# Passive Frequency Selective Surface Array as a Diffuser for Destroying Millimeter Wave Coherence

Authors: Saiful Islam; Johan Stiens; Gert Poesen; Irina Jaeger; Roger Vounckx
Journal: Active and Passive Electronic Components
 (2008)

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## Abstract

This paper presents the design, construction, and testing of grounded frequency selective surface (FSS) array as a diffuser for destroying millimeter wave  coherence which is used to eliminate speckle in active millimeter wave imaging. To create stochastically independent illumination patterns, we proposed a diffuser based on random-phase distributions obtained by changing the incident frequency. The random-phase diffuser was obtained by mixing up the phase relations between the cells of a deterministic function (e.g., beam splitter). The slot length of FSS is the main design parameter used to optimize the phase shifting properties of the array. The critical parameters of the diffuser array design, such as phase relation with slot lengths, losses, and bandwidth, are discussed. We designed the FSS arrays with finite integral technique (FIT), fabricated by etching technique, and characterized theS-parameters with a free-space MVNA, and measured the radiation patterns with a BWO in motorized setup.


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## Body

## 1. Introduction

Free-space active millimeter wave
(mm-wave) systems have gained more and more attraction during the last few
years due to their indoor security applications.  There is no incoherent mm-wave
source,  and highly coherent mm-wave sources produce speckle in active mm-wave
imaging of conceal objects because of interference phenomenon [1]. The speckle
problem is especially important for active mm-wave imaging as the wavelength in
this frequency range is close to the object dimension [2, 3]. We present here a
frequency selective surface (FSS)-based diffuser array to destroy the coherence
of mm-wave sources. This optical technique utilizes stochastically independent phase
patterns obtained from a grounded FSS array. Nongrounded FSSs have limited bandwidth
and can be viewed as
filters for plane waves at any angles of incidence [4]. They are well
known in the literature for their filtering characteristics at microwave and
millimeter wave frequencies. Generally, FSSs are based on two-dimensional periodic lattice decorated
with resonant elements—including
dielectric or metallic circuit designs [5]. This paper considers the building block of a
simpler and more versatile architecture, where the reflection phase depends on
the resonant slot length.  Such elements
are widely employed as grounded FSS. Using ground plane to the back side of FSS
and also by choosing the proper slot dimensions and unit cell dimensions, such
structure can be designed for full W-band (75–110 GHz)
application. The resonant frequency and the phase of such slotted FSSs can be controlled by varying  slot lengths [6, 7]. The phase variation with
slot length variation is more significant near the resonant frequency [7]. This
property of the grounded FSS is important to design a random-phase diffuser to
destroy the coherence of mm-wave sources. So, it is a novel idea to use FSS
cells with different slot length to control the phase of individual element of
a diffuser array. A diffuser system is an antenna array which receives coherent
plane wave and reflects noncoherent wave by introduction different phase delay
in the reflected wave at each single frequency within the W-band.
The diffuser applies the temporal phase variation to the reflected wave. Actually, due to the different amount
of phase delay, the coherent plane wave after reflection will convert to noncoherent
illumination. The diffuser is like a phase shifter to modulate the phase
properties of coherent wave. If we excite the proposed array with a
monochromatic wave (single-frequency), the reflected wave is still a monochromatic,
but the phase pattern will be different, and the amplitude will be direction-dependent.
To
design such a diffuser different phase delay, elements are needed. In the
proposed diffuser system, the delay element is replaced with FSS cells of
different slot lengths.Reflect array with patch antenna
requires tight fabrication tolerances to achieve desired phase value, as the
patch size versus phase curves are extremely nonlinear [8]. Because of the
rapid phase change around resonance, most reflectarray elements have lengths
within ±5% of the nominal resonant length [8, 9]. This causes phase errors which results for
changes in frequency greater than a few percent. Random phase errors due to
etching tolerances, is usually more critical for patch antenna than Slot FSS
because of the large slope of the phase versus patch-size curves. This effect
also limits the bandwidth. So, it is difficult to design deterministic function
or to get controlled phase response at the desired frequency. By using thick
substrate, the slope of phase versus patch size curve can be reduced but the
quality factor (Q) and the total phase range decrease. As explained in [10], the dual resonant
response of a two layer-grounded FSS array of dissimilar size patch elements was
used to overcome the limitations associated with the use of thick substrates,
but the structure cannot be printed on a single substrate surface; double-side
mask alignment is needed. This means difficulties with the design accurately. The
present design excludes the possibility of obtaining dual frequency operation
since independent control of the dimensions of the slot length is normally
required in each unit cell. It is easier than multilayer design in “[10].” The
phase versus frequency curve of grounded FSS is more linear so no need of tight
fabrication tolerances like patch antenna. The proposed periodic array
structure can be printed on a single substrate surface; double-side mask
alignment is not needed [11]. The structure is the superior alternative to
other broadband elements as the construction of the structure is very much
simpler and cheaper.This paper is organized as follows. Section2 describes
the design, fabrication, and testing of slot length dependence phase variation
of grounded FSS. In practice, the designs of FSSs with different slot lengths
show that FSS can be used as phase-delay circuit. In Section 3, the same
concept is applied to design an FSS array compose of different slot lengths to split
the coherent mm-wave beam for a deterministic function analysis. In Section 4,
the FSS cells of the beam splitter array explained in Section 3 were rearranged
to get a stochastically independent
phase patterns. The reshuffled array gives diffused radiation pattern at every
frequency in W-band which proves that the proposed coherent destroyer is
capable to destroy the coherence of mm-wave by generating random-phase
reflection.


