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Point-Spread-Function (PSF) Characterization of a 340-GHz ImagingRadar Using Acoustic Levitation
Yurduseven, O., Cooper, K., & Chattopadhyay, G. (2019). Point-Spread-Function (PSF) Characterization of a340-GHz Imaging Radar Using Acoustic Levitation. IEEE Transactions on Terahertz Science and Technology,9(1), 20 - 26. https://doi.org/10.1109/TTHZ.2018.2876418
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Abstract—In this paper, resolution characterization and beam
analysis of a 340 GHz imaging radar are demonstrated by means
of a point-spread-function (PSF) study by imaging an
acoustically levitated point-like target. It is shown that at THz
frequencies, conventional PSF measurement techniques are
limited by the presence of strong scattering response of
background objects, such as suspension threads, within the
imaging field-of-view (FOV). Using acoustic levitation, it is
possible to eliminate secondary objects within the FOV and
achieve a pure PSF characterization of the radar. It is shown that
the PSF patterns obtained using acoustic levitation exhibit high
fidelity and are free from artifacts. We demonstrate this using a
small water droplet suspended in air at the focus of the 340 GHz
radar. The measured PSF characteristics of the radar are in
excellent agreement with physical optics (PO) simulations and
analytical results.
Index Terms—Radar, submillimeter, acoustics, point-spread-
function (PSF), acoustic levitation, imaging, antenna, beam.
I. INTRODUCTION
maging using electromagnetic (EM) waves has been the
subject of much research and proven to be useful across a
large number of applications, from through-wall imaging [1-
5], to non-destructive testing [6, 7], biomedical imaging [8-11]
and security-screening [12-22]. Historically, EM imaging has
mostly involved the microwave and millimeter-wave regimes
because of trade-offs between penetration, antenna size,
imaging resolution, losses, signal-to-noise ratio (SNR) and
component cost. For applications that prioritize imaging
resolution and small antenna size, it might be beneficial to
operate at higher frequencies. The traditional THz regime of
the electromagnetic (EM) spectrum, 0.3 THz – 3 THz, brings
several advantages, including large bandwidths improving the
range resolution, high spatial resolution that can be achieved
using relatively small sized antennas and non-ionizing
radiation. However, a major factor that has prevented the
submillimeter-waves from being widely adopted in imaging
applications has been the lack of mature technology available
O. Yurduseven, K. Cooper and G. Chattopadhyay are with the Jet
Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove
Dr., Pasadena, CA 91109, USA (e-mail: [email protected]; [email protected]; [email protected]). Copyright
Caltech 2018, Government sponsorship acknowledged.
at these frequencies. Over the last couple of decades,
considerable progress has been made in THz electronics that
has resulted in several imaging systems operating at
submillimeter-wave frequencies [23-37].
The beam shape and imaging resolution of a radar can be
assessed by analyzing its point-spread-function (PSF)
response using a point scatterer as an imaging target [18, 38,
39]. Metal beads with a size smaller than or on the order of the
radar resolution can be used to achieve this goal [15-18, 25].
However, using this approach, the reconstructed PSF pattern
includes not only the contribution of the point scatterer, but
also the objects that are used to suspend the point scatterer at
its position within the imaging domain. Such distortions can
significantly degrade the fidelity of the reconstructed PSF
patterns at THz frequencies.
In this work, we demonstrate the application of a low-cost
acoustic levitator [40-42] to obtain the PSF characterization of
a 340 GHz radar system developed by the Jet Propulsion
Laboratory [23-25]. A small droplet of water is levitated and
used as the point scatterer to be imaged. The reconstructed
PSF pattern is compared to the PSF pattern obtained using a
metal bead suspended by a thread, and it is shown that the PSF
pattern obtained with the acoustic levitator exhibits good SNR,
high fidelity and is free from artifacts. The outline of this
paper is as follows: In Section II, the THz radar together with
the imaging process leveraging the acoustic levitator is
described. In Section III, the PSF characterization of the THz
radar is shown. Comparisons between different PSF
characterization methodologies are demonstrated. The PSF
patterns of the 340 GHz radar are compared to numerical and
analytical results. Finally, in Section IV concluding remarks
are provided.
