Optics of Intraocular Lenses (IOLs)
I. IOL Overview
II. Monofocal IOLs
III. Accommodating IOLs
IV. Multifocal IOLs
I. IOL Overview
Primary (optical) functions of the crystalline lens:
1. Provide additional refractive power (~ 20 D) to
supplement cornea (~ 40 D) for distance vision.
2. Provide accommodation for near vision (~ 4 D).
3. Provide aberrations that are opposite in sign to those of the
cornea in order to reduce total aberrations of eye.
When it becomes necessary to remove the crystalline lens, an
intraocular lens (IOL) replacement is (hopefully) designed to
provide as many of these same functions as possible.
Additionally, the use of phakic IOLs is being developed to
supplement the optics of the cornea and crystalline lens as a
means to correct vision rather than laser surgery. Since the
crystalline lens is not removed, its functions do not necessarily
need to be replaced by the IOL.
Three primary classes of IOLs:
1. Monofocal – have a single, fixed power to provide correct
distance vision
2. Multifocal – have a more than one power to provide
correct distance and near vision
3. Accommodating – have continuously tunable power that
mimics the accommodative ability of
the crystalline lens
1
In this discussion we will consider the optics of several types
of IOLs that are currently in use or being developed.
II. Monofocal IOL’s
Optical features:
1. Can be relatively simple (single thin lens)
2. Many feature aspheric surfaces to reduce aberrations
(particularly spherical) introduced by cornea. Eventually,
wavefront techniques could be used to customize the
shape to the individual patient. Current techniques simply
use data from a study of “typical patients” to take into
account average spherical aberration of the typical cornea.
3. One interesting phakic IOL under development (Vision
Membrane) utilizes diffractive optics. More on this
later…
III. Accommodating IOLs
Optical features:
1. Single or multiple thin lenses used to effectively make a
“zoom lens” within the eye.
2. Aspheric surfaces could be used (although not currently as
far as I can tell) to help reduce the aberrations introduced
by cornea.
How it works (optically): Thin lens model eye (mostly)
Suppose we replace the crystalline lens with a single IOL to
make an emmetropic eye that can be modeled as shown:
2
Pc = 40 D
n=1
PIOL = 20 D
n = 1.33
19 mm
6 mm
image location
for cornea
cornea
(SSRI)
IOL
3.3 cm
retina
Let’s prove that this eye really is emmetropic. How? Locate
the image of an object at optical infinity – the image should
form on the retina.
1. Find image produced by cornea:
V = U + P, but U = 0  V = P = +40 D
Reduced vergence  V = n/v
so, v = 1.33/40  v = 3.3 cm
(note that this is behind the retina)
2. Image due to cornea acts as image for IOL. Find
image produced by IOL.
V=U+P
Reduced vergence  U = n/u
where u = 3.3 cm – 6 mm = 2.7 cm
so V = 1.33/0.02725 + 20 = 69.3 D
so, v = 1.33/69.3  v = 19 mm
3
To gain some further intution, let’s think of the cornea and
IOL together as a single thick lens. Recall equivalent power
of a thick lens:
Pe = P1 + P2  (d/n) P1 P2
equivalent
power of
system
power of
first lens or
surface
power of
second lens
or surface
correction term for
vergence transfer
through the thickness of
the lens
d is the distance between the first and second elements
n is the refractive index of the material between first
and second elements
Question: Consider the cornea and IOL together acting as a
single thick lens. In what direction would the IOL need to
move in order to increase the overall power of the eye (i.e.
accommodate)?
A. toward the cornea
B. toward the retina
Find equivalent power of emmetropic eye above as thick
lens:
Pe = Pc + PIOL – (d/n)PcPIOL
Pe = 40 + 20 – (0.006/1.33)(40)(20) = 56.4 D
Now find equivalent power of same eye if IOL is moved 1
mm in the direction determined in the question above:
Pe = Pc + PIOL – (d/n)PcPIOL
Pe = 40 + 20 – (0.005/1.33)(40)(20) = 57.0 D
4
Note that the thick lens equivalent power calculations show
that the overall power of the eye has increased as the IOL
moves. However, quantitative calculations about near point
location are difficult to do using this information because the
principal points and nodal points would have to be located
for the eye and these change as the IOL moves.
Question: Suppose we want the near point of the eye to be
40 cm in front of the cornea. How far does the IOL need to
move in order to provide the appropriate amount of
accommodation?
