LABORATORY SCIENCE
Light distribution in diffractive multifocal
optics and its optimization
Valdemar Portney, PhD
PURPOSE: To expand a geometrical model of diffraction efficiency and its interpretation to the
multifocal optic and to introduce formulas for analysis of far and near light distribution and their
application to multifocal intraocular lenses (IOLs) and to diffraction efficiency optimization.
SETTING: Medical device consulting firm, Newport Coast, California, USA.
DESIGN: Experimental study.
METHOD: Application of a geometrical model to the kinoform (single focus diffractive optical
element) was expanded to a multifocal optic to produce analytical definitions of light split between
far and near images and light loss to other diffraction orders.
RESULTS: The geometrical model gave a simple interpretation of light split in a diffractive multifocal
IOL. An analytical definition of light split between far, near, and light loss was introduced as curve
fitting formulas. Several examples of application to common multifocal diffractive IOLs were developed; for example, to light-split change with wavelength. The analytical definition of diffraction
efficiency may assist in optimization of multifocal diffractive optics that minimize light loss.
CONCLUSION: Formulas for analysis of light split between different foci of multifocal diffractive
IOLs are useful in interpreting diffraction efficiency dependence on physical characteristics, such
as blaze heights of the diffractive grooves and wavelength of light, as well as for optimizing multifocal diffractive optics.
Financial Disclosure: Disclosure is found in the footnotes.
J Cataract Refract Surg 2011; 37:2053–2059 Q 2011 ASCRS and ESCRS
Supplemental material available at www.jcrsjournal.org.
The design and optical performance of multifocal
intraocular lenses (IOLs) have been described by Davison and Simpson.1 These authors provide an excellent
overview of different multifocal IOL designs with
description of blaze-shape diffractive optic characteristics such as diffraction efficiency as a percentage of
light to diffraction orders. The blaze type of diffractive
surface implies sawtooth-shaped diffraction grooves.
The authors also describe the apodized multifocal
Submitted: November 10, 2010.
Final revision submitted: April 12, 2011.
Accepted: April 21, 2011.
From Vision Advancement LLC, Newport Coast, California, USA.
Financial disclosure: The author has a proprietary interest in the Optivis multifocal diffractive optic.
Corresponding author: Valdemar Portney, PhD, 8 Via Ambra,
Newport Coast, California 92657, USA. E-mail: [email protected].
Q 2011 ASCRS and ESCRS
Published by Elsevier Inc.
diffractive design using the example of the Restor multifocal IOL (Alcon Laboratories, Inc.).
For historical perspective, the concept of apodized
lenses was originally introduced by Cohen,2 who
described a “progressive intensity phase bifocal” lens.
Although diffraction efficiency at a given diffraction
order plays a central role in the imaging characteristics
at that order,3,4 this determination usually lies within
the realm of optical science, leaving a potentially large
gap in understanding by the surgeons who are the
ultimate users of this technology. An additional issue
is the complexity of mathematical diffraction efficiency calculations that plays a negative role in the
ability to optimize diffraction efficiency and improve
the overall image performance of a multifocal diffractive optic.
In this study, I applied the geometrical model to diffraction multifocal optics to interpret light distribution
between far and near foci in terms of refraction, which
offers a more intuitive understanding of diffraction
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doi:10.1016/j.jcrs.2011.04.038
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LABORATORY SCIENCE: LIGHT DISTRIBUTION IN DIFFRACTIVE MULTIFOCAL OPTICS
optics by surgeons who are interested in diffractive multifocal IOLs. This article also provides formulas that allow an analytical determination of light split between
far and near in relationship to blaze height (step height
of the diffractive groove) and light wavelength as well
as a determination of light loss (ie, light directed to the
diffraction orders that are outside far and near foci
and thus play a negative role in image quality and photic phenomena). Examples are provided for application
to common multifocal diffractive optics.
MATERIALS AND METHODS
The theory of scalar diffractive optics was used as a basis for
the determination of light distribution in multifocal diffractive IOLs. A broader description of scalar diffractive theory
can be found in the article by O’Shea et al.5 Londo~
no and
Clark6 introduced a geometrical model for modeling diffraction efficiency in the kinoform. The geometrical model
applied to a single-focus optic was expanded to a blazetype multifocal diffraction optic in this paper.
