1. ARTICLE
Correlation between optics quality of multifocal
intraocular lenses and visual acuity
Tolerance to modulation transfer function decay
Adelina Felipe, PhD, Francisco Pastor, MD, PhD, Jose M. Artigas, PhD, Amparo Diez-Ajenjo, OD, MSc,
´
Andres Gene, OD, MSc, Jose L. Menezo, MD, PhD, FEBO
´ ´ ´
PURPOSE: To study the relationship between the optics quality of multifocal intraocular lenses
(IOLs) and distance-corrected near, intermediate, and distance visual acuity to determine the
degree to which optics quality must change to produce a significant difference in visual acuity.
´ ´ ´
SETTING: Fundacion Oftalmologica del Mediterraneo, Valencia, Spain.
METHODS: Monocular distance-corrected visual acuity (decimal and logMAR) was measured at
4 m, 70 cm, and 30 cm under photopic and mesopic conditions in eyes with 1 of 3 multifocal
IOL models. Visual acuity versus the ‘‘average modulation’’ of the IOL was assessed.
RESULTS: The pupil diameter and patient age were similar between the 3 IOL groups (20 eyes
each). A difference in average modulation (ie, optics quality) up to 15% did not produce significant
differences in mean visual acuity between 2 groups; however, there was a significant difference in
mean visual acuity between 2 groups when the average modulation values differed by at least 25%.
The slope of the linear correlation between visual acuity and average modulation was 0.018 (r2 Z
0.91) under photopic conditions and 0.024 (r2 Z 0.089) under mesopic conditions.
CONCLUSIONS: There was a strong linear correlation between IOL optics quality and visual acuity
with distance correction under photopic conditions with a pupil of approximately 3.5 mm in a cohort
in which the patient age was controlled. The correlation was similar under mesopic conditions. The
eye’s tolerance to modulation transfer function decay was approximately 15% of the average mod-
ulation value.
Financial Disclosure: No author has a financial or proprietary interest in any material or method
mentioned.
J Cataract Refract Surg 2010; 36:557–562 Q 2010 ASCRS and ESCRS
In recent years, many clinical and technology-related device.19 When an optics system is perfect (free from
cataract surgery studies have sought to improve the op- aberrations), the MTF function has a characteristic tri-
tics quality of intraocular lenses (IOLs) and to develop angular shape. The modulation value is 1 at a spatial
new IOL designs to improve performance. Advances frequency of zero; the value decreases with the spatial
include pseudoaccommodation,1–5 astigmatism correc- frequency until it reaches the cutoff frequency for
tion,6 and phakic IOLs (pIOLs) for correction of high a particular pupil diameter. The shape of the MTF is al-
ametropia.7–9 Numerous studies in the literature report tered as a result of the aberration effect when the pupil
a reduction in aberration by surgical techniques such size increases or when an IOL is decentered or tilted,
as refractive surgery10–13 and by implantation of con- which decreases the modulation value. In general,
ventional and other IOLs to correct ametropia.14–18 any loss in optics quality affects the shape and value
Thus, it is important to develop IOLs with optimized of the MTF.15,20–22
optics to improve patients’ comfort and visual quality. Moreover, the MTF is the Fourier transform of the
The modulation transfer function (MTF) is used in point-spread function (PSF); a Fourier transform
physical optics as the most suitable parameter for eval- changes a spatial coordinate space into a frequency
uating the optics quality of any optics element or space or vice versa. Although the same information
Q 2010 ASCRS and ESCRS 0886-3350/10/$dsee front matter 557
Published by Elsevier Inc. doi:10.1016/j.jcrs.2009.10.046

2. 558 CORRELATION BETWEEN MULTIFOCAL IOL OPTICS QUALITY AND VISUAL ACUITY
Z 100
can be obtained from the MTF and the PSF, the latter is 1
defined in the ordinary coordinate space rather than in VmZ MTFðf Þ Â df
100 0
the spatial frequency space, and for this reason, it is
easier to understand the PSF. In the PSF, if a system where f is the spatial frequency and df is the differen-
were perfect, the image of a point would be a point; be- tial of the variable f. Thus, the ratio between the 2 pa-
cause the optics elements or lenses are not usually per- rameters is a constant (Average modulation [from
fect, the point is imaged as a spread point. The PSF of 0 to 100] Z 1/100 Area [from 0 to 100]) and the corre-
an optics system shows the exact shape of the image lation holds using a parameter that is proportional to
point formed by the system; the narrower the PSF, the parameter.