PIOL = 20 D
n = 1.33
Pc = 40 D
n=1
19 mm
6 mm
image location
for cornea
d
cornea
(SSRI)
IOL
3.5 cm
retina
1. Find image produced by cornea:
V = U + P, where U = 1/-0.4 D
 V = -2.5 D + 40 D = 37.5 D
Reduced vergence  V = 1.33/37.5 = 3.5 cm
2. Image due to cornea acts as image for IOL.
Important: want final image to still be on retina!
Find distance IOL must move to make this happen.
5
V=U+P
Reduced vergence  U = n/u and V = n/v
where u = 29 + d mm and v = 19 + d mm
 1.33/(19 + d) = 1.33/(29 + d) + 20 D
this gives a quadratic equation for d to solve
result  d = 2.2 mm
How is the IOL made to move in practice? This is
accomplished by attaching the IOL to the ciliary muscle of
the eye. This muscle can move the IOL by approximately 1
mm. In the case of a single 20 D IOL lens this would provide
a near point of approximately 67 cm (rather than 40 cm in the
example above).
Greater accommodation can be achieved by using an IOL
that consists of two lenses rather than one. In this case, the
lenses are designed to move closer together (or farther apart)
as the ciliarly muscle contracts or relaxes.
IV. Multifocal IOLs
Optical features:
1. Single lens consisting of either regions with different
curvature or diffractive and refractive regions to provide
several focal points (and several images on the retina) at
the same time. The brain selectively chooses which image
to pay attention to and which to ignore based on the
relative brightness of the images and other visual cues.
2. Aspheric surfaces are used in some cases to help reduce
the aberrations introduced by cornea.
6
Two primary types of multifocal IOLs:
1. Refractive – Single lens consisting of regions with
different curvature to provide two focal points.
2. Diffractive – Single lens consisting of diffractive and
refractive regions to provide two focal points
We will consider the optics of these two cases separately.
1. Refractive multifocal IOLs
One particular lens is described here:
http://www.rezoomiol.com/rezoom_multifocal_lens.html
(Note: I am not endorsing this particular product, it is just a
convenient example.)
Some features to notice:
1. Each region of the lens has a radius of curvature that
corresponds to either a power for distance or near
vision.
2. A greater percentage of the total lens area has a
power for distance vision.
3. In bright viewing conditions the pupil will be small
and only the central distance viewing part of the IOL
will be used.
4. In lower light conditions the pupil will be larger
which will lead to two images on the retina, one for
distance and one for near. The distance image will
be brighter since more of the light entering the eye
will experience the distance power regions of the
lens.
7
2. Diffractive multifocal IOLs
Diffraction Grating and Zone Plate Review
A. Path Length Difference and Interference
Idea: The degree to which two mutually coherent waves
constructively or destructively interfere at some point in
space depends on the relative distance that each wave has
traveled in getting to that point.
Consider two light sources that are emitting coherent light
waves. You are standing at a location where one source is
further from you than the other by a distance x. Therefore,
the path length difference (how much farther one wave has
traveled than the other) between the two waves is x.
light
sources
Δx
For constructive interference: x = m (m = integer)
For destructive interference: x = m/2 (m = odd integer)
8
B. Two-slit interference
Coherent light
source
OPD = d sin()

Constructive interference (bright fringes):
d sin mm = 0,  1,  2,…
Question: The figure below shows the pattern created by a two slits
when illuminated by a red He-Ne laser. If the slits are illuminated
by a green laser, which pattern below might results?
red
A
B
9
B. Diffraction Grating
Screen with several hundred (or thousands or tens of thousands)
of very closely spaced slits. Since the slit spacing (d) can be
very small, the angles to the primary maxima can be very large.
The primary maxima locations are still given by the equation:
d sin  = m 
Why?
OPD = d sin()
OPD = d sin()
The OPD between waves
from neighboring slits is
identical since spacing
between slits is same
They are used to separate and measure wavelengths of light in
spectrometers and many other instruments.
m = -2
m = -1
m=0
C. What is a zone plate?
10
m=1
m=2
A zone plate is a type of circular diffraction grating that
uses diffraction (instead of refraction) to focus light.
Since a zone plate focuses light, it can be used as a type
of lens.
