Effect of intraocular lens implantation on visual acuity, contrast sensitivity, and depth of focus

Effect of intraocular lens implantation on visual acuity, contrast sensitivity, and depth of focus Ying-Khay Nio, MD, Nomdo M. Jansonius, MD, PhD, Ed Geraghty, Sverker Norrby, PhD, Aart C. Kooijman, PhD Purpose: To determine the role of spherical and irregular aberrations in the optics of the natural eye and after intraocular lens (IOL) implantation in terms of visual acuity, contrast sensitivity, and depth of focus. Setting: Laboratory of Experimental Ophthalmology, University of Groningen, Groningen, The Netherlands. Methods: Visual acuity and defocus-specific contrast sensitivity in 11 pseudophakic patients (IOL group) and 27 age-matched phakic subjects were compared. The results were obtained psychophysically. Spherical and irregular aberrations were subsequently estimated by comparing the measured myopic shift (optimum focus of contrast sensitivity at 4 cycles per degree [cpd] compared to that at 16 cpd) and depth of focus with those of theoretical eye models with varying amounts of irregular and spherical aberrations. Results: The best corrected visual acuity and best corrected contrast sensitivity in the IOL group did not significantly differ from that in the phakic group. The depth of focus was larger in the IOL group at a pupil diameter of 6.0 mm (P⬍.05). Comparison with theoretical eye models suggested a higher amount of spherical aberration in the IOL group; irregular aberration was almost the same in both groups. Conclusions: There was a higher amount of spherical aberration in the IOL group, related to a larger depth of focus, without loss of contrast sensitivity at optimum focus or loss of visual acuity. This might contribute to better quality of vision in pseudophakic subjects than in presbyopic phakic subjects. J Cataract Refract Surg 2003; 29:2073–2081  2003 ASCRS and ESCRS

S

nellen visual acuity insufficiently describes the quality of the eye’s optics before and after cataract surgery.1⫺5 Patients may, for example, be dissatisfied as a

Accepted for publication July 21, 2003. From the Laboratory of Experimental Ophthalmology, University of Groningen (Nio, Jansonius, Kooijman), and Pharmacia (Geraghty, Norrby), Groningen, The Netherlands. Supported by Pharmacia, Groningen, The Netherlands. None of the authors has a financial or proprietary interest in any product mentioned. Mrs. T. Coeckelbergh provided statistical support. Reprint requests to Y.K. Nio, MD, Department of Ophthalmology, University Hospital Groningen, PO Box 30.001, 9700 RB Groningen, The Netherlands.  2003 ASCRS and ESCRS Published by Elsevier Inc.

result of postoperative changes in optical aberrations even though they have good visual acuity. Measurements of contrast thresholds for sinusoidally modulated gratings, ie, contrast sensitivity, at various spatial frequencies provide more insight into postoperative spatial vision. Contrast sensitivity is determined by the product of optical and neural modulation transfer. Defocus decreases optical modulation transfer because it reduces the contrast of sinusoidally modulated gratings on the retina6; however, it has no effect on neural modulation transfer. Charman7 used this fact when he defined relative modulation transfer at a specific spatial frequency as the ratio of contrast sensitivity at a certain level of defocus to contrast sensitivity at optimum focus. Because neural modulation transfer is eliminated in this ratio of contrast sensitivity values, relative modulation 0886-3350/03/$–see front matter doi:10.1016/j.jcrs.2003.07.007