the wider the MTF (more frequencies in the image; The frequency 100 cycles per millimeter (c/mm) is
each frequency having good contrast if its modulation approximately equivalent to 30 cycles per degree
value is high) and the better the image quality.23 Given (cpd) and is equal to the unit of decimal visual acuity.
that any object or picture is imaged by the system Moreover, human contrast sensitivity has a maximum
point by point, if the PSF is wide, every point in the im- value at approximately 2 to 8 cpd, which shows the
age will be defocused. importance to vision of the low and middle frequen-
It is possible, therefore, to compare the optics quality cies. Therefore, in this study we considered all fre-
of IOLs by measuring and comparing their MTFs. To quencies from 0 to 100 c/mm (ie, approximately 0 to
simplify the comparison, we used the ‘‘average modu- 30 cpd).
lation’’ value in previous studies.22 This is the value of Nevertheless, knowing there is a difference in the
modulation averaged in the range of frequencies from MTF between 2 IOLs is not enough to determine
0 to 100. In this way, each MTF is represented by only whether a patient would appreciate a difference in vi-
a numeric value (average modulation). The area under sual quality with 1 IOL or the other. For example, Ar-
the MTF curve has been used in studies of the quality tigas et al.9 found differences from 10% to 14% in
of different optics elements, such as lenses and contact modulation values between 2 pIOLs but found no sig-
lenses.24 Nevertheless, studies published in the past nificant difference in the visual response between the 2
few years9,22 used average modulation instead of the IOLs.25 The question is how much the average modu-
area under the curve because the information pro- lation of an IOL must change to cause a significant dif-
vided by both parameters (area under the MTF and av- ference in visual acuity. In this study, we attempted to
erage modulation) is of equal value and almost answer that question. We measured the monocular
equivalent. Moreover, it is easier to obtain and under- distance, near, and intermediate visual acuities after
stand average modulation because the value is in- cataract surgery in patients with 1 of 3 models of mul-
cluded in recently released devices for measuring tifocal IOLs. Nine MTFs (3 IOLs with 3 focuses) sum-
MTF.21,22 It is easily proved that the 2 parameters are marized by 9 average modulation values and 9
proportional. The area under the MTF is 100 times visual acuity values (3 IOLs evaluated at 3 distances)
the value of average modulation under the conditions were available to calculate a linear regression between
used in our study, as follows: the 2 variables. In our study, it was necessary to limit
the age range and pupil size as much as possible to iso-
Z 100
late the influence of average modulation on visual acu-
AreaZ MTFðf Þ Â df ity from the effect of other parameters.
0
with the mean value
PATIENTS AND METHODS
This retrospective nonrandomized study evaluated 1 eye of
patients having cataract surgery with implantation of 1 of
3 multifocal IOL models. Inclusion criteria were cataract in
both eyes, corneal astigmatism less than 1.00 diopter (D), po-
Submitted: July 2, 2009. tential postoperative photopic acuity better than 0.6 decimal
Final revision submitted: October 20, 2009. (0.20 logMAR), signed informed consent, IOL power of
Accepted: October 22, 2009. 21.00 D G 3.00 (SD), age between 65 years and 70 years,
and photopic pupil diameter between 3.2 mm and 4.0 mm.
´ ´ ´
From the Fundacion Oftalmologica del Mediterraneo (Felipe, Pastor, Exclusion criteria were previous refractive or glaucoma
´
Artigas, Diez-Ajeno, Menezo) and Departamento de Optica (Felipe, surgery, degenerative optical disease, and disease that could
´
Artigas), Facultad de Fısica, Universitat de Valencia, Burjassot affect the final results.