## 2. W-Band Grounded FSSs

The
design of W-band quasioptical filters, consisting of periodically perforated
slots on metal backed Roger 4003C substrate, is considered. As shown in Figure1,
the structure consists of rectangular
slots in 1.5 μm, aluminum on top of 1489 μm grounded Roger 4003C substrate of
dielectric constant εr = 3.38, and loss
tangent 0.0027. Before metallization, a 10 μm benzo-cyclo-butene (BCB)
layer was deposited between the aluminum layer and Roger 4003C to level the
roughness of the Roger 4003C surface. As the thickness of the dielectric wafer Roger 4003C is in
the order of the half wavelength, the structure behaves like a Fabry-Perot resonator.
During the simulation, the structure can be tuned out so that the FSS geometry
can be adapted to a slightly different wafer thickness, without deterioration
of the device characteristics. The resonant frequency can be set properly by
choosing the space between the slots (A and B in Figure 1) and the slot length “a”
and slot width “b.” The simulations of the
structure were carried out by using commercial CST microwave studio software.
Starting the simulation with initial values obtained from calculation of
the approximate resonance condition, final values were determined from CST
simulation results. The unit cell
dimensions were optimized to the value of A = B = 1400 μm.Figure 1
Unit
cell of rectangular slot grounded FSS.We considered three grounded FSSs with slot lengths of
896μm , 970 μm and 1076 μm  and their sloth width of 400 μm
to check the slot length dependence phase variation.  These values are obtained
from the CST simulation. The CST simulation software performs simulation by
using numerical tools of finite integral technique (FIT). In this case, the numerical method
provides a universal spatial discrimination scheme, applicable to various
electromagnetic problems, ranging from static field calculations to high-frequency
applications in time domain. FIT is static up to the THz range. Due to the fact that a computer is only
capable of calculating problems which have finite expansion, we need to specify
the boundary conditions. The basic
functions are calculated numerically by using the perfect boundary approximation.
The perfect boundary conditions were chosen to get the tangential electric and
tangential magnetic fields components uniform inside the slot but outside to
zero. The electric boundary Et=0 (i.e., all tangential electric
fields and normal magnetic fluxes are set to zero) was chosen in the “y” axis direction
and the perfect magnetic boundary
Ht=0 (i.e., all tangential magnetic fields
and normal electric fluxes are set to zero) was chosen in the “x” axis direction
as  in Figure 1.