SPHERICAL AND IRREGULAR ABERRATIONS AFTER IOL IMPLANTATION

transfer is determined purely by the eye’s optics. By performing psychophysical contrast sensitivity measurements at different levels of defocus, one can study the quality of the eye’s optics. The effect of spherical and other optical aberrations on relative modulation transfer was studied by Jansonius and Kooijman.8 They found that in contrast to monochromatic aberrations, chromatic aberrations hardly influence relative modulation transfer. Monochromatic aberrations can be roughly classified into spherical, irregular, and coma like, with each having an effect on relative modulation transfer. Spherical aberration causes an increase in relative modulation transfer, an effect that is larger at negative values of defocus than at positive values. This asymmetry around optimum focus occurs particularly at lower spatial frequencies, typically below 8 cycles per degree (cpd), and with large pupil diameters. Irregular aberration is a rotationally symmetrical aberration that consists of other aberrations with a large intersubject variability.9 The presence of irregular aberration increases relative modulation transfer at higher spatial frequencies, typically above 2 cpd. Irregular aberration does not cause asymmetry in contrast sensitivity around the optimum focus. However, it does reduce the effect of spherical aberration on this asymmetry.10 Coma-like aberrations have no significant effect on contrast sensitivity function or relative modulation transfer.8 In a study of the effect of spherical aberration on vision quality, Nio et al.10 describe myopic shift as a measure of spherical aberration. This shift, which can be readily extracted from through-focus curves at low and high spatial frequencies, is based on the finding by Green and Campbell11 that optimum focus for contrast sensitivity depends on spatial frequency. When Green and Campbell compared spatial frequencies of 3 cpd and 45 cpd, for example, they found a myopic shift of about –0.9 diopter (D) at optimum focus of an eye with a 6.0 mm pupil. This shift was directly related to spherical aberration. Spherical and irregular aberrations influence relative modulation transfer and are therefore of importance for spatial vision. Although spherical and other aberrations can be measured objectively, indirect estimation of aberrations on the basis of psychophysical contrast sensitivity measurements forms a necessary supplement in the assessment of the eye’s optics because it evaluates functional vision instead of only the refractive optic 2074

Figure 1. (Nio) Through-focus modulation transfer curves of a diffraction-limited eye model and a realistic eye model with aberrations (eye model 2 with an irregular aberration of 0.5 D standard deviation at 8 cpd and with a 6.0 mm pupil). For details see Nio et al.10

properties. Minimizing aberrations increases the modulation transfer of the eye’s optics.12 Although this effect could result in better visual acuity and contrast sensitivity at optimum focus, it will decrease relative modulation transfer, leaving the optical system more vulnerable to defocus. As a result, the depth of focus will be smaller in a diffraction-limited system than in a system with aberrations, which may cause problems, especially in an eye that can no longer accommodate. This is illustrated in Figure 1, in which through-focus modulation transfer curves at 8 cpd in a diffraction-limited eye model are compared with an approximation of a realistic physiologic eye model. Cataract surgery should strive for a fine balance between modulation transfer and relative modulation transfer; ie, a balance between visual acuity and contrast sensitivity on one hand and depth of focus on the other. In this study, through-focus contrast sensitivity in pseudophakic patients was determined for a range of pupil diameters and spatial frequencies. The results were compared with those in a reference population to evaluate spherical and irregular aberrations after cataract surgery.

Patients and Methods Patients and Surgical Techniques Eleven pseudophakic patients were compared with an age-matched reference group of 27 phakic patients from an

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Table 1. Characteristics of the IOL group and the age-matched reference group. The latter was taken from the population described by Nio et al.13 The 2 groups were similar in characteristics. IOL Group (n ⫽ 11)

Reference Group (n ⫽ 27)

64.00 ⫾ 4.30

62.70 ⫾ 3.90

Stray light*

1.03 ⫾ 0.13

1.03 ⫾ 0.13

Visual acuity

1.14 ⫾ 0.14

1.28 ⫾ 0.22

Parameter Age (y)

All means ⫾SD Two groups were similar in parameters shown (P⬎.05) *Method described by van den Berg and Spekreijse14

ETDRS letter chart at a viewing distance of 2 meters. Contrast sensitivity at 6 spatial frequencies (1 cycle per degrees [cpd], 2 cpd, 4 cpd, 8 cpd, 16 cpd, and 32 cpd) was measured at the same viewing distance. The contrast sensitivity function was then determined in each group at 3 pupil diameters (2.0 mm, 4.0 mm, and 6.0 mm) and 6 levels of defocus (⫺1.0 D, ⫺0.5 D, defocus level zero, ⫹0.5 D, ⫹1.0 D, and ⫹2.0 D).

