This document describes an experiment using a spatial light modulator to model optical aberrations, specifically Zernike aberrations, and observe their effects. Zernike polynomials were used to generate images of defocus, oblique astigmatism, coma, and spherical aberration at phase factors of 1, 10, and 25. These images were displayed on the spatial light modulator and their impact on the point-spread function was recorded with a CCD camera. While the experiment demonstrated modeling of aberrations affecting vision, issues around phase wrapping need further investigation.

1. Modelling
Zernike
AberraFons
with
a
SpaFal
Light
Modulator
Kelsey
Darrah1,2
and
Dr.
Brian
Vohnsen2
1.
Case
Western
Reserve
University
2.
UCD
College
of
Physics
Kelsey
Darrah
Case
Western
Reserve
University
Email:
kmd122@case.edu
Contact
1. Jewel,
A.
R.,
V.
Akondi,
and
B.
Vohnsen.
"A
Direct
Comparison
between
a
MEMS
Deformable
Mirror
and
a
Liquid
Crystal
Spa7al
Light
Modulator
in
Signal-­‐based
Wavefront
Sensing."
JEOS:RP
Journal
of
the
European
Op7cal
Society:
Rapid
Publica7ons
8
(2013):
n.
pag.
Web.
2. Liang*,
Junzhong,
Bernhard
Grimm,
Stefan
Goelz,
and
Josef
F.
Bille.
"Objec7ve
Measurement
of
Wave
Aberra7ons
of
the
Human
Eye
with
the
Use
of
a
Hartmann-­‐Shack
Wave-­‐front
Sensor."
Journal
of
the
Op7cal
Society
of
America
A
J.
Opt.
Soc.
Am.
A
11.7
(1994):
1949.
Web.
References
This
experiment
will
demonstrate
the
effect
of
aberra7ons
on
a
collimated
beam
of
monochroma7c
green
light.
Aberra7ons
of
the
human
eye
effect
our
vision.
These
aberra7ons
can
be
represented
using
Zernike
Polynomials.
This
experiment
creates
four
types
of
aberra7ons
using
Zernike
Polynomials:
defocus,
oblique
as7gma7sm,
coma,
and
spherical.
They
are
then
observed
with
three
different
phase
scaling
factors:
1,
10,
and
25.
These
aberra7ons
are
generated
by
means
of
a
liquid
crystal-­‐based
spa7al
light
modulator
SLM
(Holoeye
LC2012).
Their
impact
on
the
point-­‐spread
func7on
PSF
is
recorded
at
the
focal
point
of
a
lens
with
a
CCD
camera.
Large-­‐scale
aberra7ons
are
represented
via
phase
wrapping
which
causes
increased
scavering
and
should
ideally
be
resolved
with
a
modulator
that
would
allow
mapping
of
phase
values
beyond
2 π.
Abstract
Images
were
sent
to
the
SLM
for
phase
scaling
factors
of
1,
10,
and
25.
These
were
viewed
by
a
camera.
Each
of
the
aberra7ons
had
mul7ple
diffrac7on
orders.
The
image
to
the
leN
shows
the
an
image
of
no
aberra7ons
being
sent
to
the
camera.
The
smaller
markings
around
the
brighter
central
one
are
the
diffrac7ons
seen.
The
following
images
focus
on
a
diffrac7on
for
each
phase
factor
(1,
10,
25)
for
defocus,
oblique
as7gma7sm,
coma,
and
spherical
aberra7ons.
IntroducFon
Op7cal
aberra7ons
represent
varia7ons
in
the
light
propaga7on
direc7on
from
the
ideal
of
either
parallel
or
collimated/divergent
rays
as
represented
with
geometric
op7cs.
These
aberra7ons
are
seen
both
in
the
human
eye
and
in
other
areas
of
op7cs,
such
as
astronomy
and
microscopy.
Zernike
polynomials
are
func7ons
of
radius
and
angle
and
therefore
ideally
suited
to
describe
aberra7ons
in
the
human
eye
due
to
the
circular
ocular
pupil.
