Suppression of Zeroth-Order Diffraction in Phase-Only Spatial Light
Modulator via Destructive Interference with a Correction Beam
Wynn Dunn Gil D. Improso, Giovanni A. Tapang and Caesar A. Saloma
National Institute of Physics, University of the Philippines, Diliman, Quezon City, Philippines
Keywords: 42.30.Kq Fourier Optics, 42.30.Lr Modulation and Optical Transfer Functions, 42.30.Rx Phase Retrieval,
42.40.Jv Computer Generated Holograms.
Abstract: We suppress the unwanted zeroth order diffraction (ZOD) contributed by the dead areas of a spatial light
modulator with a correction beam that is independently created from the desired target. We use the Gerchberg-
Saxton algorithm to generate the phase of the correction beam profile that would match correctly with that of
the ZOD. The correction beam intensity is regulated using a coefficient to match also with that of the ZOD.
Numerical simulation reveals a ZOD suppression that is as high as -99% but only -32% has been achieved so
far experimentally.
1 INTRODUCTION
The increasing capability to manipulate the properties
of light accurately and reliably has opened many
interesting practical possibilities in optics in the past
decade and a half (Eriksen et al, 2002; Polin et al,
2005; Palima and Daria 2007; Nikolenko et al, 2008;
Jenness et al, 2010; Hilario et al, 2014). Complicated
light intensity distributions could be realized by
manipulating the phase or the amplitude, or both.
Most applications have employed the more efficient
phase-only modulation where light loss (from spatial
filtering) is minimal (Zhu and Wang 2014). In phase
modulation, light is tailored through the use of phase
objects such as lenses, prisms, and recently, the
spatial light modulator (SLM).
The SLM allows for the full control of the spatial
phase profile of the propagating beam. The desired
phase distribution is imposed pixel by pixel to the
incident light using a computer generated hologram
(CGH) that serves as the input to the SLM (Eriksen et
al, 2002). Because of its versatility, the SLM has been
widely used in diverse applications such as optical
trapping (Dufresne 2001; Melville 2003),
microfabrication (Jenness et al, 2010; Farsari et al,
1999), microscopy (Shao et al, 2012; Fahrbach et al,
2013) and astronomy (Alagao et al, 2016).
In between two adjacent pixels of an SLM is a non-
functional (dead) area, the size of which is described
by the fill factor F. The light that hits these dead areas
are not modulated by the SLM, and hence results to a
zero order diffraction beam (ZOD) at the optical axis
in the Fourier plane (Palima and Daria 2007). The
ZOD introduces a high intensity illumination that
distorts the desired light profile and undermines the
reconstruction quality.
A commonly used solution to bypass the dire effects
of the ZOD is to shift the light pattern away from the
optical axis. This technique limits the size of the
functional area and reduces diffraction efficiency.
Another approach is to place in an intermediate plane
a physical beam block that fully removes the ZOD
(Polin et al, 2005). This results in a non-accessible
region in the final reconstruction since any part of the
desired pattern that is near the ZOD location of the
ZOD would also be affected. Daria and Palima (2007)
proposed to create a correction beam with the same
profile as that of the ZOD together with the desired
target. Destructive interference is induced between
the correction beam and the ZOD by forcing a -
phase difference resulting in a suppressed ZOD.
However, the technique becomes slow in cases that
involve different desired targets that require a set of
unique CGH profiles. The ZOD and the
corresponding correction beam profile also have to be
precisely matched thereby lengthening the CGH
calculation time.
In this paper, we suppress the ZOD with a correction
beam that is generated via the SLM without a physical
208
Improso W., Tapang G. and Saloma C.
Suppression of Zeroth-Order Diffraction in Phase-Only Spatial Light Modulator via Destructive Interference with a Correction Beam.
DOI: 10.5220/0006129802080214
In Proceedings of the 5th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2017), pages 208-214
ISBN: 978-989-758-223-3
Copyright
c
2017 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
block or a grating. The required phase profile for the
correction beam is independently calculated from the
desired light configuration. The final phase input to
the SLM is described by the field addition method as
discussed by Hilario et al. (2014).
We calculate the hologram input that contains the
phase information needed for constructing the
correction beam and the desired target. The
holograms serve as inputs to the SLM. The technique
is described and evaluated in the next Section.
2 FIELD ADDITION METHOD
AND EXPERIMENTAL
VERIFICATION
The SLM that is used is Hamamatsu PPM X8267,
with F = 0.8. The SLM has a 20 20
window corresponding to768 768 pixel size.
2.1 Phase Calculation
For suppression to succeed at the Fourier plane, there
must be full destructive interference between the
unwanted ZOD and the correction beam, which is
possible when their profiles are correctly matched -
the total energies of the correction beam and the ZOD
are equal and their phase difference is equal to
(destructive interference).
The phase needed to construct the correction beam
ϕ