Data Processing: Statistical Analysis, Myopic Shift, and Depth of Focus Contrast sensitivity is the inverse of the contrast at threshold. Contrast according to Michelson is Contrast ⫽

13

earlier study by Nio et al. Informed consent was obtained from all patients, and the study was approved by the Ethics Committee of the University Hospital Groningen. Two pseudophakic patients had Rayner 105U biconvex poly(methyl methacrylate) (PMMA) intraocular lenses (IOLs), and 9 had Ophtec PC265Y biconvex PMMA IOLs. Except for cataract, the pseudophakic patients had no ophthalmologic history. All pseudophakic patients were operated on from 1996 to 1997. A 6.0 mm corneoscleral incision was placed at 12 o’clock, with a simple shoelace suture used to close the wound. All surgical procedures and postoperative courses were uneventful; no posterior capsule opacification was seen in any patient during routine ophthalmologic screening. Preoperative and postoperative astigmatic power was typically less than 1.0 D and did not change more than 0.3 D as a result of surgery. No IOL abnormalities such as scratches, tilting, luxations, and decentrations were tolerated. Characteristics of both groups are shown in Table 1. There was no significant difference in age, visual acuity (Early Treatment Diabetic Retinopathy Study [ETDRS] letter chart), or stray light (direct compensation method described by van den Berg and Spekreijse14).

Psychophysical Measurement of Contrast Sensitivity Routine ophthalmologic screening, experimental setup, and the psychophysical testing method used in this study were similar to those used by Nio et al.13 Briefly, visual acuity, optical correction, corneal curvature, intraocular pressure, stray light, and biometry were measured. Contrast sensitivity was measured with the use of the von Be´ke´sy tracking method and vertical sinusoidally modulated gratings displayed on a monitor screen (Joyce DM4, P31 phosphor, peak wavelength 520 nm, luminance 600 td) that extended 6 degrees ⫻ 6 degrees. Two drops of cyclopentolate hydrochloride 1% with a 30-minute interval between drops were administered before contrast sensitivity measurements to prevent accommodation and ensure stable pupil dilation. Defocus level zero was defined as the optimal optical correction in mydriasis measured with an

Lmax ⫺ Lmin Lmax ⫹ Lmin

(1)

where Lmax represents the maximum and Lmin the minimum luminance of a sine wave pattern. An analysis of variance (SPSS 10.0, general linear model [GLM] for repeated measurements) was performed to investigate the effects of between-patient factors (IOL and reference) and within-patient factors (pupil diameter, defocus, and spatial frequency). Where necessary, the Bonferroni adjustment for multiple comparisons was applied. All data for the 32 cpd spatial frequency were deleted because some patients could not detect these gratings even at defocus level zero. Myopic shift, the measure for spherical aberration, was defined as the difference between optimum focus for contrast sensitivity at 4 cpd and at 16 cpd. Optimum focus at these spatial frequencies was determined by fitting a parabola to the averaged and individual contrast sensitivity values as a function of defocus. The parabola was fitted to the highest contrast sensitivity value measured and the 2 adjacent points. The focus at which the top of the parabola was located was considered the optimum focus of the spatial frequency concerned. As a rule, the optimum focus at 4 cpd was located at a more myopic focus than that at 16 cpd. The experimental myopic shift was then compared with the shift in 2 theoretical eye models described by Jansonius and Kooijman8: Eye model 1 estimates a typical upper limit of spherical aberration; eye model 2 estimates the average spherical aberration in the human eye. The myopic shift in these model eyes for different values of irregular aberration is described by Nio et al.10 The irregular aberration consisted of a random distribution of dioptric power in the eye’s optics around a mean value, as shown by van den Brink,15 who found that this random distribution could be described by a normal distribution with a standard deviation of 0.5 D. The various amounts of irregular aberration were modeled by varying this standard deviation. Spherical aberration in the human eye can be caused by the cornea and the crystalline lens. Analysis of topographic pictures made with a corneal topographer (TMS-1 version

