findings, as we also obtained a higher RMS value following IOL tilt. In a clinical study by Taketani et al., 40 patients were implanted with spherical capsular fixation IOLs [13]. The level of IOL misalignment was quantified using a Scheimpflug topographer, and HOAs were assessed with a Hartmann–Shack aber- rometer [13]. They identified the mean (standard deviation), a 3.43 (1.55 ) tilt, and a 0.303 (0.168) mm decentration [13]. Taketani et al. reported a significant correlation of coma aberrations with tilt. However, no correlation was found between lens decentration and HOAs [13], which might have resulted from a smaller decentration range in their patients. In subsequent work, Oshika and co-workers applied a similar methodology to measure HOAs under the misalignment of sclera-sutured IOLs [10]. The level of tilt and decentration reported in that study was 4.43 (3.02 ) and 0.279 (0.162) mm, respectively. Thus, they confirmed Taketani’s findings on the significant correlation of tilt with coma aberrations, with a minimal impact of decentration in their cohort [10,13]. Of the 45 eyes assessed by the Oshika group, only one had tilt beyond the range of the current study (i.e., 10 ) [10]. In the Taketani et al. measurements, IOL tilt was found to be below 10 in all patients, with a maximum of approximately 7 and 0.7 mm of decentration [13]. A similar range of tilt in eyes implanted with either spherical or aspheric IOL was found by Baumeister et al. [2]. However, the mean value was lower, which was 2.85 for spherical IOLs and 2.89 for aspheric ones [2]. The mean decentration was 0.19 (0.12) mm for Photonics 2021, 8, 309 7 of 9 the former group and 0.27 (0.16) mm for the latter [2]. IOL misalignment observed by Baumeister et al. did not cause a significant reduction in the optical quality [2], indicating that moderate tilt and decentration have a low potential to affect the eye’s visual function, which is in line with the conclusions of our current study. The extent of IOL misalignment on the retinal image in pseudophakic eyes has been assessed in numerous studies [2–4,6,7,10–13]. Although in those publications, the average tilt typically did not exceed 4 [4], Phillips et al. reported the mean value of 7.8 [11]. Taketani et al., Oshika et al., and Baumeister et al. [2,10,13], discussed in detail in the preceding paragraph, provided evidence for improved tilt outcomes in modern cataract surgery, with mean values well below the level found by Phillips et al. Crnej et al. presented the results of their analysis of misalignment in eyes having plate-haptic IOLs, as well as one- and three-piece AcrySof lenses [3]. They used a Purkinje-image-based system to assess the lens position [3]. In the postoperative examination performed three months after the surgical procedure, tilt ranged from 1.9 (1.4 ) to 2.9 (0.9 ) in the plate-haptic group, 2.6 (4.1 ) to 5.3 (2.4 ) in the three-piece group, and 1.9 (0.3 ) to 2.2 (7.2 ) in the one-piece group, with a significant variability indicated by a high SD in this group [3]. In that study, decentration was within a 0.07 (0.28) mm and 0.34 (0.15) mm range after plate-haptic IOL implantation, from -0.08 (0.57) mm to 0.32 (0.48) mm with three-piece IOLs, and 0.08 (0.30) mm to 0.19 (0.20) mm with one-piece IOLs [3]. Decentration was generally within the 1.0–1.0 range, with only one case falling beyond this margin. The mean levels reported by Crnej et al. [3] were in agreement with the conclusions of Eppig et al. [4], who has also shown the populational variability of IOL decentration, with approximately 0.3 mm on average. The range observed in those publications helped select the lens displacement limits applied in this in vitro model to align our simulation with clinically relevant situations. Given that the secondary implantation of a sulcus-fixated lens is performed less frequently than standard capsular fixation implantation, the available data on the mis- alignment of sulcus-fixated supplementary IOL are limited. One of the first reports on tilt and decentration in sulcus IOLs was presented by Kahraman and Amon [7]. Although they did not present the average level of misalignment in their series, they found <0.5 mm decentration in one of their 12 cases, which did not compromise the visual function [7]. Prager et al. compared the decentration of capsular fixation and sulcus-fixated IOLs in a polypseudophakic configuration [12]. They found that the secondary (sulcus) IOLs yielded a smaller shift from the pupil center as compared to the primary (capsular fixation) IOLs (0.22  0.02 mm vs. 0.29  0.03 mm) in their population of 43 patients [12]. Gerten et al. recorded the largest off-axis deviation of 0.8 mm in one eye [6]. However, the decentration level was below the 0.5 mm threshold in 98.2% of their population [6]. The misalignment observed in that study did not affect the patients’ vision despite the lens being bifocal [6]. The impact of the misalignment of a trifocal sulcus-fixated IOL has recently been studied by our group [8]. We found that