II. THZ RADAR, ACOUSTIC LEVITATION AND PSF
CHARACTERIZATION
A. THz Radar
The THz radar is a frequency-modulated-continuous-wave
(FMCW) system, transmitting a chirped signal centered
around 340 GHz. The block diagram of the RF backend and
submillimeter-wave frontend hardware architectures together
with a picture of the radar is shown in Fig. 1.
Point-Spread-Function (PSF) Characterization
of a 340 GHz Imaging Radar using Acoustic
Levitation
Okan Yurduseven, Senior Member, IEEE, Ken Cooper, Senior Member, IEEE, and Goutam
Chattopadhyay, Fellow, IEEE
I
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(a)
(b)
Fig. 1. (a) Block diagram of the 340 GHz radar’s RF backend
and submillimeter-wave frontend chains showing the
generation of the transmit signal and the down conversion of
the received signal to the IF baseband. (b) Experimental setup
with the three main building blocks of the radar: optics, RF
backend and submillimeter-wave hardware.
As shown in Fig. 1, in the transmit chain, a 16 GHz local
oscillator (LO1) is mixed with a 1.9-3.5 GHz chirp source. The
mixed signal goes through several power amplifiers and
frequency multipliers and is transmitted at 322.2 – 351 GHz
frequency band. The signal reflected from the imaged object is
received by the radar optics and fed to a mixer for down-
conversion. The local oscillator for the receive chain (LO2) is
16.2 GHz, 200 MHz offset from the LO frequency of the
transmit chain, fLO1=16 GHz. The receive chain has the same
power amplifier and frequency multiplier configuration as the
transmit chain, and operates at 325.8 – 354.6 GHz frequency
band. The down-converted IF signal is centered at 3.6 GHz,
which is mixed with a 3.6 GHz signal that is produced by
mixing the tapped off signals from LO1 (16 GHz) and LO2
(16.2 GHz) sources in the transmit and receive chains, and
then frequency-multiplying by a factor of 18.
The transmitted FMCW waveform has a bandwidth of
ΔF=354.6-325.8 GHz = 28.8 with a chirp time tchirp=82.5 μs.
This results in a chirp rate of K=349 MHz/μs. The IF signal is
offset from DC baseband by fIF=2Kd/c, where d=5.3 m is the
total path length (one-way), which is the combination of the
target distance (4 m) and the beam path length in the quasi-
optics chain (1.3 m), and c is the speed of light, resulting in
fIF=12.3 MHz. This IF signal can easily be digitized using
modern analog-to-digital (ADC) converters. Data acquisition
is achieved using a National Instruments DAQ connected to a
host machine with Labview software (National Instruments,
Texas) and a field-programable-gate-array (FPGA). The
measured I and Q data from the IF chain is Fast-Fourier-
Transformed (FFT) using the FPGA board, producing a 1024-
point spectrum of range bins for each spatial sampling point
across the imaged field-of-view (FOV). The range resolution
of the radar is determined by the bandwidth of the transmitted
FMCW waveform as 2
r
c
F =
, 0. 52 cm. Each bin of the
calculated spectrum corresponds to one range resolution cell.
The extraction of the PSF patterns from the range profiles is
achieved by choosing the maximum intensity in the
corresponding range bins in the vicinity of the imaged target.
The transmit and receive antennas are diagonal horns
sharing the same primary reflector illuminating the scene and
collecting the received signal from the imaged object. The
scene is raster scanned in the elevation and azimuth axes using
two flat mirrors mounted on rotary motors (azimuth and
elevation). The optics design is depicted in Fig. 2.
Fig. 2. Quasi-optics design of the 340 GHz radar. Duplexing
of the transmit and receive channels is achieved using a silicon
wafer while the FOV is scanned using rotating mirrors in the
elevation and azimuth axes.
As shown in Fig. 2, the duplexing between the transmit and
receive channels is achieved using a silicon wafer as a 50/50
beam-splitter.