Equation 1 is the basis of the scalar diffractive optic and is
called sinc envelope.
hðm; mÞ Z Sinc2 ½pðm m0 mÞ
m0 Z 1; which is the diffraction order for near focus;
m Z 0; which is the diffraction order for far focus; and
0%m%1
F function FðmÞ Z
(1)
SinðxÞ
with x Z ½pðm m0 mÞ
x
where h is the diffraction efficiency at m-order of diffraction,
m0 is the diffraction order for which the diffraction efficiency
is 100% at the design wavelength, and parameter m Z 1. A
physical meaning of the parameter m is explained below.
Equation 1 is called sinc envelope in scalar diffractive optics
with blaze-shape diffraction grooves because it defines the
amplitude of light at the diffraction order. Sinc envelope in
the form of h(m) Z Sinc2[p(m a)] is a well-known scalar
diffraction optic formula used for diffractive multifocal
optics with diffraction grooves approximated by a parabolic
profile and where the parameter a is a phase shift at the maximum depth of the diffraction groove step.7–9 Conceptually,
different profiles, such as sinusoidal or binary, can be used,
which would result in a different formula for diffraction efficiency.7,10 Details of the actual profiles of the blaze diffractive
multifocal IOLs referenced in this article are not in the public
domain. Nevertheless, there is indication that these profiles
can be approximated by a parabolic profile and the sincenvelope definition can be applied to their diffraction
efficiencies.8,11,12
The geometrical model introduces a blaze ray as an imaginable ray refracted at a surface point of a diffraction groove,
and the sinc envelope is centered over this blaze ray and
defines light distribution around it along the optical axis.6
The actual light split between different diffraction orders is
defined by the intersection of this light distribution around
the blaze ray with the locations of the diffraction orders
along the optical axis. Figure 1 shows the sinc envelope
and the meaning of blaze ray and the corresponding terminology used with multifocal diffractive optics.
In the case of a multifocal ophthalmic diffractive lens, the
parameters in equation 1 are
SincðxÞ Z
The parameter m is called the blaze-ray ratio because it defines a relative direction of the blaze ray in relation to the directions toward the far and near foci. According to the
geometrical mode, the blaze-ray ratio replaces the phaseshift parameter a in the sinc envelope, as shown in equation
1. Thus, instead of dealing with phase shift, which is an abstract term, and corresponding complex mathematics, one
can work with blaze-ray ratio defined by the refraction of
the blaze ray. The term refraction is more commonly understood and offers a more physically tangible explanation of
light split by a diffractive multifocal optic.
In a small-angle approximation, m is the ratio of the angle
between the blaze ray and the direction toward 0-order
diffraction (far focus) to the angle between the directions
toward 0-order and (1)-order (near focus). For example,
the blaze-ray ratio equals 1 if the blaze-ray direction coincides with the direction toward (1)-order diffraction
(near), as shown by sinc envelope A in Figure 1, B.
Using diffraction efficiencies per equation 1 at far focus
(m Z 0) and near focus (m Z 1), we can construct the functions defining diffraction efficiencies at far focus, near focus,
and the light loss to other diffraction orders as functions of
the blaze ray ratio m as follows:
N-function NðmÞ Z
hð0; mÞ
hð0; mÞ þ hð1; mÞ
hð1; mÞ
hð0; mÞ þ hð1; mÞ
L-function LðmÞ Z 1 FðmÞ NðmÞ
(2)
(3)
(4)
where F-function defines a fraction of light between far and
near directed to far focus as the function of the blaze-ray ratio
m, N-function defines a fraction of light between far and near
directed to near focus as the function of the blaze-ray ratio m,
and L-function defines a fraction of light outside far and near
foci as the function of the blaze-ray ratio m.
Diffraction efficiency determined by a blaze-ray relative
position within the sinc envelope varies between the blaze
rays at different locations in the presence of ocular aberrations. To generalize a blaze-ray application to light distribution between the diffraction orders to a diffraction lens as
a whole, a contribution of ocular aberrations is ignored.
This enables a comparison of different designs of the diffraction multifocal IOLs based on the geometrical model of the
diffraction efficiency.