decentration of up to 0.6 mm did not affect the far-focus performance of a zero-power trifocal lens in that laboratory investigation [8]. A slight reduction of the MTF was observed at the intermediate and near focus, and the negligible impact of a 5 tilt [8]. That finding agrees with the current study’s results on monofocal technology, as we also observed virtually no change in the MTFa of sulcus-fixated IOLs up to 5 . Vega et al. studied the association of the MTFa with clinically measured visual acu- ity [24]. They set the MTFa reference level = 20, above which the IOL’s optical performance does not compromise visual acuity [24]. Given that the MTFa was above this level in all studied sulcus-fixated lenses, the expected impact of their misalignment on visual acuity is minimal. Although with a combined tilt and decentration, the bag-fixated lens demonstrated an MTFa = 31.6, which is still above the reference level. The increase in coma and astigmatism aberrations may affect the patients’ vision beyond the recognition of high-contrast letters. The presence of shadowing effects, reduced contrast sensitivity, or photic phenomena, typically associated with increased HOAs [26,27], might not be Photonics 2021, 8, 309 8 of 9 detected if only visual acuity is used in the postoperative assessment, as shown by our MTFa analysis. Another limitation of our model is that it may not reflect the variability in the popula- tion. For instance, in this study, the off-the-center position of the pupil was marked by a 0.5 mm decentration. However, studies have shown that besides intersubject variability, pupil dilation may further influence the pupillary center ’s shift [28]. This variability in the natural centration of the pupil may influence how the misaligned IOL affects optical performance, as both a slight improvement or a deterioration, more substantial than ob- served in the current study, might be expected depending on the direction and the extent of each element’s shift. In addition, we did not include corneal HOAs [29] or the dynamic behavior of the tear film [30]. However, further increasing the complexity of our model could introduce additional confounders, which would not necessarily improve the accuracy of our prediction as the complex interactions between each factor would then need to be studied in order to unmask the impact of IOL misalignment on optical quality. Including population data appears to be essential in the study of our results’ repeatability, which warrants further research. 5. Conclusions Ray-tracing simulations showed good imaging quality in a two-lens configuration. Decentration of up to 1 mm and tilt up to 7.5 did not affect the optical performance of low-power sulcus-fixated IOLs in this simulated eye model. Although greater tilt (above 7.5 ) resulted in a more substantial MTFa loss, its impact on visual performance might be limited. One would expect a similar effect in a pseudophakic eye. The precise alignment of a high-power capsular-bag-fixation lens appears to be essential in both standard single-lens implantation and the two-lens configuration. Author Contributions: Conceptualization, G.Ł., G.U.A. and R.K.; methodology, G.Ł.; software, G.Ł.; validation, G.Ł., G.U.A. and R.K.; investigation, G.Ł., G.U.A., W.Y., T.M.Y. and R.K.; data analysis, G.Ł., W.Y. and T.M.Y.; resources, G.U.A. and R.K.; writing—original draft preparation, G.Ł., W.Y. and T.M.Y.; writing—review and editing, G.Ł., G.U.A. and R.K.; supervision, G.Ł., G.U.A. and R.K.; project administration, G.Ł., G.U.A. and R.K.; funding acquisition, G.U.A. and R.K. All authors have read and agreed to the published version of the manuscript. Funding: This study was funded by unrestricted research grants from the Klaus Tschira Stiftung and Rayner Ltd. The sponsors had no role in the design, execution, interpretation, or writing of the study. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The datasets used and analyzed for the present study are available from the corresponding author upon request. Acknowledgments: Donald J. Munro contributed to the review of the manuscript. Conflicts of Interest: G.U.A. reports grants, personal fees, non-financial support, and consulting fees from Johnson & Johnson and Alcon; grants, personal fees, and non-financial support from Carl Zeiss Meditec, Hoya, Kowa, Oculentis/Teleon, Rayner, Santen, Sifi, and Ursapharm; grants and personal fees from Biotech, Oculus, and EyeYon; grants from Acufocus, Anew, Contamac, Glaukos, Physiol, and Rheacell, outside the submitted work. R.K. reports grants, personal fees, and non-financial support from Alcon, Johnson & Johnson, Hoya, Physiol, and Rayner; personal fees and non-financial support from Kowa, Ophtec, Oculentis/Teleon, Santen, and Acufocus, outside the submitted work. G.Ł., W.Y., and T.M.Y. have nothing to disclose. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Aug 2, 2021

Keywords: supplementary IOLs; lens tilt and decentration; MTF; HOAs; polypseudophakia

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