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B. Acoustic Levitator for PSF Analysis
The acoustic levitation principle has been shown to be
promising in a variety of applications, ranging from studying
cloud particles [43] to remote detection [44], Raman
spectroscopy [45] and wireless power transfer [46]. The
acoustic levitator is an inexpensive commercial product [40-
42] and is shown in Fig. 3. It consists of two parabolic
surfaces, top and bottom, with an array of transducers placed
on each surface. The transducers are fed using a 40 kHz
square-wave signal generated by an Arduino microcontroller.
The transducers on each parabolic surface are in phase. Such a
geometry enables the creation of acoustic standing waves
between the top and bottom surfaces, giving rise to peaks and
nulls between the two surfaces.
Fig. 3. Acoustic levitator for PSF analysis of the 340 GHz
imaging radar.
Placing an object at the null of the acoustic standing wave
enables the object to be trapped at that position, and this
process is called acoustic levitation. The application of this
principle for PSF characterization of the radar is low-cost and
easy to set up. The acoustic levitator used in this work can
levitate objects with a density of up to 2 g/cm3.
III. PSF ANALYSIS, RESULTS AND DISCUSSION
Imaging resolution of a radar can be characterized by
analyzing the full-width-at-half-maximum (FWHM) of the
PSF pattern [38, 47]. The 340 GHz radar performs imaging in
a two-way process, involving illuminating the target and
receiving the reflected signal. As the 340 GHz radar has a
monostatic system layout, the measured PSF pattern of the
radar is equivalent to the multiplication of the beam pattern of
the primary reflector antenna for the transmit and receive
chains. This suggests that the PSF pattern is correlated to the
one-way beam pattern of the reflector antenna by the square of
the beam pattern. As a result, characterizing the PSF pattern of
the radar also enables us to characterize the beam pattern of
the radar antenna.
The PSF characterization of the 340 GHz radar was first
studied using a metal bead (1 mm diameter) suspended on a
thread as shown in Fig. 4(a). The target is placed at the focal
distance of the primary reflector, d=4 m, and the scene is
raster scanned within a FOV of 0.7. Given the monostatic
nature of the 340 GHz radar, in order to reduce the specular
reflections of the thread in the direction of the antenna beam,
the thread was rotated by 20 in the elevation axis as shown in
Fig. 4(b).
(a)
(b)
Fig. 4. Imaging setup for a metal bead (1 mm diameter)
secured with a thread at the focus of the radar for PSF
analysis. (a) Thread placed facing directly the primary
reflector. (b) Thread is rotated by 20 degrees to reduce the
specular reflection in the direction of the primary reflector.
It should be noted that whereas placing the thread at an
oblique angle can significantly reduce the reflections received
from the thread, such a technique might not be effective for a
radar with a bistatic or a multistatic system layout. This is due
to the fact that, in such aperture layouts, the scattered signal
from the thread can be received by an antenna probing the
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object in a different direction. As a result, this technique has
considerable limitations. Nevertheless, it can be considered
useful to observe the effect of background objects in the radar
beam characterization at THz frequencies, even if the specular
reflections are minimized by means of adjusting the
geometrical alignment of these objects.
(a) (b)
(c)
Fig. 5. PSF pattern of the 340 GHz radar obtained using a
metal bead attached to a thread. (a) The PSF pattern is shown
for the metal bead attached to the thread rotated to minimize
the specular reflections in the direction of the antenna beam.
Distortion in PSF is highlighted in dashed circle. (b) The PSF
pattern for the thread not rotated (colorbar scale is dB). (c) 1D
cuts along the elevation and azimuth directions of the PSF
pattern with rotated thread.