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Results

Figure 2. (Nio) Contrast sensitivity functions at defocus level zero with a 6.0 mm pupil. There was no significant statistical difference between the IOL and reference groups.

1.61, Computed Anatomy) resulted in the average spherical aberration in the cornea in the IOL and the reference groups, assuming a 6.0 mm pupil. This analysis anticipated flattening of the cornea toward the periphery. The exact method of analysis is described by Nio et al.10 One definition of the depth of focus for a specific spatial frequency is the dioptric range at which contrast sensitivity for that spatial frequency exceeds half its maximum value.16 Depth of focus was evaluated at a spatial frequency of 8 cpd, an intermediate between the frequencies important for reading newspaper letters (ie, 12 cpd) and detecting edges (ie, 3 cpd).17,18 To determine the depth of focus, a curve was fitted through the average and the individual contrast sensitivity data points as a function of defocus using a standard spline routine (EasyPlot V4, Spiral Software). Because of the limited range of negative defocus values, depth of focus was defined as twice the positive half of the dioptric range in which contrast sensitivity exceeds half its maximum value. The range and amount of defocus values were limited because of the large number of threshold measurements that had to be performed in 1 day for each patient.

Figure 2 shows the phakic and pseudophakic contrast sensitivity functions with a 6.0 mm pupil at defocus level zero. Similar results were obtained with 2.0 mm and 4.0 mm pupils. At defocus level zero, the pseudophakic contrast sensitivity function was less than that in the phakic reference group in most conditions. However, the Student t test showed no between-group difference (P⬎.05) at any combination of pupil diameter and spatial frequency. There was an expected effect of pupil diameter, defocus, and spatial frequency on contrast sensitivity. The 2-way and 3-way interactions were also significant. Most effects did not differ between the IOL and reference groups. Exceptions were the effect of defocus and the interaction between defocus and spatial frequency. Figure 3 shows that with positive values of defocus, the attenuating effect of defocus on contrast sensitivity, averaged over all pupil diameters, was greater at higher spatial frequencies, ie, 4 cpd, 8 cpd, and 16 cpd, and larger in the reference group than in the IOL group. At negative values of defocus, the contrast sensitivity was higher in the reference group than in the IOL group. Based on individual data, the between-group difference in myopic shift was greatest with a 6.0 mm pupil. Since spherical aberration does not play a significant role in spatial vision with small pupil diameters, only myopic shift data with the 6.0 mm pupil were analyzed. Table 2 shows the experimental myopic shift with averaged and individual contrast sensitivity data. The individual myopic shift differed significantly from zero in both groups (P⬍.05). The between-group difference was not statistically significant (Student t test, P ⫽ .08) despite the apparently large (0.36 D) difference. Table 3 shows the theoretical myopic shift for the 2 eye models with different amounts of spherical and irregular aberration. The central 6.0 mm of the corneal topography pictures was analyzed. The difference between the mean spherical

Table 2. Experimental myopic shift with a 6.0 mm pupil determined on the basis of the averaged and individual contrast sensitivity curves as a function of defocus. Myopic shift was defined as the difference between optimum focus for contrast sensitivity at 4 cpd and at 16 cpd. Experimental Myopic Shift (D) Parameter

IOL Group ⫺0.59

Averaged contrast sensitivity curves Individual contrast sensitivity curves (mean ⫾ 1 SE)