It consists of concentric circular apertures of varying
radii and width: wider near the center and more narrow
in the periphery. This is different than an ordinary
diffraction grating in which the slits are spaced evenly
from one another.
D. How does a zone plate work?
1. Suppose plane waves are incident on a circular
aperture. We would like to make point Po (that is
downstream a distance b from the aperture) the focal
point of the zone plate.
Divid
11
e the aperture into circular “zones” (these are the
concentric rings in the zone plate pictured above). The
edge of each zone is /2 farther away from Po than the
edge of the neighboring zone.
2. Notice that the wave that travels along the axis of the
aperture experiences constructive interference with
waves from some of the zones (OPD = m, m=integer)
and destructive interference with waves from other
zones (OPD = m/2, m=odd integer) . If we block the
light from the zones that lead to destructive interference
and allow through the light from the zones that lead to
constructive interference we can produce a net
constructive interference at Po. Therefore, the zone
plate acts like a lens with a focal length f2 = b.
3. “Dioptric power” of a zone plate
The dioptric power of the zone plate is related to
the radii of each zone. In particular:
P

h 12
where h1 is the radius of the 1st zone and is the
design wavelength.

Question: Is the focal length of a zone plate shorter for red or blue
light?
12
Some important features:
a. Chromatic aberration: the power of the zone
plate is proportional to , so different colors focus
at different distances from the zone plate.
Ordinary refractive lenses have chromatic
aberration as well, but much less pronounced than
zone plates.
For example:
+10 D lens made of glass with an Abbe number of
30 (high dispersion) has CA ~ 0.3 D
+10 D zone plate designed for use at 550 nm has
CA ~ 5 D!
b. Multiple focal points due to higher order
diffraction, which is unlike an ordinary refractive
lens which only has one focal point.
c. Light is diffracted both toward and away from
the zone plate’s optical axis. Therefore, the plate
can be designed as either a positive or negative
lens.
E. Zone Plate Images
An interesting comparison of photographs taken with lenses,
zone plates, and pinholes can be found at:
http://www.lensbaby.com/optic-comparison.php
Note the poor quality of the zone plate image (from an optics
point of view, not an artistic one!) This fuzziness of the zone
plate image is due to chromatic aberration and the fact that a
13
significant portion of the diffracted light is spread out into
higher orders than the one making the image.
F. Zone Plates as IOLs
Advantages:
1. No need for curved surfaces so lens can be made flat
and more easily rolled up for surgical insertion.
2. Optical properties such as percentage of light going to
distance and near vision images, aberrations, and
power can be fine tuned by proper design of the zones
without the need for aspheric surfaces.
Disadvantages – Optical quality not as good as standard,
monofocal lens
G. Diffractive IOL Designs
Here we will consider some issues that can be addressed to
improve the optical quality of a zone plate.
(Note: I am not endorsing any of the products shown in this
section, these are just to illustrate some specific examples of
designs currently in use or being developed.)
1. Image dimness – this is partly due to the fact that a large
fraction of the incident light is blocked (by design) by the
zone plate in order to eliminate the waves that would be
destructively interfering at the image.
Solution – Alter the phase of the light from those zones
(rather than blocking them) in such a way that they also
contribute constructively at the image location. How?
14
Review - Optical Path Length
Recall that the wavelength of light changes when the light
enters a medium other than vacuum because of the index of
refraction.
Idea: Since the wavelength of light depends on the index of
refraction of the medium it is traveling in and the phase of
the light depends on the wavelength and the distance traveled
 the phase of the light will depend on the index of
refraction of the medium it is traveling in as well as the
distance traveled.
Light traveling
in vacuum
End at different
points along the
sine curve even
though same
distance traveled
x
Same light
traveling in
glass
Define optical path length as the product of the index of
refraction of a medium and the distance traveled by a light
wave inside that medium.
Alter thickness of zone plate
material so that the optical
path length is increased by ½
 in these regions
+½
+½
15
2. Chromatic aberration – as described above, this is due to
the fact that the process of diffraction inherently separates the
wavelengths because constructive interference occurs at
different angles for each.
Solution – Design the zone plate so that different diffracted
orders of different wavelengths meet at the same location.
(Called Multi-Order Diffraction, or MOD).