In Fig. 5, we demonstrate the PSF patterns for two different
scenarios. In Fig. 5(a), the PSF of the metal bead placed on the
20 rotated thread is shown. In Fig. 5(b), the PSF pattern of
the same metal bead placed on the same thread is shown, but
without any thread rotation. The PSF pattern in Fig. 5(b) is
heavily distorted by the specular reflection of the thread, with
no distinct image of the point scatterer. Comparing Figs. 5(a)
and 5(b), it is evident that the effect of the thread on the
measured PSF pattern has been reduced significantly by tilting
the thread to minimize the specular reflections in the direction
of the antenna beam. However, as highlighted in Fig. 5(a), the
obtained PSF pattern is still affected by the presence of the
thread used to position the metal bead in the elevation
direction. In Fig. 5(c), the FWHM values of the PSF pattern
(or spatial resolution) along the azimuth and elevation
directions are measured to be 0.1080 (7.54 mm) and 0.1310
(9.14 mm), respectively. Given the maximum frequency of the
transceiver chain, 354.6 GHz, the expected PSF FWHM value
at the focal plane of the primary reflector at d=4 m is
calculated using a physical optics (PO) simulation software,
GRASP (Ticra, Denmark). The PO simulated FWHM value is
found to be 0.1120 (7.8 mm). From Gaussian optics [48, 49],
the theoretical FWHM value is calculated to be 0.1060 (7.4
mm). It should be noted that for the PO simulation and
Gaussian optics result, first, the one-way beam pattern of the
primary reflector antenna at the focal plane is calculated.
Following, to be consistent with the two-way imaging
measurements from the radar, the simulated and analytical
one-way beam patterns are squared. Therefore, the analytical
and simulated FWHM analyses are performed on the squared
one-way beam patterns. Whereas the FWHM value of the
radar beam waist along the azimuth direction exhibits good
agreement with the analytical and simulated values, in the
elevation direction, due to the distortion caused by the thread,
the FWHM characteristic of the PSF pattern is significantly
wider than the expected values. The PSF SNR level in Fig.
5(c) is measured to be greater than 40 dB.
From these results, it is evident that alternative techniques
are needed to achieve a more accurate characterization of the
radar system. Although the demonstration involves a
monostatic radar, our goal in this paper is to seek a cost-
effective and simple technique that could be implemented to
any system layout: monostatic, bistatic, or multistatic.
For the scenario studied in Fig. 4, an ideal case would the
elimination of the secondary background objects (thread)
within the FOV. However, using this setup, achieving this
goal is not feasible as the metal bead needs to be secured
within the imaged FOV. To address this challenge, we use
acoustic levitation to position the imaged object and suspend it
at the focus of the primary reflector of the radar. Different
from the magnetic levitation principle, using the acoustic
levitation technique, any material with sufficiently low density
can be levitated. Due to light density of water, 1 g/cm3,
combined with its strong reflection response at THz
frequencies, we choose to suspend a water droplet as the point
scatterer.
The imaging setup is shown in Fig. 6. A water particle of 1
mm size is acoustically levitated at the focal point of the
primary reflector of the 340 GHz radar for imaging. As seen in
Fig. 6, the water particle is not attached to any secondary
background objects but instead is suspended in air. It should
be noted that when suspended in air, initially, the size of the
water droplet is about 2 mm and the droplet exhibits a rather
flattened geometry (wider in azimuth than in elevation) due to
the pressure waves pushing the droplet in the elevation
direction. The shape of an acoustically levitated water droplet
in air medium is governed by two parameters; diameter of the
droplet and the strength of the acoustic field [50, 51].
Increasing the acoustic field strength increases the non-
uniform pressure distribution on the surface of the droplet,
resulting in an increased droplet aspect ratio. The aspect ratio
is defined as the droplet size in the direction normal to the
acoustic pressure waves to the droplet size in parallel to the
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nodal plane. From this definition, ideally, it is desired for PSF
imaging that the aspect ratio is unity. In order to minimize the
flattening in the droplet shape, we keep the acoustic field
strength at minimum. This is achieved by optimizing the
voltage level (Vf) provided to the acoustic levitator to generate
the acoustic fields of minimum strength which is enough to
achieve the levitation, Vf=9.5 V. Moreover, as shown in [50],
for a fixed acoustic field strength, reducing the size of the
water droplet improves the uniformity of the aspect ratio.