(Valencia), Spain.
´
Corresponding author: Adelina Felipe, PhD, Departamento de Opti- Multifocal Intraocular Lenses
´
ca, Facultad de Fısica, Universidad de Valencia, C/Dr Moliner, 50, Eyes in the acrylic refractive–diffractive group received an
E46100-Burjassot (Valencia), Spain. E-mail: adelina.felipe@uv.es. AcrySof ReSTOR SN60D3 IOL (Alcon, Inc.). This acrylic
J CATARACT REFRACT SURG - VOL 36, APRIL 2010

3. CORRELATION BETWEEN MULTIFOCAL IOL OPTICS QUALITY AND VISUAL ACUITY 559
refractive–diffractive monoblock IOL has a biconvex optic, Early Treatment Diabetic Retinopathy Study chart at 4 m.
square edges, and a yellow filter to protect the macula in Each letter on the chart that is read correctly adds 0.02 log-
the blue zone of the solar spectrum. The optic design is MAR units to the visual acuity. All visual acuity mea-
refractive at the periphery for distance vision and apodized surements were performed under photopic (85 candelas
diffractive at the central 3.6 mm portion of the anterior [cd]/m2) and mesopic (3 cd/m2) conditions. Visual acuity re-
surface for distance and near vision. The diffractive steps sults are presented in logMAR and decimal values.
are greater in the center of the optic to give a greater propor- Visual acuity values 3 months after surgery was used in
tion to near vision. this study because the visual response is relatively stable
Eyes in the acrylic refractive group received a ReZoom by this time.14 Corrected distance visual acuity was measured
NXG IOL (Abbott Medical Optics, Inc.). This acrylic refrac- at 4 m (vergence À0.25 D), near visual acuity at 33 cm (ver-
tive IOL has 3 biconvex optic components with a triple- gence À3.00 D), and intermediate acuity at 70 cm (vergence
edge design to minimize optical phenomena and capsule À1.50 D), the approximate distance for working in front of
opacification. The optic has 5 concentric rings; the 3 rings a computer monitor.
with odd numbers are for distance vision and rings 2 and 4
are for near vision. The IOL has an addition (add) of 3.50 D
and an aspheric transition between zones for intermediate Statistical Analysis
vision. Statistical analysis was performed by means of the Stu-
Eyes in the silicone refractive–diffractive group received dent t test analysis of variance. A P value less than 0.05
a Tecnis ZM900 (Abbott Medical Optics, Inc.). This 3-piece was considered statistically significant.
silicone IOL has a biconvex optic with refractive–diffractive
characteristics because both optic systems are used simulta-
neously. The refractive zone is on the anterior surface and is RESULTS
for distance focus. The diffractive zone comprises 32 concen- This study comprised 60 eyes, 20 in each IOL group.
tric rings on the posterior surface and provides near focus.
The add is 4.00 D. The edges are square, and the anterior sur-
The mean age of the patients was 67.9 G 1.6 years
face is prolate to compensate for spherical aberration. and the mean pupil diameter, 3.5 G 0.4 mm under
photopic conditions and 5.4 G 0.7 mm under mesopic
Patient Assessment conditions. There was no statistically significant differ-
ence between IOL groups in age or pupil diameter.
Before surgery, patients had a full ophthalmologic exam-
ination including manifest refraction, corrected distance vi- Table 1 shows the mean modulation values for each
sual acuity, keratometry, slitlamp biomicroscopy, corneal IOL for distance, near, and intermediate vision and the
endothelial cell count, and Goldmann applanation tonome- relative difference between the values. The relative dif-
try. Binocular indirect ophthalmoscopy was performed ference represents the difference in optics quality.
