point-spread-function (psf) characterization of a 340 ghz ... · the acoustic levitation principle...

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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1

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




2

(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.




3

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




4

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




5

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.




6

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

https://doi.org/10.1007/978-94-017-8828-1_9

https://doi.org/10.1007/978-94-017-8828-1_9

https://doi.org/10.1063/1.4959862

https://doi.org/10.1063/1.4989995

https://doi.org/10.1175/1520-0426(2000)017%3C0940:AELSFS%3E2.0.CO;2

https://doi.org/10.1175/1520-0426(2000)017%3C0940:AELSFS%3E2.0.CO;2

https://doi.org/10.1007/s00216-003-2403-2

https://doi.org/10.1039/b706997a

https://doi.org/10.1145/3161182

https://doi.org/10.1038/nprot.2011.407

https://doi.org/10.1063/1.4973345




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.

point-spread-function (psf) characterization of a 340 ghz ... · the acoustic levitation principle...

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