Therefore, imaging is performed after evaporating the droplet
down to 1 mm diameter, minimizing the flattening in shape
and ensuring that the droplet has the same size as the metal
bead. The droplet-measured PSF pattern of the radar is shown
in Fig. 7.
Fig. 6. Imaging setup showing the water droplet acoustically
levitated at the focus of the primary reflector of the radar.
From Fig. 7(a), it is evident that no distortions due to a
secondary background object are present in the reconstructed
PSF pattern. Careful investigation of the reconstructed PSF
pattern reveals that the PSF pattern is slightly wider in the
elevation direction. This can be attributed to the offset feed of
the transceiver primary reflector antenna in the elevation
direction. Indeed, the PO analysis of the quasi-optics chain in
GRASP reveals that the PSF FWHM in the elevation direction
is 4% wider in elevation than the FWHM in the azimuth
direction. (The previously mentioned 0.1120 (7.8 mm) beam
FWHM for the PO analysis is the averaged FWHM value of
the beam in the azimuth and elevation directions.)
Analyzing the 1D cuts along the azimuth and elevation
directions, the SNR is measured to be greater than 38 dB,
close to the SNR level achieved from the metal bead scenario
but without the secondary distortions in the PSF pattern. The
spatial resolution of the radar is obtained by means of
analyzing the FWHM points of the 1D PSF patterns along the
azimuth and elevation axes, which are measured to be 0.1090
(7.6 mm) in azimuth and 0.1100 (7.7 mm) in elevation,
respectively, exhibiting good agreement with the PO
simulation result, 0.1120 (7.8 mm), and the analytical
Gaussian Optics result, 0.1060 (7.4 mm).
(a)
(b)
Fig. 7. PSF of the radar obtained from a water droplet levitated
using the acoustic levitator (a) 2D PSF pattern (b) 1D cuts
along the elevation and azimuth directions.
IV. CONCLUSION
PSF analysis of a radar plays a crucial role in assessing the
imaging characteristics of the radar. We have analyzed the
beam characteristics of the 340 GHz radar developed by the
Jet Propulsion Laboratory. It has been shown that using the
conventional PSF measurement techniques, such as a point
scatter attached to a thread, results in distorted PSF patterns
due to strong reflections from the background objects at THz
frequencies. In order to address this challenge, we have
leveraged the acoustic levitation principle. Relying on the
standing waves generated by the acoustic levitator, we have
shown that a water droplet can be levitated at the focal point
of the 340 GHz radar, forming an excellent target to resolve
the PSF pattern of the radar. It has been demonstrated that the
water droplet provides a comparable dynamic range to a metal
bead for imaging at 340 GHz but presents no distortions
caused by the presence of additional objects within the FOV.
Although shown for a monostatic system layout, the presented
technique can readily be employed to resolve the PSF
characteristics of bistatic and multistatic radar architectures.
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ACKNOWLEDGMENT
The research was carried out at the Jet Propulsion
Laboratory, California Institute of Technology, under a
contract with the National Aeronautics and Space
Administration. Dr. Yurduseven’s research was supported by
an appointment to the NASA Postdoctoral Program at the
NASA Jet Propulsion Laboratory, administered by
Universities Space Research Association under contract with
NASA. Reference herein to any specific commercial product,
process, or service by trade name, trademark, manufacturer, or
otherwise, does not constitute or imply its endorsement by the
United States Government or the Jet Propulsion Laboratory,
California Institute of Technology.
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Okan Yurduseven (S’09-M’11-
SM’16) received the B.Sc. and
M.Sc. degrees in electrical
engineering from Yildiz Technical
University, Istanbul, Turkey, in
2009 and 2011, respectively, and
the Ph.D. degree in electrical
engineering from Northumbria
University, Newcastle upon Tyne,
United Kingdom in 2014.
From 2009 to 2011, he was a Research Assistant within the
Department of Electrical and Electronic Engineering at
Marmara University, Istanbul, Turkey. From 2011 to 2014, he
worked as a Lecturer (part-time) within the Faculty of
Engineering and Environment at Northumbria University.