### 2.1. Measurement Results of FSSs

As
discussed in our paper [7], the measurement amplitude and phase of a grounded
FSS fit well with simulation results. To show the slot length dependence phase
variation (i.e., phase delay), only the measurement amplitude and phase curves
of the FSSs measured with free-space millimeter wave vector network analyzer (MVNA)
are presented here. The reflection amplitudes of the three FSSs are shown in Figure 2. The minimum reflections (S11) at
resonant frequencies are −2.17 dB, −2.53 dB, and −2.68 dB for curves
(i), (ii), and (iii), respectively, which prove that the FSSs reflect in full
W-band, and the total W-band phase is useable in reflection mode. The
realization of slot FSS in compare to the patch demonstrate that for FSS, the
maximum transmission occurs at the resonant frequency. Therefore, there are
losses at resonance since some portion of the energy is lost in the area
between FSS and the ground plane. The FSS suffers higher losses at the
resonance in compare to patch, but the phase variation with frequency of the
FSS is more linear than patch antenna. This property is more advantageous than
the higher reflection gain.Figure 2
Measured
reflection amplitudes of different slot length grounded FSSs. (Slot length of curve
(i) 1076μm, curve (ii) 970 μm, and curve (iii) 896 μm.)Figure3 shows the effect of slot length variation on phase of FSSs in W-band. Near
resonance, a small change of resonant slot length causes a large phase
variation in the FSS phase curve. For example, in Figure 3, at 91.61 GHz, the
phase values of the curves (i), (ii), and (iii) are −259.3˚, −176.6˚, and
−79.16˚, respectively. So, the phase delay between the curve (i) and curve
(iii) is 180˚. At 91.61 GHz, the slot length variation of 106 μm [curve (i)-(ii)]  gives a phase delay  82.7 degree,
and resonance slot length difference of 180 μm [(i)–(iii)] gives a
phase delay of 180 degree. Figure 3
also shows that by changing the slot lengths, the phase delay and phase
gradient can be controlled. We measured total 350˚ phase variation in the
W-band. This value can be increased by decreasing the slot length and by
introducing higher order modes.Figure 3
Measured phase versus frequency
curves, slot lengths as variable parameter. (Slot length of curve
(i) 1076μm, curve (ii) 970 μm, and curve (iii) 896 μm.)


## 2.1. Measurement Results of FSSs

As
discussed in our paper [7], the measurement amplitude and phase of a grounded
FSS fit well with simulation results. To show the slot length dependence phase
variation (i.e., phase delay), only the measurement amplitude and phase curves
of the FSSs measured with free-space millimeter wave vector network analyzer (MVNA)
are presented here. The reflection amplitudes of the three FSSs are shown in Figure 2. The minimum reflections (S11) at
resonant frequencies are −2.17 dB, −2.53 dB, and −2.68 dB for curves
(i), (ii), and (iii), respectively, which prove that the FSSs reflect in full
W-band, and the total W-band phase is useable in reflection mode. The
realization of slot FSS in compare to the patch demonstrate that for FSS, the
maximum transmission occurs at the resonant frequency. Therefore, there are
losses at resonance since some portion of the energy is lost in the area
between FSS and the ground plane. The FSS suffers higher losses at the
resonance in compare to patch, but the phase variation with frequency of the
FSS is more linear than patch antenna. This property is more advantageous than
the higher reflection gain.Figure 2
Measured
reflection amplitudes of different slot length grounded FSSs. (Slot length of curve
(i) 1076μm, curve (ii) 970 μm, and curve (iii) 896 μm.)Figure3 shows the effect of slot length variation on phase of FSSs in W-band. Near
resonance, a small change of resonant slot length causes a large phase
variation in the FSS phase curve. For example, in Figure 3, at 91.61 GHz, the
phase values of the curves (i), (ii), and (iii) are −259.3˚, −176.6˚, and
−79.16˚, respectively. So, the phase delay between the curve (i) and curve
(iii) is 180˚. At 91.61 GHz, the slot length variation of 106 μm [curve (i)-(ii)]  gives a phase delay  82.7 degree,
and resonance slot length difference of 180 μm [(i)–(iii)] gives a
phase delay of 180 degree. Figure 3
also shows that by changing the slot lengths, the phase delay and phase
gradient can be controlled. We measured total 350˚ phase variation in the
W-band. This value can be increased by decreasing the slot length and by
introducing higher order modes.Figure 3
Measured phase versus frequency
curves, slot lengths as variable parameter. (Slot length of curve
(i) 1076μm, curve (ii) 970 μm, and curve (iii) 896 μm.)