A relative direction of a blaze ray and, therefore, the blazeray ratio m, depends on 3 factors: blaze height, wavelength of
the light, and dispersion of the material. Each factor is consecutively represented in the formula below:
hðrÞ
l0
nðlÞ nw ðlÞ
(5)
ðmÞ y
l
h1
nðl0 Þ nw ðl0 Þ
where h(r) is the blaze height as a function of distance (r)
from the lens center; h1 is the blaze height that produces
the kinoform at (1)-order, that is 100% diffraction efficiency
at (1)-order; l0 is the design wavelength, that is the wavelength at which the diffraction efficiency and add power of
the multifocal IOL is designed, and this is usually set at the
peak of retinal response l0 Z 0.55 mm; l is a wavelength of
light that is actually diffracted by the multifocal diffractive
optic; n(l) and n(l0) are the refractive indices of the lens material at wavelengths l and l0, respectively; nw(l) and nw(l0)
are the refractive indices of the eye medium adjacent to the
IOL diffractive surface at wavelength l and l0, respectively.
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LABORATORY SCIENCE: LIGHT DISTRIBUTION IN DIFFRACTIVE MULTIFOCAL OPTICS
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Figure 1. A: Light diffraction by a diffraction optic towards diffraction orders. The imaginable blaze ray is defined by the refraction at a diffraction
groove surface. The blaze ray is refracted along the middle direction between directions toward far and near foci (direction B), which is equivalent
to the Tecnis multifocal IOL design. Directions toward diffraction order serve as the “channels” along which light can only travel but the direction of the blaze ray determines the light split between these channels as explained in Figure 1, B. B: Sinc envelope is centered over a blaze ray
according to scalar diffraction optics. Sinc envelope A is centered over the blaze-ray direction coinciding with the direction to (-1)-diffraction
order. It results in 100% of light allocation to this order because values of sinc envelope are zeros at all other diffraction orders. Sinc envelope
B is centered over the blaze ray direction at the middle between 0-order (far) and (1)-order (near), as shown in A. Sinc envelope B shows light
diffraction to multiple orders because it has approximately 40% value at each 0-order (far) and (1)-order (near) and the remainder approximately 20% at other orders.
The contribution of a material dispersion particularly in
the aqueous humor is fairly small (Appendix, available at
http://jcrsjournal.org) and is neglected in this paper, bringing the blaze-ray ratio m to the following expression:
hðrÞ
l0
(6)
mðr; lÞ y
l
h1
An objective of this article is to define all 3 functions of
equations 2, 3, and 4 in an analytical form for direct calculation of light split between far, near, and outside the image range (light loss) for different multifocal diffractive
optic designs and to allow optimization of a multifocal diffractive optic that reduces the light loss outside far and
near foci.
The following multifocal IOLs are considered in the
analysis for light distribution: the Tecnis multifocal (Abbott
Medical Optics), for which the equal light split for the design
wavelength is 0.55 mm; the Acri.Lisa (Carl Zeiss Meditec),
which has a multifocal surface consisting of phase and
main subzones, where the phase subzone acts as the blaze
height and the main subzones as a blaze multifocal, with
light split 65/35 for far to near13,14; and the Restor, which
has an apodization form. The apodization, in general, was
described by Lee and Simpson,15 but not as a specific function h(r). Nevertheless, the apodization form of the Restor
IOL can be determined from published information on the
light split for a given pupil diameter.1 The OptiVis multifocal
IOL uses the principle of more unequal light split between
far and near foci.A The IOL design is more complex than
that of a traditional diffractive multifocal IOL because it includes a refractive zone of progressively varying power
that incorporated intermediate foci into the IOL specifications.16 The progressive power variation incorporated a similar principle in the previously introduced refractive
multifocal IOLs, such as the Array (Abbott Medical Optics)
and Rezoom (Abbott Medical Optics).17,18
RESULTS
Functions of diffraction efficiencies at far, near, and
outside the vision range shown in equations 2, 3, and
4 are depicted graphically in Figure 2: 100% diffraction
efficiency at near corresponds to the blaze ray ratio
m Z 1, and at far to m Z 0.
Equation 1 was applied to equations 2, 3, and 4 to
calculate the corresponding diffraction efficiencies
and then the curve fitting was applied in order to
arrive at simple analytical formulas that can be more
easily included for optical design software or even
for “by hand” calculations in diffraction multifocal
Figure 2. Relative light split between far (F-function) and near (Nfunction) as fractions of their sum and relative light loss outside
far and near foci (L-function) as functions of blaze ray ratio m. The
maximum light loss occurred at the blaze ray ratio m Z 0.5, where
approximately 80% of light is equally split between far and near
foci. The light loss is reduced with a more unequal split between
far and near.