through a dilated pupil when needed. Axial length (AL) Table 2 shows the monocular visual acuity by IOL
and anterior segment size were measured by optical coher-
ence biometry (IOLMaster, Carl Zeiss Meditec). Topography group. Under photopic conditions, there were no sta-
was assessed using a Scheimpflug scanning-slit system (Pen- tistically significant differences in acuity between the
tacam, Oculus) to monitor possible postoperative changes in 2 acrylic IOL groups at any distance; however, the dif-
corneal shape that could cause misinterpretation of the re- ferences between the silicone IOL group and each of
sults; these data were used only to avoid false differences be- the 2 acrylic IOL groups were statistically significant
tween IOLs. Postoperative assessments were performed at 1
day, 1 week, and 1 and 3 months. at all distances. The results were the same under mes-
The MTF was calculated from the cross line–spread func- opic conditions except that differences between the sil-
tion recorded with an Opal Vector System (Image Science, icone IOL group and each of the 2 acrylic IOL groups
Ltd.) using fast Fourier transform techniques. The device were statistically significant only at distance and near.
and details about the technique have been described.22 The Figure 1 shows the linear regression of the 9 phot-
MTF measurements were performed using an artificial eye
model that included an artificial cornea and a wet cell con- opic visual acuity values compared with the 9 average
taining physiological solution, where the IOL was modulation values obtained with a 3.5 mm pupil.
positioned. Figure 2 shows the linear regression for visual acuity
and average modulation mesopic values with 5.5 mm
Surgical Technique pupils.
All cataract surgeries were performed by the same experi-
enced surgeon (F.P) using topical anesthesia. Standard pha- DISCUSSION
coemulsification was performed through a 2.75 mm clear
corneal incision. After irrigation and aspiration of the cortex, Our study found no statistically significant differences
the IOL was implanted in the capsular bag using the injector between the 2 acrylic multifocal IOLs at any distance,
developed for the specific IOL. Postoperatively, patients which agrees with the results in other studies.26–29
used tobramycin–dexamethasone for 4 weeks. Nevertheless, Chang30 found a significant difference
in near vision between the 2 IOLs. The ReZoom
Visual Acuity Measurements NXG is the only refractive IOL of the 3 IOL models
Monocular logMAR visual acuity was measured with dis- studied. This explains why the MTF and visual acuity
tance refractive correction with nondilated pupils using an with this IOL were significantly different from those of
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4. 560 CORRELATION BETWEEN MULTIFOCAL IOL OPTICS QUALITY AND VISUAL ACUITY
Table 1. Average modulation values* and the relative difference between the values.
Intraocular Lens
Acrylic Refractive–Diffractive Acrylic Refractive Silicone Refractive–Diffractive Acrylic Refractive–Diffractive
Parameter AM Diff (%) AM Diff (%) AM Diff (%) AM
3.5 mm pupil
Distance 40 15 46 48 31 29 40
Near 27 4 28 29 36 33 27
Intermediate 20 11 18 39 25 25 20
5.5 mm pupil
Distance 36 6 38 41 27 33 36
Near 24 4 25 28 32 33 24
Intermediate 16 6 17 14 18 13 16
AM Z average modulation; Diff Z relative difference between the average modulation values on either side
*Obtained from MTF measured with 3.5 mm pupil based on mean photopic diameter of 3.5 G 0.4 mm and with 5.5 mm pupils based on mean mesopic diameter
of 5.4 G 0.7 mm
the other 2 IOLs, as reported in a comparative techni- difference had differences of 25% or over. We per-
cal study between refractive and diffractive multifocal formed a statistical analysis and found that a decrease
IOLs.22 in the average modulation value of 25% or 24% is
In all cases in which no significant difference was enough to cause a significant decrease in visual acuity
found, the difference in average modulation values with a statistical error of 0.03 and 0.05, respectively;
was 15% or lower; all cases with a significant this error increases to 0.08 and 0.10 when the decrease
Table 2. Monocular visual acuity with best distance correction.
