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

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



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:



η, χ  Aη, χe

ϕ



,

(1)





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:





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

corr

and c

target

are constants multiplied to U

corr

and

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





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



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



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

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

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

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

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

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

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

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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