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optic analysis. Curve fitting yields the following analytical descriptions of F-, N-, and L-functions within
G0.3% tolerance of the curves in Figure 2:
(7)
NðmÞ Z 1:012 exp 5 m2:9
The F-function and the N-function are symmetrical
around the blaze-ray ratio m Z 0.5; therefore
FðmÞ Z Nð1 mÞ
(8)
and
LðmÞ Z 0:096 sinP
180
ð6:1 mÞ 1:5R þ 0:094
p
(9)
where the argument of sine function is in degrees. The
Excel program uses (Microsoft Corp.) radian in trigonometric functions, and a multiplication by 180/p in
sine argument should be omitted if the Excel program
is used in the calculation.
A blaze-ray ratio m is defined by equation 6 and is
a constant in monochromatic light if the blaze height
h(r) is also a constant. On the other hand, m is variable
with distance to the lens center (r) if blaze height h(r)
varies with the distance to the lens center due to
apodization.
Let us apply the F-, N-, and L-functions to multifocal
diffractive IOLs.
Tecnis Multifocal Intraocular Lens
Let us look into light split at different wavelengths:
design wavelength 0.55 mm (green color), 0.45 mm
(blue color), and 0.63 mm (red color). The constant
blaze height of the Tecnis multifocal IOL is such that
the blaze ray is refracted exactly at the middle between
far and near foci for the design wavelength 0.55 mm resulting in m Z 0.5. Blaze-ray ratios are calculated from
equation 6 at different wavelengths, and light split is
determined from equations 7 to 9. Table 1 shows the
results.
Acri.Lisa Multifocal Intraocular Lens
The Acri.Lisa multifocal IOL is not a blaze-shape
multifocal but can be converted to the form equivalent
to a blaze shape for light-split analysis. Phase subzones of this IOL are shaped to provide far refraction
power. A measurement indicates that a phase subzone
is approximately equal to 0.16th of the total diffractive
groove size, meaning that the additional approximately equal to 0.16th of light is directed to far focus
that otherwise is lost from the corresponding groove
area.
Using equations 7 to 9 and the iterative process for m,
one can correlate the 65/35 ratio with the corresponding blaze diffractive lens that directs 52% of light to far,
30% to near, and 18% is light loss. The phase subzones
provide an additional 0.16 $ 18%, approximately equal
to 3% of light for far focus bringing the total fraction of
far light to 55%, thus making the far to near ratio equal
to 55/30 to approximately 65/35 as per the published
specification. Thus, the phase subzones reduce the
light loss from 18% to about 15%.
The far:near ratio without the contribution of the
phase subzones is approximately 63/37, according to
52% for far distribution and 30% for near distribution,
with the remainder being light loss. The iteration of
equation 7 yields a blaze-ray ratio m approximately
equal to 0.433 for the design wavelength 0.55 mm for
near-split fraction of 0.37. Blaze-ray ratios at different
wavelengths are calculated per equation 6, and the
corresponding light split is determined from equations
7 to 9 assuming a blaze shape of the diffractive surface
(ie, without phase-subzone contribution). The light
distribution for far is increased by 3% at each wavelength with the contribution of the phase subzones
and with material dispersion neglected. Table 2 shows
the corresponding chromatic light split and percentage of light loss.
Restor Multifocal Intraocular Lens
Apodization results in the blaze-ray ratio m being
a function of distance to the lens center (r) per equation
6, where the blaze height h(r) is a function of the distance (r). It is more useful in the case of apodization
to convert F-, N-, and L-functions into functions of
(r), which is a means of demonstrating the
apodization.
Figure 3, A, shows the light split with the addition of
a Restor light-loss graph calculated as the residual to
Table 2. Acri.LISA multifocal IOL chromatic light split.
Table 1. Tecnis multifocal IOL chromatic light split.