From 2014 to 2018, he was a Postdoctoral Research Associate
within the Department of Electrical and Computer
Engineering at Duke University, working in collaboration with
the U.S. Department of Homeland Security. He is currently a
NASA Postdoctoral Fellow at the Jet Propulsion Laboratory,
California Institute of Technology and an Adjunct Assistant
Professor at Duke University.
His research interests include microwave and millimeter-wave
imaging, multiple-input-multiple-output (MIMO) radar,
wireless power transfer, antennas and propagation, antenna
measurement techniques, and metamaterials. He has authored
more than 100 peer-reviewed technical journal and conference
articles. He has organized and chaired numerous sessions in
international symposiums and conferences, including IEEE
International Symposium on Antennas and Propagation (AP-
S) and European Conference on Antennas and Propagation
(EuCAP).
Dr. Yurduseven was the recipient of an Academic Excellence
Award from the Association of British – Turkish Academics
(ABTA) in London in 2013. He also received a best paper
award at the Mediterranean Microwave symposium in 2012
and a travel award from the Institution of Engineering and
Technology (IET). In 2017, he was awarded a NASA
Postdoctoral Program (NPP) Fellowship administrated by
Universities Space Research Association (USRA) under
contract with NASA. In 2017, he received an Outstanding
Postdoctoral Award from Duke University and a Duke
Postdoctoral Professional Development Award. He is a
member of the European Association on Antennas and
Propagation (EurAAP).
Ken Cooper (M'06-SM’14)
received the A.B. degree in
physics (summa cum laude) from
Harvard College, Cambridge,
MA, USA, in 1997, and the Ph.D.
degree in physics from the
California Institute of
Technology, Pasadena, CA, USA,
in 2003. Following post-doctoral
research in superconducting
microwave devices, he joined the Jet Propulsion Laboratory,
Pasadena, CA, USA, as a Member of the Technical Staff in
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8
2006. His current research interests include radar systems up
to terahertz frequencies, molecular spectroscopy, and devices.
Goutam Chattopadhyay (S’93-
M’99-SM’01-F’11) is a Senior
Research Scientist at the NASA’s
Jet Propulsion Laboratory,
California Institute of Technology,
and a Visiting Associate at the
Division of Physics, Mathematics,
and Astronomy at the California
Institute of Technology, Pasadena,
USA. He received the B.E. degree
in electronics and
telecommunication engineering from the Bengal Engineering
College, Calcutta University, Calcutta, India, in1987, the M.S.
degree in electrical engineering from the University of
Virginia, Charlottesville, in 1994, and the Ph.D. degree in
electrical engineering from the California Institute of
Technology (Caltech), Pasadena, in 1999. From 1987 until
1992, he was a Design Engineer with the Tata Institute of
Fundamental Research (TIFR), Pune, India. His research
interests include microwave, millimeter-, and submillimeter-
wave heterodyne and direct detector receivers, frequency
sources and mixers in the terahertz region, antennas, SIS
mixer technology, direct detector bolometer instruments; InP
HEMT amplifiers, mixers, and multipliers; high frequency
radars, and applications of nanotechnology at terahertz
frequencies. He has more than 300 publications in
international journals and conferences and holds more than
fifteen patents. Among various awards and honors, he was the
recipient of the Best Undergraduate Student Award from the
University of Calcutta in 1987, the Jawaharlal Nehru
Fellowship Award from the Government of India in 1992, and
the IEEE MTT-S Graduate Fellowship Award in 1997. He
was the recipient of the best journal paper award in 2013 by
IEEE Transactions on Terahertz Science and Technology,
IETE Prof. S. N. Mitra Memorial Award in 2014, best antenna
application paper award at the European Conference on
Antennas and Propagation (EuCAP) in 2017, and
distinguished alumni award from Indian Institute of
Engineering Science and Technology (IIEST) in 2017. He also
received more than 35 NASA technical achievement and new
technology invention awards. He is an associate editor of the
IEEE Transactions on Antennas and Propagation, a Fellow of
IEEE (USA) and IETE (India) and an IEEE Distinguished
Lecturer.