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⫺0.64 ⫾ 0.20

Reference Group ⫺0.39 ⫺0.28 ⫾ 0.09

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Difference IOL–Reference Group ⫺0.20 ⫺0.36 ⫾ 0.22

SPHERICAL AND IRREGULAR ABERRATIONS AFTER IOL IMPLANTATION

Figure 3. (Nio) Contrast sensitivity (log CS), averaged over all measured pupil diameters, as a function of defocus for spatial frequencies of 1 cpd ( top left ), 2 cpd ( top right ), 4 cpd ( middle left ), 8 cpd ( middle right ), and 16 cpd ( bottom ) (䊐---䊐, IOL group; O---O, reference group).

aberration of the cornea in the IOL group (1.32 D ⫾ 0.12 [SE]) and in the reference group (1.45 ⫾ 0.09 D) was not statistically significant (P⬎.05). There was no difference in the cylindrical axis.

The depth of focus was calculated in 2 ways: from the mean contrast sensitivity curve as a function of defocus (Table 4) and from the individual contrast sensitivity curves (Table 5). The mean curve in the IOL

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group was calculated on the basis of 11 patients and that in the reference group, of 27 patients. Table 4 shows a consistently higher depth of focus in the IOL

Table 3. Myopic shift for theoretical eye models 1 and 2 with a 6.0 mm pupil and various amounts of irregular aberrations. Theoretical Myopic Shift at Eye Model*

IA ⫽ 0.3 D

IA ⫽ 0.5 D

IA ⫽ 0.7 D

1

⫺0.67

⫺0.53

⫺0.29

2

⫺0.28

⫺0.33

⫺0.22

IA ⫽ irregular aberration *Eye models 1 and 2 represent an estimation of the upper limit and the mean spherical aberration of the human eye, respectively.8 Data from Nio et al.10

Table 4. Experimental depth of focus on the basis of mean contrast sensitivity as a function of defocus. The depth of focus determined for a spatial frequency of 8 cpd was defined as twice the positive half of the dioptric range in which the contrast sensitivity exceeded half the maximum value. Depth of Focus (D) Pupil Diameter (mm)

IOL Group (n ⫽ 11)

Reference Group (n ⫽ 27)

2

3.2

2.1

4

2.5

1.5

6

2.2

1.4

Table 5. Experimental depth of focus on the basis of the individual contrast sensitivity as a function of defocus. The IOL group had a significantly higher depth of focus at both pupil diameters (P⬍.05). Pupil Diameter (mm)

Depth of Focus (Mean D ⫾ 1 SE) IOL Group

Reference Group

4

1.82 ⫾ 0.34 (n ⫽ 7)

1.22 ⫾ 0.09 (n ⫽ 22)

6

1.81 ⫾ 0.27 (n ⫽ 10)

1.32 ⫾ 0.10 (n ⫽ 25)

Table 6. Depth of focus for theoretical eyes models 1 and 2 with a 6.0 mm pupil. Various amounts of irregular aberrations (IA) were implemented in the theoretical eye models: 0.3 D, 0.5 D, and 0.7 D standard deviation. Depth of Focus with 6.0 mm Pupil at Eye Model

IA ⫽ 0.3 D

IA ⫽ 0.5 D

IA ⫽ 0.7 D

1

1.36

1.66

2.04

2

1.01

1.38

1.82

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group than in the reference group. The significance of the differences could not be determined. Because of this, the depth of focus in each patient was determined and the results averaged. In some cases, the individual depth of focus could not be determined with sufficient certainty because of multiple contrast sensitivity maximums or because of the absence of a clear maximum when the maximum contrast sensitivity was measured at the most negative defocus level used (⫺1.0 D). The exclusion of these patients resulted in such a limited amount of IOL data for the 2.0 mm pupil that only the individual depth of focus results for the 4.0 mm and 6.0 mm pupils were calculated (Table 5). The IOL group had a significantly higher depth of focus at both pupil diameters (P⬍.05). This result corresponds with the higher depth of focus in the IOL group found on the basis of the averaged curves. No significant difference in individual depth of focus was found between pupil diameters of 4.0 mm and 6.0 mm in either group (P⬎.05). Table 6 shows the theoretical depth of focus for eye models 1 and 2 using varying amounts of irregular aberration and a 6.0 mm pupil, at which the effects of aberrations were studied.