η, χ where η and χ are the coordinates, is
calculated using the Gerchberg-Saxton algorithm, a
phase retrieval algorithm consisting of forward and
inverse Fourier transforms. The constraint in the SLM
and reconstruction plane is the aperture and the ZOD
amplitude distribution, respectively. The correction
beam will then have a similar profile to the ZOD
The ZOD amplitude distribution is obtained by
simulating the field caused by the dead areas of the
SLM as described by the fill factor. The aperture of
the SLM is oversampled 400 times, meaning each
pixel is sampled to 20 20. Thus the 768 768
SLM will be oversampled to 15360 15360. The
outer pixels of each 20 20 pixel is imposed to have
zero phase shift to simulate the non-modulating dead
areas. The field caused by these non-modulating areas
is then separated and propagated using Fourier
transform to obtain the ZOD amplitude distribution.
The middle 768 768 of the reconstruction is the
ZOD amplitude. This is shown in Figure 1.
Figure 1: The calculation for ZOD target.
The phase to construct a desired target, ϕ

η, χ,
is also calculated. The desired target represents the
application that will be done using the SLM. In this
work, the change in the ZOD intensity is measured
and therefore the target must not have any intensity
near the ZOD.
The fields due to ϕ

η, χ and ϕ

η, χ are
then given by:
U

η, χ Aη, χe
ϕ

,
(1)
U

η, χ Aη, χe
ϕ

,
(2)
where Aη, χ is the amplitude at the aperture of the
SLM. The phase input to the SLM, ϕ

η, χ is then
given by:
ϕ

η, χ
Arg







(3)
where Arg function gives the phase, ϕ

the
constant phase added to induce destructive
interference between ZOD and correction beam, and
c
corr
and c
target
are constants multiplied to U
corr
and
U
target
, respectively. The constants are used to control
the amount of light used to reconstruct the correction
beam and target, and has the following constraint:
c

c

1
(4)
Coefficients c
corr
and c
target
are scanned from zero to
1. If c
corr
is greater than c
target
, this means that the
correction beam has higher total light intensity than
the target. The best result is when ZOD is suppressed
at low values of c
corr
since this means that more
energy is used to create the desired target. ϕ

,
is
scanned from 0 to 2 in increments. It is assumed that
the dead areas impose constant phase shift over the
whole SLM aperture and thus we need to obtain the
correct phase shift so that destructive interference
occurs between the ZOD and correction beam.
Suppression of Zeroth-Order Diffraction in Phase-Only Spatial Light Modulator via Destructive Interference with a Correction Beam
209
The calculation of ϕ

is shown in Figure 2. ϕ

is
converted to 8-bit images using the phase response of
the SLM.
Figure 2: Calculation for the phase input SLM, ϕ

η, χ.
2.2 Optical Implementation
Light hits M1 and then a half-wave plate that ensures
a correct polarization of the incident light to the SLM
(see Figure 3). It is then directed to 10 expander
set-up by M2. The expander set-up is composed of L1
and L2 ( 10 and 100,
respectively). This expands the beam 10 to fill the
back aperture of the objective lens (OL, 4, 
0.16). At the focus, a pinhole (PH, 25μ) is
placed to spatially filter the light. L3 ( 300)
is positioned 300mm from the PH. The output is a
collimated plane wave directed to the SLM (
0.8, 20 20) using a beam splitter (BS).
Hologram is inputted to the SLM using a computer.
Light that is reflected from the SLM then is focused
by L4 ( 300) to a camera. Neutral density
filters (NDF) are placed before L4 to control the
intensity of light that hits CCD (6.40
4.80, 640 480) and avoid
light saturation. The images from the CCD are
captured by computer (not shown).
Figure 3: The optical set-up.
The initial ZOD value is determined with a hologram
that reconstructs the desired target only in the
experiment. NDFs are added or subtracted to avoid
saturating the camera. The image is then captured and
the original ZOD intensity is obtained by summing
the total intensities around the ZOD area to yield the
I
ZOD
information. The computed phase is then
inputted to the SLM. We used 33 values of c
corr
from
0 to 1. For each c
corr
value, the phase shift ranges from
0 to 2. For each phase input, we obtain the I
method.
Which is given by total ZOD intensity at a constant
NDF value. The relative intensity R is then calculated
using the following equation:




100% (5)
where R > zero means a decrease in ZOD intensity
indicating either a constructive interference between
the correction beam and the ZOD, or a total correction
beam energy that is overshooting that of the ZOD.
Even when the destructive interference is total,
sufficient energy can still remain in the correction
beam to create another ZOD. A value of R = 0
indicates that nothing has changed while R < 0
implies a decrease in the total ZOD intensity. The
ideal suppression result is: I
method
= 0 or R = -100%.
3 RESULTS AND DISCUSSIONS
3.1 Experimental Results
Figure 4 illustrates the dependence of R with ϕ

for different values of c
corr
. The minimum R value is
located at ϕ

= 0, 2Linear behaviour happens
when c
corr
~ 1 due to saturation in the camera. When
constructive interference happens, the highest
possible intensity can saturate the camera.
Figure 4: Relative intensity R vs.

for different c
corr
.
PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology
210
For each c
corr
value, the corresponding ZOD image is
taken with the minimum R value (see Fig. 5). The
total ZOD intensity is visually observed to gradually
reduce as c
corr
increases.
Figure 5: ZOD with lowest R per c
corr
(frame size: 15
2
pixels).
Figure 6 plots the average minimum R for a given c
corr
(three trials per point). The minimum R is steady for
low c
corr
values (up to c
corr
equal to 0.3). The R value
then decreases until c
corr
= 0.82, where a ZOD
suppression of -32% is achieved relative to its
original value. It does not change significantly for
c
corr
> 0.82.
Figure 6: Average minimum R for a given c
corr
.
3.2 Numerical Simulation
To describe the effects of ZOD suppression with a
correction beam, we numerically model the
performance of an SLM with a fill factor F of less
than 1. We assume that only the dead areas affect the
phase input and contribute to the ZOD intensity.
The simulation with F < 1 is performed by
oversampling each hologram similar to the
calculation of the ZOD (see Fig. 1). Oversampling is
achieved by sampling each pixel at intervals that is
much less than the pixel dimensions. In our case, each
pixel is sampled 400times20 20 sampling
points). To simulate the effect of the non-working
(dead) areas, the outer pixels are assumed to have a
zero phase shift contribution. We use a fill factor of F
= 0.81.
First, we compare the correction beam profile with
that of the ZOD. Propagating the field without the
oversampling results to a reconstruction without the
ZOD that produces only the desired target and the
correction beam. The correction beam profile (S
corr
)
is compared to the ZOD (S
ZOD
) using the Linfoot’s
criteria of method (Tapang and Saloma 2002). The
following figures of merit are calculated: fidelity (F)
which measures the overall similarity of two profiles:
1






; structural content (C)
which measures the relative sharpness of peak
profiles: 




; and correlation quality (Q),
which measures the alignment of peaks:
|

||

|


. F ranges from -1 to 1 and C and Q
ranges from 0 to 1. If S
corr
and S
ZOD
are perfectly the
same, we have F = C = Q = 1.
Next, we model the suppression of the ZOD by
propagating the field with both the working areas and
the dead areas. We Fourier transform the entire
oversampled field that include the dead areas.
Propagating the oversampled field results to a
reconstruction with higher frequencies. We take the
middle reconstruction, in the zeroth order, and
consider the total ZOD intensity within a 40 40
square area to obtain the ZOD intensity without the
desired target (see Fig. 7).
Figure 7: Simulating the effect of dead areas on the
calculated hologram.
Suppression of Zeroth-Order Diffraction in Phase-Only Spatial Light Modulator via Destructive Interference with a Correction Beam
211
Figures 8a and 8b present the ZOD and the correction
beam reconstructions for different c
corr
, and the line
profiles, respectively. Figure 8c presents the
Linfoot’s criteria of merit versus c
corr
. The results
show that the correction beam profile matches with
that of the ZOD, to allow destructive interference to
occur.
Figure 8: Comparison of ZOD and correction beam
profiles. (a) ZOD reconstruction and correction beam
reconstruction only. (b) Cross section profile of ZOD and
the correction beam for different c
corr
. (c) Linfoot’s criteria
of merit versus c
corr
.
Figure 9 plots R versus ϕ

for different values of
c
corr
. The minimum R is found when ϕ

is equal to
0 and 2, similar to the experimental result.
Figure 9: Relative intensity R versus.