Common
Zernike
terms
include
defocus,
as7gma7sm,
coma,
and
spherical
aberra7on
that
all
need
to
be
determined
prior
to
their
correc7on
with,
for
example,
adap7ve
op7cs.
Zernike
Polynomials
can
be
displayed
as
gray-­‐scale
images
on
the
SLM
to
cause
aberra7ons
that
deviate
the
light.
Measuring
these
aberra7ons
can
be
applied
to
correc7ng
problems
in
the
human
eye.
This
can
be
done
using
a
simple
adap7ve
op7cs
systems
that
combines
the
SLM
with
a
wavefront
sensor
that
in
closed
loop
operate
as
an
adap7ve
op7cs
system.
Results
Procedure
This
experiment
uses
an
op7cal
set
up
with
a
green-­‐
light
laser
diode
(535
nm
wavelength),
magnifying
lens,
polarizer,
Holoeye
LC2012
SLM,
analyzer,
and
CCD
camera.
To
create
the
Zernike
polynomials,
the
following
equa7ons
are
used
where
r
and
θ
represents
any
point
in
the
pupil
plane:
Defocus
à
Z(r,
θ)
=
√3(2r2-­‐1)
Oblique
As7gma7sm
à
à
Z(r,
Θ)
=2√3r2sin(θ)
Coma
à
Z(r,
Θ)
=2√2(3r3-­‐2r)sin(θ)
Spherical
à
Z(r,
θ)
=
√5(6r4-­‐6r2+1)
These
polynomials
are
scaled
as
phase
factors
here
chosen
as
1,
10,
and
25
and
the
corresponding
grey-­‐scale
images
are
mapped
onto
the
SLM.
Their
impact
on
the
PSF
is
monitored
by
a
CCD
camera.
Examples
of
the
images
sent
to
the
SLM
are
shown
in
the
figures
to
the
right.
This
experiment
was
able
to
model
aberra7ons
that
have
an
effect
on
visual
acuity
of
the
human
eye.
Using
Zernike
polynomials,
the
SLM
displayed
the
aberra7ons
on
the
screen
and
the
impact
of
the
aberra7ons
were
viewed
in
the
PSF
using
a
CCD
camera.
However,
there
are
s7ll
issues
with
the
phase
of
the
aberra7ons
being
wrapped
onto
2π
prior
to
mapping
onto
the
SLM.
This
could
be
overcome
with
future
progression
of
the
work.
This
experiment
could
be
con7nued
using
a
closed
loop
adap7ve-­‐op7cs
system
to
sense
and
correct
these
aberra7ons
in
real
7me
directly
in
the
living
human
eye.
More
types
of
aberra7ons
could
also
be
tested
along
with
combina7ons
of
aberra7ons.
I
would
like
to
thank
Dr.
Brian
Vohnsen
for
allowing
me
to
do
this
research
in
his
lab
and
Dr.
Tadhg
O’Croinin
for
coordina7ng
this
module.
Figure
1:
image
of
coma
aberra7on
Figure
2:
image
of
defocus
aberra7on
Figure
3:
image
of
oblique
as7gma7sm
aberra7on
(with
phase
scaling
factor
=
10)
Figure
4:
image
of
spherical
aberra7on
(with
phase
scaling
factor
=
10)
Conclusions
Figure
5:
image
from
camera
with
no
aberra7ons
show
mul7ple
diffrac7on
orders
from
the
SLM
Figures
6-­‐8:
image
from
camera
with
defocus
aberra7ons
with
phase
factor
=
1,
10,
25
(leN
to
right)
Figure
6
Figure
7
Figure
8
Figure
9
Figure
10
Figure
11
Figure
12
Figure
13
Figure
14
Figure
15
Figure
16
Figure
17
Figures
15-­‐17:
image
from
camera
with
defocus
aberra7ons
with
phase
factor
=
1,
10,
25
(leN
to
right)
Figures
9-­‐11:
image
from
camera
with
as7gma7sm
aberra7ons
with
phase
factor
=
1,
10,
25
(leN
to
right)
Figures
12-­‐14:
image
from
camera
with
coma
aberra7ons
with
phase
factor
=
1,
10,
25
(leN
to
right)