Intraocular Lens
Acrylic Refractive–Diffractive Acrylic Refractive Silicone Refractive–Diffractive Acrylic Refractive–Diffractive
Mean G SD P Value* Mean G SD P Value† Mean G SD P Valuez Mean G SD
Photopic (85 cd/m2)
Distance .30 .001 .001
Decimal 0.96 G 0.11 0.99 G 0.11 0.84 G 0.09 0.96 G 0.11
LogMAR 0.022 G 0.04 0.006 G 0.044 0.080 G 0.045 0.022 G 0.046
Near .45 .013 .001
Decimal 0.78 G 0.09 0.80 G 0.10 0.88 G 0.09 0.78 G 0.09
LogMAR 0.110 G 0.050 0.099 G 0.055 0.058 G 0.045 0.110 G 0.050
Intermediate .33 .001 .002
Decimal 0.54 G 0.09 0.51 G 0.07 0.64 G 0.10 0.54 G 0.09
LogMAR 0.275 G 0.068 0.294 G 0.058 0.201 G 0.071 0.275 G 0.068
Mesopic (3 cd/m2)
Distance .11 .001 .001
Decimal 0.80 G 0.11 0.85 G 0.12 0.65 G 0.10 0.80 G 0.11
LogMAR 0.103 G 0.059 0.074 G 0.060 0.189 G 0.066 0.103 G 0.059
Near .51 .021 .003
Decimal 0.68 G 0.10 0.70 G 0.11 0.78 G 0.10 0.68 G 0.10
LogMAR 0.174 G 0.063 0.161 G 0.067 0.112 G 0.057 0.174 G 0.063
Intermediate .78 .46 .63
Decimal 0.34 G 0.06 0.34 G 0.06 0.35 G 0.07 0.34 G 0.06
LogMAR 0.470 G 0.079 0.478 G 0.082 0.459 G 0.084 0.470 G 0.079
*Between acrylic refractive–diffractive IOL and acrylic refractive IOL
†
Between acrylic refractive IOL and silicone refractive–diffractive IOL
z
Between silicone refractive–diffractive IOL and acrylic refractive–diffractive IOL
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5. CORRELATION BETWEEN MULTIFOCAL IOL OPTICS QUALITY AND VISUAL ACUITY 561
acuity. According to our results and statistical calcula-
tions, with a 25% decrease in the average modulation
value, the difference in visual acuity is highly signifi-
cant; this suggests that an approximate 20% difference
in average modulation could be enough to produce
a significant difference in visual acuity (with 0.13 sta-
tistical error). Thus, visual quality impairment begins
with a 20% to 25% decrease in the average modulation
value. It is not realistic to establish a more specific
value because we focused on statistical variables and
the specific limit would depend on factors such as
IOL properties, the individual eye, and the viewing
distance.
Figure 1. Mean visual acuity at distance, near, and intermediate un-
der photopic conditions versus the average modulation of the IOL
Although it was not the main objective of this study
(3.5 mm pupil diameter). to find differences between the IOLs, we did find some
difference. Our results were obtained using specific ex-
is 23% and 22%, respectively. We conclude from these perimental conditions; the results might be different if
results that when the MTF of an IOL decreases, in par- the pupil diameter and patient age ranges were
ticular when the average modulation value decreases changed. We were more interested in determining
by 15%, the patient’s visual acuity will probably not whether there is a correlation between IOL optics
be affected. Fortunately, the visual system has a level and visual properties. We found a correlation between
of tolerance to defocus.31 This conclusion could be ap- the optics quality of the IOL, represented by the aver-
plied to studies of factors such as IOL tilt, IOL decen- age modulation parameter, and the patient’s visual
tration off-center, and aberrations because knowing quality, represented by the visual acuity. The slope
the amount of MTF decrease these factors induce of the fitted regression line for photopic vision was
makes it possible to predict the approximate effect 0.18 decimal visual acuity units/10 average modula-
on the patient’s visual outcomes. Pepose1 lists factors tion units and the r2 value was 0.91. This means that
that cannot be determined reliably before cataract sur- 91% of the variability in the visual acuity values was
gery but can affect the performance of multifocal IOLs. the result of the variation in the average modulation
These include the final effective lens position, IOL cen- parameter. The linear regression of visual acuity ver-
tration with regard to the pupil and visual axis, IOL sus average modulation for mesopic vision had a slope
tilt, residual refractive error, and surgically induced of 0.24 decimal visual acuity/10 average modulation
changes in astigmatism or higher-order corneal aber- units; however, the correlation was lower than for
rations. Our results show that if these factors change photopic vision (r2 Z 0.89). In short, the visual acuity
the MTF by less than 15% of the average modulation varied 0.18 decimal units per 10 units of average mod-
value, the effect on visual acuity would likely be ulation variation under photopic conditions and 0.24
negligible. decimal units per 10 units of average modulation var-
Another aspect is to what degree optics quality must iation under mesopic vision.