## 3. Deterministic Function

Till now, we have shown how phase
delay can be introduced by using FSS of different slot lengths. This investigation
demonstrates that each FSS cell with unique slot length is equivalent to a
delay element, and the amount of delay is determined by the slot length. As an
example of deterministic function realization, mm-wave beam splitter by FSS
array is consider in this section. The idea of this design is to introduce
variable phase delay in constant phase of a coherent mm-wave plane wave to
split the beam in two directions to observe the phase-delay effect. The
schematic diagram of the beam splitter array is shown in Figure4, where every
pattern represents a different slot length. As the slot length variation is in
the order of micron and is less significant in figure, schematic diagrams are
presented instead of real photo arrays. The beam splitter array was designed
with 20 × 20 cells of FSS composite of 20 different
slot lengths, divided in to two subarrays as shown in Figure 4. Each pattern of
Figure 4 represents unique slot length. The column wise patterns represent
different slot lengths and their phase values are listed in Table 1. In the left
10 × 20 cells subarray, all the cells have negative phase values and in the right
10 × 20 cells subarray, all cells have positive phase values. The different
length FSS cells were distributed column wise in such a way that from the center
of the array, the phase delay will increase in both left and right sides of the
array shown in Figure 4. Table 1 shows the slot lengths of FSS cells, their corresponding
phase values (obtained from CST simulations at 94 GHz), and the respective phase
delays. The amounts of phase delays were calculated by using the formula of
geometrical optics, considering the interspacing distances of the FSS cells
(i.e., distance between the centers of two successive unit cells) and for an
off axis beam focal distance of 30 cm from the antenna surface. The FSS array
was designed in a way that both subarrays will bend the beam and will focus 30 cm away from the antenna face. Due to left and right bending, splitted
radiation will be obtained in each frequency.Table 1
Slot lengths,
corresponding phase values, and phase delays of beam splitter. The patterns  of the left most column of the table represent
different columns of Figure4.
Phase
(degree)Slot length
(μm)Delay
(degree)−138˚1097−61˚−128˚1048−54˚−116˚1013−47˚−103˚990−40˚−89˚972−34˚−75˚959−29˚−61˚949−23˚−47˚941−17˚−30˚931−11˚0˚9170˚32˚90332˚49˚89549˚63˚88863˚78˚87978˚91˚87091˚105˚858105˚116˚846116˚127˚832127˚138˚812138˚147˚785147˚Figure 4
Schematic drawing of beam splitter FSS array. (Patterns
follow the values listed in Table1.)


### 3.1. Measurement Results of Beam Splitter

The radiation patterns of the arrays were
measured with backward-wave oscillator (BWO) in motorized setup. The measurement
was carried out with 45˚ angular position of the antenna axis to the BWO
millimeter wave source axis (in measurement Figures 5(b) and 7(b)). The antenna
broad side axis was at 135˚. At 94 GHz measurement, two lobes were obtained at 130˚
and 118˚ due to the phase variation of beam splitting. The measured rectangular and polar radiation
patterns of the beam splitter are shown in Figures 5(a) and 5(b), respectively. In
Figure 5(a), the calibration of the measurement system is shown (marked in legend).
This is the radiation pattern without antenna and just with the antenna holder.
A result shows a good calibration for the antenna measurement setup.Measured near field
radiation pattern of random phase diffuser: (a) rectangular plot (b) polar
plot.
(a)(b)Measured near
field radiation pattern of beam splitter array at different incident frequencies: (a) rectangular plot (b) polar plot.
(a)(b)The measurement radiation patterns at
90 GHz, 94 GHz, and 100 GHz frequencies are presented. The results show that at
each frequency, we get two main lobes on both sides of the antenna broad side
axis. The position of lobes changes with frequency as the phase values of the
FSS cells changes with frequency. Figure5(b) shows the radiation patterns in
polar plot. Maximum reflection for side lobes is obtained at 94 GHz. With the
decreasing or increasing of measurement frequency, the side lobes reflection
power decreases.


## 3.1. Measurement Results of Beam Splitter

The radiation patterns of the arrays were
measured with backward-wave oscillator (BWO) in motorized setup. The measurement
was carried out with 45˚ angular position of the antenna axis to the BWO
millimeter wave source axis (in measurement Figures 5(b) and 7(b)). The antenna
broad side axis was at 135˚. At 94 GHz measurement, two lobes were obtained at 130˚
and 118˚ due to the phase variation of beam splitting. The measured rectangular and polar radiation
patterns of the beam splitter are shown in Figures 5(a) and 5(b), respectively. In
Figure 5(a), the calibration of the measurement system is shown (marked in legend).
This is the radiation pattern without antenna and just with the antenna holder.
A result shows a good calibration for the antenna measurement setup.Measured near field
radiation pattern of random phase diffuser: (a) rectangular plot (b) polar
plot.
(a)(b)Measured near
field radiation pattern of beam splitter array at different incident frequencies: (a) rectangular plot (b) polar plot.
(a)(b)The measurement radiation patterns at
90 GHz, 94 GHz, and 100 GHz frequencies are presented. The results show that at
each frequency, we get two main lobes on both sides of the antenna broad side
axis. The position of lobes changes with frequency as the phase values of the
FSS cells changes with frequency. Figure5(b) shows the radiation patterns in
polar plot. Maximum reflection for side lobes is obtained at 94 GHz. With the
decreasing or increasing of measurement frequency, the side lobes reflection
power decreases.