Discussion This study investigated visual acuity, stray light, and through-focus contrast sensitivity in phakic and pseudophakic patients. The depth of focus and myopic shift were derived from these data, and an estimation of spherical and irregular aberrations was made. Visual acuity and stray light were similar in both groups, as was contrast sensitivity at defocus level zero. The latter might be due to insufficient numbers of patients considering the constantly lower position of the mean pseudophakic contrast sensitivity function. The pseudophakic group had a larger depth of focus. From an optical point of view, the overall effects on pupil diameter and spatial frequency are clear: A larger pupil diameter is expected to decrease contrast sensitivity,19 and the effect of spatial frequency is displayed in the well-known contrast sensitivity function. The effect of defocus depends on spatial frequency, as illustrated in Figure 3. At low spatial frequencies, especially 1 cpd, there was hardly any effect. These

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results do not differ from existing theories or experiments on through-focus contrast sensitivity.19,11 There are, however, conflicting opinions about the similar contrast sensitivities at defocus level zero in phakic and pseudophakic patients. Some studies report similar results.20,21 Navarro and coauthors20 used the same inclusion criteria as in this study and found that the optical modulation transfer function in pseudophakic patients resembled that in age-matched phakic subjects, which implies no optical degradation in the IOL group. Our results also did not show a significant decrease in contrast sensitivity. Other studies, however, report lower contrast sensitivity in the IOL group. This could be due to lower visual acuity22 or an age difference between the groups. Negishi and coauthors23 studied pseudophakic and phakic groups with mean ages of 64 years and 32 years, respectively, and found a spatial-frequency-dependent difference in contrast sensitivity that resembles the difference found by Nio et al.13 in corresponding age groups of phakic subjects. Mela and coauthors,24 who did not measure stray light, mention a possible subclinical amount of posterior capsule opacification as a possible cause of their differing results. So, implantation of a monofocal PMMA IOL presumably does not lead to a significant decrease in visual acuity or contrast sensitivity at defocus level zero or to an increase in stray light if the age in the IOL and phakic groups is the same. The IOL group in the present study showed a larger depth of focus than the reference group, which could be caused by a larger amount of spherical and/or irregular aberrations. The reference group resembled theoretical eye model 2 with an irregular aberration of 0.5 D, whereas the IOL group resembled eye model 1 with an irregular aberration of 0.5 D. This was concluded from the myopic shift and depth of focus data, as will be explained. A subgroup of the population of phakic patients measured by Nio et al.10 was age matched to our IOL group and was therefore used as a reference group in this study. The myopic shift based on the mean contrast sensitivity was ⫺0.39 D in this phakic group. The IOL group showed a higher shift (⫺0.59 D). The myopic shift on the basis of individual curves showed similar results: a higher mean shift in the IOL group (⫺0.64 ⫾ 0.20 D) than in the reference group (⫺0.28 ⫾ 0.09 D). However, the between-group difference in myopic shift was