To understand this, consider a regular diffraction grating
where constructive interference is found from:
d sin mm = 0,  1,  2,…
m = -2
m = -1
m=0
m=1
m=2
If we design the grating properly, we could make it so the 2nd
order (m = 2) red line occurs at the same location as the 3rd
order (m = 3) blue line. To make this happen we would just
need to have:
d sin redand d sin blue
Notice that the left side of each of these is the same since the
wavelengths are both being diffracted by the same grating
and the wavelengths are being sent to the same angle.
What does this mean in practice? We would follow the
following procedure:
1. Choose our two wavelengths of interest in such a way that
16
2red = blue
(this puts a restriction on which wavelengths will work)
2. Choose an angle (want) that you want the light to be at on
the screen and then manufacture the grating so that:
d
2 red
sin( want )
This grating will then send the 2nd order red light and 3rd
order blue light
 to the same location on the screen.
In fact, we could make a grating that sends even more
wavelengths to the same location as long as the ratios of each
pair of wavelengths are ratios of integers!
A similar procedure can be done for zone plates (since they
are just circular diffraction gratings) so that multiple
wavelengths all have the same focal point.
MOD diffractive lenses are being developed by Vision
Membrane Technologies for use as phakic IOL’s.
Optics and Photonics News, p. 29, September 2004.
17
3. Light Optimization – Zone plates have multiple focal
points leading to multiple images formed on the retina. The
percentage of light found in each of these images may not be
optimal for all viewing conditions. In fact, higher order
diffraction can lead to image degradation.
Solution – Design the zone plate with varying zone optical
thickness (called “apodization”) so that the appropriate
amount of light is sent to each image.
Slowly reduce the optical
thickness of the zones. This
alters the degree of
constructive interference and
the amount of light found at
each focal point.
+¼
+ 3/8 
+½
Apodized diffractive lenses are offered by Alcon Surgical for
use as IOL’s.
Journal of Cataract and Refractive Surgery, Vol. 32, p. 854, May 2006.
18
Figure 1: Small-scale planar computer-generated simulation of diffraction at an
apodized diffractive structure overlaid with a sketch of an eye [Davidson &
Simpson, 2006]
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Figure 2: Aclon ReStor IOL: twelve diffractive rings over the central 3.6 millimeters
of the lens optic. The inner most ring has a step height of 1.3 microns with
subsequent rings gradually decreasing in height until the outer ring with a height of
0.2 microns. The inner rings are further apart and the distance between rings
gradually decreases toward the periphery.
From: http://webeye.ophth.uiowa.edu/eyeforum/tutorials/restor.htm
19
References
M.P. Keating, Geometric, Physical, and Visual Optics, 2nd ed.,
Butterworth-Heinemann (2002).
G.M. Morris and L.T. Nordan, “The New Focus in Refractive
Surgery,” Optics & Photonics News, 27-31, September 2004.
M.J. Simpson, “Diffractive Multifocal Intraocular Lens Image
Quality,” Applied Optics, Vol. 31, No. 19, 3621-3626 (1992).
T. Terwee, H. Weeber, M. van der Mooren, and P. Piers,
“Visualization of the Retinal Image in an Eye Model With
Spherical and Aspheric, Diffractive, and Refractive Multifocal
Intraocular Lenses,” Journal of Refractive Surgery, Vol. 24, 223232 (2008).
S.S. Lane, M. Morris, L. Nordan, M. Packer, N. Tarantino, and
R.B. Wallace III, “Multifocal Intraocular Lenses,” Ophthalmology
Clinics of North America, Vol. 19, 89-105 (2006).
D. Fakalis and M.G. Morris, “Spectral Properties of Multiorder
Diffractive Lenses,” Applied Optics, Vol. 34, No. 14, 2462-2466
(1995).
J.A. Davidson and M.J. Simpson, “History and Development of the
Apodized Diffractive Intraocular Lens,” Journal of Cataract and
Refractive Surgery, Vol. 32, 849-858 (2006).
A. Rana, D. Miller, and P. Magnante, “Understanding the
Accommodating Inraocular Lens,” Journal of Cataract and
Refractive Surgery, Vol. 29, 2284-2287 (2003).
20
J.M. Artigas, J.L. Menezo, C. Peris, A. Felipe, and M. Diaz-Llopis,
“Image Quality With Multifocal Intraocular Lenses and the Effect
of Pupil Size: Comparison of Refractive and Hybrid RefractiveDiffractive Designs,” Journal of Cataract and Refractive Surgery,
Vol. 33, 2111-2117 (2007).
21