Light Split
Wavelength (mm)
0.55 (green)
0.45 (blue)
0.63 (red)
Blaze-Ray Ratio m
Far to Near
Loss %
Wavelength
(mm)
Blaze-Ray
Ratio m
0.5
0.611
0.437
50/50
29/71
62/38
19
17
18
0.55 (green)
0.45 (blue)
0.63 (red)
0.433
0.529
0.379
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Light Split with Phase-Subzone
Contribution
Far to Near
Loss %
65/35
46/54
76/27
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LABORATORY SCIENCE: LIGHT DISTRIBUTION IN DIFFRACTIVE MULTIFOCAL OPTICS
corresponding blaze ray ratio as a function of lens
radius. A function of the blaze-ray ratio is defined
numerically per small steps of the lens radius by
iteration of equation 7 for near-light fraction. Blazeray ratios are then calculated from equation 6 for
different wavelengths at each lens radial step, and
the corresponding apodization forms for short and
long wavelengths are determined from equations
7 to 9. The effective light splits at 3.0 mm diameter at
different wavelengths are then defined by integration
of the corresponding apodization form for the diameter. Table 3 shows the results.
Figure 3. A: Light split within a pupil diameter. The graphs include
a combination of diffraction and refraction contributions outside the
diffraction zone and do not illustrate a light split at a given diameter
of the diffraction zone, which is shown by the apodization form in B.
B: Restor multifocal IOL apodization form. The light split at each optic diameter shows an equal and constant light split for up to approximately 2.0 mm diameter and then a gradual increase of a fraction of
light directed to far, thus reaching 100% at 3.6 mm diameter at the
edge of the diffraction zone.
100% from the sum of far and near. Light-split graphs
in Figure 3, A, define the fractions of light within
different pupil diameters, and the apodization form
defines a light split at each optic diameter to help characterize the light split by the diffraction zone itself.
An apodization is then calculated by differentiating
the light split within the pupil; the corresponding
apodization form of the Restor multifocal IOL is shown
in Figure 3, B. The blaze-ray ratio function m(r),
and therefore the apodization defined by a blaze height
function h(r). can be determined by combining the local
loss graph of the apodization form in Figure 3, B, and
equation 9.
Blaze-ray application to the Restor multifocal IOL
takes a slightly more complex form because the
blaze-ray ratio varies with the distance from the lens
center (lens radius) according to the apodization design. Light distribution varies with the lens radius
and can be defined at a certain lens diameter as effective light distribution, for instance at 3.0 mm diameter
corresponding to a nominal photopic pupil size. The
apodization form of the Restor multifocal IOL for the
design wavelength 0.55 mm is used to determine the
OptiVis Multifocal Intraocular Lens
Figure 2 shows that light loss can be reduced by
apodizing the OptiVis multifocal IOL in such a way
that it splits the larger fraction of light to far focus or
to near focus.
The use of the equations 7 to 9, together with
a Zemax ray-tracing program for image quality calculation, yielded the OptiVis multifocal IOL apodization
form shown in Figure 4, A, and the relative energy
distribution with pupils for far, intermediate, and
near with small light loss shown in Figure 4, B.
Blaze-ray application to the OptiVis multifocal IOL
takes a more complex form because of the presence
of a central refractive zone of intermediate and far
powers in addition to apodization within the diffraction annular zone of 1.5 mm and 3.8 mm diameters.
The calculation of light split at different wavelengths
follows the procedure described for the Restor multifocal IOL without a contribution of the central refraction
zone (ie, refractive zone contribution to far is assumed
to be zero). Then, the light split is scaled by the inclusion of the additional light contribution to far by the
central 1.5 mm refraction zone, where the far to intermediate split is 35/65. No light loss is contributing
from the central zone because of the refraction nature
of the zone. Table 4 shows the results.
DISCUSSION
The curves of diffraction efficiencies for far and near in
Figure 2 are equivalent to the one in Figure 2, B, by
Cohen.7 The advantage of the functions per equations
Table 3. Restor multifocal IOL chromatic light split for 3.0 mm
diameter.
Light Split
Wavelength (mm)
0.55 (green)
0.45 (blue)
0.63 (red)
J CATARACT REFRACT SURG - VOL 37, NOVEMBER 2011
Far to Near
Loss %
68/32
50/50
75/25
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Table 4. OptiVis multifocal IOL chromatic light split for 3.0 mm
diameter.
Light Split with Central Refraction
Zone Contribution
Wavelength (mm)
0.55 (green)
0.45 (blue)
0.63 (red)
Figure 4. A: OptiVis multifocal IOL apodization form of the multifocal diffractive zone shows that a relatively small area of the lens corresponds to a substantially equal light split between far and near
associated with larger light loss. The local loss shows a relative light
loss at a given radial distance from the lens center. B: OptiVis multifocal IOL light split within pupil diameter shows relative energies
between foci within different pupils. The light loss graph is the integration of local loss of the apodization form within a pupil diameter.