.
Finally, Fig. 10a presents sample images of the ZOD
for different c
corr
, while Fig. 10b plots minimum R
versus c
corr
. The minimum R plot reveals the
possibility of -99% suppression at c
corr
= 0.3125. A
zero ZOD intensity is possible when the correction
beam profile matches perfectly with that of the ZOD
(see Fig. 8) and the remaining task is now matching
the total energies of the two beams. The required total
energy of the correction beam is obtained by tuning
the c
corr
, value.
Figure 10: (a) The ZOD and the correction beam for
different values of c
corr
. (b) Minimum R versus c
corr
. Inlet
shows that minimum R reaches -99% at c
corr
equals 0.3125.
Our experiments produce a degree of suppression that
differs from the numerical prediction. The
experimental results yield a negative value for the
minimum R for all c
corr
. As c
corr
increases, the
minimum R also decreases until c
corr
= 0.82l. On the
other hand, our simulation shows a decreasing
minimum R only until c
corr
= 0.3125. Second, the
simulation predicts a 99% decrease in the ZOD
intensity when c
corr
= 0.3125 but only a 32% decrease
is obtained experimentally and at c
corr
= 0.82.
The difference between simulation and experimental
results at low c
corr
values (low suppression regime),
may be attributed to a low correction beam energy
that limits the degree of suppression. At high c
corr
,
values the discrepancy happens since in calculating
for c
corr
and in simulating the SLM, we have assumed
that only the dead areas of the SLM contributed to
ZOD generation. In practice there might be other
sources that add to the total ZOD intensity that
requires a higher correction beam energy (i.e. a larger
c
corr
value) for suppressing the ZOD. Other possible
sources include imperfection in the anti-reflection
coating (Sars et al, 2012), phase fluctuations (Lizana
et al, 2008) and pixel crosstalk (Engstrom et al, 2012).
Other physical SLM limitations may also affect the
profiles of the ZOD and the correction beam. They
are unaccounted for in the simulation and produce
additional mismatches between the ZOD and
correction beam profiles and limits the strength of the
destructive interference. The input hologram is also
affected by spatial phase variations brought about by
uneven illumination, imperfect flatness and pixel
crosstalk which results to changes in the profile of the
PHOTOPTICS 2017 - 5th International Conference on Photonics, Optics and Laser Technology
212
correction beam, thereby further limiting the
suppression that occurs.
4 CONCLUSIONS
The ZOD suppression has been demonstrated
experimentally by inducing destructive interference
between the ZOD and the correction beam. The
correction beam is created with a desired target using
the SLM. We have assumed that only the dead areas
in the SLM contribute to the ZOD.
We calculate the fields necessary to create the desired
target and correction beam separately, the input
source to the GS algorithm being the aperture
amplitude of the SLM. The final phase input to the
SLM is obtained by calculating the phase of the sum
of the two fields as described by Hilario et al. (2014).
The energy directed to the correction beam is
controlled using multiplicative constants c
corr
and
c
target
.
The calculated holograms were inputted to the SLM,
and the intensity of the ZOD was obtained from the
captured images. We decreased the total intensity of
the ZOD by 32% of its original value when c
corr
is
equal to 0.82.
We have simulated the potential of our technique and
found a degree of a ZOD suppression that is as high
as -99% of its original value which is possible if
perfect similarity is achieved between the profiles of
the ZOD and correction beam.
Differences in the numerical and experimental results
may be attributed to other physical limitations of the
real SLM that are unaccounted for in the numerical
simulations. The said limitations alter the total ZOD
intensity and require a different (higher) c
corr
value for
achieving the highest possible suppression. They can
also alter the phase profiles of the ZOD and the
correction beam with the dissimilarity limiting the
degree of destructive interference that is realized.
Possible misalignments of the optical elements may
contribute to the profile differences as well as change
the relative location of the ZOD and the correction
beam. Addressing the abovementioned limitations
would improve the degree of ZOD suppression that is
achieved experimentally.
ACKNOWLEDGEMENTS
This work was partly funded by the UP System
Emerging Interdisciplinary Research Program
(OVPA-EIDR-C2-B-02-612-07) and the UP System
Enhanced Creative Work and Research Grant
(ECWRG 2014-11). This work was supported by the
Versatile Instrumentation System for Science
Education and Research, and the PCIEERD DOST
STAMP (Standards and Testing Automated Modular
Platform) Project.
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