## 4. Coherence Destroying Diffuser

As explained for beam splitter in Section3, the columnar array of FSS cells mounted on a dielectric substrate, each
column represents a delay element. The delay of each column is determined by its
slot length. To realize the random phase diffuser system, the columns of beam
splitter FSS array of Figure 4 were reshuffled to design the diffuser array. To
get random phase pattern, the columns of Figure 4 were the reshuffled as shown
in Figure 6.Figure 6
Schematic drawing of
coherent destroying diffuser. (Patterns correspond to the phase values listed
in Table1.)


### 4.1. Measurement Results of Diffuser

As already mentioned, the amounts of phase delay listed in Table1 were
calculated at 94 GHz. So, the change of frequency will introduce different set
of phase values at the desired frequency. Due to the random reshuffling of the
FSS columns, reflection at each frequency will be diffused reflection, as the delay
element of the array introduces random phases unlike focusing of beam splitter.
The reflected beams are no longer coherent due to the fact that a random phase introduce from the
random positioning of the FSS cells. At each frequency, the reflection is also diffused
reflection. The measurement results are shown in Figure 7. The same calibration
shown in Figure 5(a) was used for this measurement. For simplicity, the
measurement radiation patterns are presented at 85 GHz, 90 GHz, 94 GHz, 100 GHz,
105 GHz, and 110 GHz. Figure 7(a) shows that every measurement is different in
amplitude direction than the others. The maximum reflection power obtained at 94 GHz
and there is no side lobes like the beam splitter. For the sake of representation,
the angular position of the
detector from 90˚ to 150˚ is shown in rectangular plots of Figures 5(a) and 7(a).


## 4.1. Measurement Results of Diffuser

As already mentioned, the amounts of phase delay listed in Table1 were
calculated at 94 GHz. So, the change of frequency will introduce different set
of phase values at the desired frequency. Due to the random reshuffling of the
FSS columns, reflection at each frequency will be diffused reflection, as the delay
element of the array introduces random phases unlike focusing of beam splitter.
The reflected beams are no longer coherent due to the fact that a random phase introduce from the
random positioning of the FSS cells. At each frequency, the reflection is also diffused
reflection. The measurement results are shown in Figure 7. The same calibration
shown in Figure 5(a) was used for this measurement. For simplicity, the
measurement radiation patterns are presented at 85 GHz, 90 GHz, 94 GHz, 100 GHz,
105 GHz, and 110 GHz. Figure 7(a) shows that every measurement is different in
amplitude direction than the others. The maximum reflection power obtained at 94 GHz
and there is no side lobes like the beam splitter. For the sake of representation,
the angular position of the
detector from 90˚ to 150˚ is shown in rectangular plots of Figures 5(a) and 7(a).


## 5. Conclusion

We have designed a coherence destroying diffuser system using passive FSS
array.  We explained the slot length dependence phase variation properties of
FSS, and also showed how phase delay can be controlled by changing slot
lengths. We presented the design of mm-wave beam splitter as deterministic
function which split the coherent beam in two directions and then shown the
coherent destroyer by reshuffling the cell columns of beam splitter array. This
coherent destroyer can also be used as multifrequency diffuser system. In
multifrequency diffuser system, at each frequency, the radiation pattern is
different, and also the reflection is diffused reflection, that is, the
reflected signal is incoherent. This type of reflector array is capable to
destroy the coherence of the coherent mm-wave sources as the array behaves like
a phase modulator which introduces random
phases. In multifrequency diffuser approach, the frequency difference
should be large enough, since a small difference generates quite similar
speckle distributions [12, 13]. The bandwidth of the proposed diffuser is whole
W-band, which gives the freedom to use enough frequency differences as multifrequency
diffuser.



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*Source: 391745-2008-07-01.xml*