The light loss is reduced because of the presence of the refractive
zones at both sides of the diffractive zone with their 100% light utilization and thanks to the optimized apodization form.
3, 4, and 5 is that they transfer diffraction efficiency calculations per scalar diffraction optic into simple Snell
law of refraction of the blaze ray defined by the geometrical optic.
This article offers analytical definitions of light split
per known blaze heights and wavelength. The importance of the material dispersion for the light split can
also be assessed. A comparison with the analysis by
Castignoles et al.,4 in which the material dispersion
was taken into account, shows that the results did
not differ substantially. The conversion of the absolute
split 0.26/0.6/0.14 for 0.45 mm wavelengths between
far, near, and loss (parabolic blaze shape) to the relative split of far to near yields approximately 30.2 to
70 in Castignoles et al.4 versus 29 to 71 in Table 1. In
the case of red light of 0.63 mm wavelength, the light
split of far to near is about 62 to 38, coinciding with
the results in Table 1. The difference at short wavelength is likely associated with the material dispersion.
The analysis by Castignoles et al.4 allows a rough assessment of the impact of light split on the modulation
Far to Near
Intermediate %
Loss %
41/59
36/64
48/52
16
16
16
4
4
8
transfer function (MTF) as the measure of retinal
image quality. For instance, a change from 50/50 of
far to near light split to about 30/70 (a split in blue
light) changes the MTF at 50 line pairs (lp)/mm from
0.33 to 0.18 for far and 0.55 for near and a change to
62/38 split (a split in red light) changes the MTF at
50 lp/mm to 0.40 for far and 0.23 for near.
The formulas of the F-, N-, and L-functions in this article allow analytic assessment of light split between
far, near, and light loss in a blaze-shape multifocal diffractive optic at different wavelengths and blaze
heights. In the case of an apodization, the functions
are converted into a apodization form, where a light
split is defined as a function of surface coordinates.
A shape of the graph in the apodization form may be
similar to the relative energy graphs as shown for
the Restor multifocal IOL; however, a particular benefit comes into play when a refractive zone contributes
to a light distribution because an apodization form
demonstrates a light split by the diffraction only. For
instance, the peripheral refractive zone of the Restor
IOL affects the light energy split outside the diffractive
zone, making the relative energy graphs different from
the Restor multifocal IOL apodization form. In another
example, the presence of the refractive zones at both
sides of the diffractive zone in the OptiVis multifocal
IOL results in the relative energy graphs being significantly different from the OptiVis multifocal IOL
apodization form.
The geometrical model of light distribution allows
comparison of different diffractive multifocal designs
for light-split sensitivity to a wavelength of light. For
instance, the far-to-near split for the Tecnis multifocal
IOL at a short wavelength is 29/71 Z 0.41 and increases to 62/38 Z 1.63 for a long wavelength, corresponding to the change by a factor of 4 as a measure
of chromatic sensitivity. Far-to-near split changes
from a short to long wavelength by a factor of 3.3 for
the Acri.Lisa IOL. Some reduction in sensitivity comes
from the non-equal light split for the design wavelength and the contribution of the phase subzones.
The far-to-near split from short to long wavelength is
reduced to a factor of 3 for the Restor multifocal IOL
for a 3.0 mm diameter. The results of the apodization
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design of the lens at a 3.0 mm diameter is similar to the
chromatic light split by the Acri.Lisa multifocal IOL.
Far-to-near split from short to long wavelength is reduced to a factor of 1.6 for the OptiVis multifocal
IOL. The chromatic sensitivity of far-to-near light split
and light loss are reduced by optimizing the apodization design and by the presence of a central refractive
multifocal zone.
The analytical definition of the diffraction efficiency
described in this article, in combination with a Zemax
ray-tracing program for retinal image quality calculation, assisted in optimizing the light split in the apodization of the OptiVis multifocal IOL by minimizing
the areas of the lens where the light split between far
and near is similar and the light loss is the largest.
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J CATARACT REFRACT SURG - VOL 37, NOVEMBER 2011
First author:
Valdemar Portney, PhD
Medical device consulting firm,
Newport Coast, California, USA