change to produce a significant difference in visual The AcrySof ReSTOR SN60D3 IOL we used is not
the currently available model. The current model
(SN6AD3) has aspheric optics rather than the spherical
optics of the model used in our study. Although this
difference would likely influence the MTF level, this
was not of primary importance in our study because
we did not compare the quality between the different
IOLs. We simply wanted to have 9 quality values to as-
sess the correlation between visual acuity and average
modulation. We did not provide MTF graphs here be-
cause similar ones have been published.22
In conclusion, the optics quality of IOLs is a decisive
factor in visual performance. Although small varia-
tions in optics quality may go unnoticed by the patient,
Figure 2. Mean visual acuity at distance, near, and intermediate un-
a difference in the MTF that produces a 25% change in
der mesopic conditions versus the average modulation of the IOL the average modulation value will significantly affect
(5.5 mm pupil diameter). the patient’s visual acuity.
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6. 562 CORRELATION BETWEEN MULTIFOCAL IOL OPTICS QUALITY AND VISUAL ACUITY
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J CATARACT REFRACT SURG - VOL 36, APRIL 2010

7. Traduction de l’article
OBJECTIF : étudier la relation entre la qualité optique des lentilles intraoculaires (LIO) multifocales et l’acuité
visuelle avec correction de la distance de près, intermédiaire et de loin afin de déterminer le degré de
modification nécessaire de la qualité optique en vue d’obtenir une différence significative en termes d’acuité
visuelle.
CADRE : Fundación Oftalmológica del Mediterráneo, Valence, Espagne.
MÉTHODES : l’acuité visuelle monoculaire avec correction de la distance (décimale et logMAR) a été mesurée à
4 m, 70 cm et 30 cm dans des conditions photopiques et mésopiques chez des patients portant un des trois
modèles de LIO multifocales. L’acuité visuelle a été évaluée par rapport à la « modulation moyenne » des LIO.
RÉSULTATS : le diamètre de la pupille et l’âge des patients étaient similaires dans les trois groupes LIO (20 yeux
chacun). Une différence de modulation moyenne (c’est‐à‐dire la qualité optique) allant jusqu’à 15 % n’a
entraîné aucune différence significative de l’acuité visuelle moyenne entre deux groupes ; cependant, une
différence non négligeable a été observée en termes d’acuité visuelle moyenne entre deux groupes lorsque les
valeurs de modulation moyenne différaient d’au moins 25 %.
La pente de la corrélation linéaire entre l’acuité visuelle et la modulation moyenne était de 0,018 (r2 = 0,91)
dans des conditions photopiques et de 0,024 (r2 = 0,089) dans des conditions mésopiques.
CONCLUSIONS : une forte corrélation linéaire a été observée entre la qualité optique des LIO et l’acuité visuelle
avec correction de la distance dans des conditions photopiques avec une pupille d’environ 3,5 mm, dans une
cohorte où l’âge des patients était contrôlé. La corrélation a été semblable dans des conditions mésopiques. La
tolérance des yeux à la désintégration de la fonction de transfert de modulation a été d’environ 15 % de la
valeur de modulation moyenne.
Divulgation financière : aucun auteur n’a d’intérêt financier ou patrimonial pour tout matériel ou toute
méthode mentionnés.
J Cataract Refract Surg 2010 ; 36:557–562 © 2010 ASCRS et ESCRS