not statistically significant (P ⫽ .08). A comparison of experimental (Table 2) and theoretical (Table 3) values of myopic shift shows that our IOL group resembles eye model 1 with an irregular aberration between 0.3 D and 0.5 D. The spherical aberration in the reference group can best be compared with that of eye model 2, in which the myopic shift is similar and rather insensitive to the amount of irregular aberration. This result agrees with that in an earlier study.10 Both spherical and irregular aberrations are known to increase the depth of focus. Our IOL group had a significantly higher depth of focus than the reference group. When the experimental values of depth of focus (Tables 4 and 5) are compared with the theoretical values (Table 6), our IOL group resembles eye model 1 with an irregular aberration between 0.5 and 0.7 D. The combination with myopic shift data leads to the conclusion that the IOL group resembles eye model 1 with an irregular aberration of 0.5 D. The reference group had depth of focus values comparable to those with eye model 2 with an irregular aberration of 0.5 D, which coincides with myopic shift data. Thus, spherical aberration in particular appears to be higher in the pseudophakic group, which may explain the higher depth of focus measured in this group. The higher amount of spherical aberration must be due to the IOL since the corneal spherical aberration did not differ between the 2 groups. Both myopic shift and depth of focus data indicate that the pseudophakic eye has a spherical aberration approximating the upper limit in normal human eyes. Eye model 1 with a pupil diameter of 6.0 mm has a spherical aberration of 1.7 D. Spherical aberration of the average pseudophakic eye can also be calculated in an independent way. Geometric optics show that an IOL with a dioptric power of 21.0 D has a spherical aberration of 0.4 D with a 6.0 mm pupil (Appendix). The mean corneal spherical aberration in the IOL group on the basis of the topographic images was 1.3 D. So, the total spherical aberration in the pseudophakic eye was 1.7 D. This equals the spherical aberration as estimated from the myopic shift and depth of focus. The larger depth of focus in the IOL group confirms the everyday clinical experience that pseudophakic people claim to see quite well even though some are not completely emmetropic postoperatively. Some emmetropes even read without additional optical correction. However, whether such an increase in depth of focus contrib-

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utes to the clinical comfort of patients remains to be evaluated by questionnaires. The larger depth of focus measured does not occur at the cost of the contrast sensitivity at defocus level zero or visual acuity. Therefore, the monofocal PMMA IOL, with its spherical and irregular aberrations, functions quite well in terms of depth of focus, contrast sensitivity, and visual acuity. It must still be determined whether the creation of aberration-free optics offers the same amount of comfort and quality of vision.

5.

6. 7.

8.

Appendix Calculation of the Spherical Aberration of the IOL All patients in the IOL group had biconvex lenses. If we assume that the anterior and posterior surfaces had similar radii, the spherical aberration of the IOL can be calculated from25 Psa(h) ⫽

n 2 ⫻ h2 ⫻ P 2n⬘2 ⫻ R 2

(2)

where Psa is the power of the spherical aberration, n the refractive index in object space, n⬘ the refractive index in image space, h the distance from the center of the IOL (ray height), R the radius of the surface, and P the power of the surface. For the anterior and posterior surfaces, P was 10.5 D (half the total power of the average IOL). The refractive indices for PMMA and intraocular fluid are 1.49 and 4/3, respectively. Consequently, R can be calculated from P R⫽

n⬘⫺n P

10.

11.

12. 13.

14.

(3)

yielding values of 0.0149 m and ⫺0.0149 m for the anterior and posterior surfaces, respectively. For a 6.0 mm pupil, h is 0.003 m, and consequently, the spherical aberration of the entire IOL equals 0.4 D. An artificial 6.0 mm pupil at the level of the cornea relates to a 5.3 mm pupil at the level of the iris. Correction of the spherical aberration for this fact does not lead to a clinically significant difference.

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19.

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23. Negishi K, Ohnuma K, Hirayama N, Noda T. Effect of chromatic aberration on contrast sensitivity in pseudophakic eyes; for the Policy-Based Medical Service’s Network Study Group for Intraocular Lens and Refractive Surgery. Arch Ophthalmol 2001; 119:1154–1158

24. Mela EK, Gartaganis SP, Koliopoulos JX. Contrast sensitivity function after cataract extraction and intraocular lens implantation. Doc Ophthalmol 1996/97; 92:79–91 25. Jenkins FA, White HE. Fundamentals of Optics, 4th ed. Auckland, McGraw-Hill, 1981; 152

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