Optics Communications 285 (2012) 2519–2524

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Optics Communications

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Mono-detection spatially super resolved microwave imaging for RADAR applications

Amir Shemer a, Isahar Gabay a, Moshe Tur b, Amir Boag b, Haim Kleinman b,Shlomo Zach c, Zeev Zalevsky a,⁎a Faculty of Engineering, Bar-Ilan University, Ramat-Gan 52900, Israelb Faculty of Engineering, Tel-Aviv University, 69978 Tel-Aviv, Israelc 10 Nachum st., Kfar Saba, 44338, Israel

⁎ Corresponding author.E-mail address: zalevsz@biu.ac.il (Z. Zalevsky).

0030-4018/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.optcom.2012.01.049

a b s t r a c t

a r t i c l e i n f o

Article history:Received 23 August 2011Received in revised form 19 January 2012Accepted 27 January 2012Available online 11 February 2012

Keywords:RF photonicsSuper resolutionImaging

In this paper we present a novel RF photonic approach to radar scanning and imaging. The operating principleis based upon a system in which several (in our case two) radiating microwave sources generate and projectat far field, a moving grating pattern over an object, e.g. by linearly modifying the relative phase between themicrowave sources. Capturing a set of such integrated reflections (we work only with a mono detector) comingfrom the object at different radio frequencies (due to a simultaneously performed spectral scanning) can spatiallyreconstruct high resolution image of the object despite the fact that the sensingwas performedwith a smallmonoreceiving antenna.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

The first imaging radar, was invented by Carl A. Wiley [1,2] in June1951, and included several technologies that gave a visually recognizablepicture of targets. Radar pictures are generally not as sharp as picturestaken by optical sensors, but on the other hand they are independentof day or night, cloud or sun and can penetrate many materials, such aswoodenbuildings. Improving the resolution of imaging radar requires in-crease in the size of the sensing antenna.

Imaging radar instruments have mapped local subsidence in resi-dential areas such as Phoenix, Arizona due to ground water depletion.It has verified shrinking of polar glaciers and ice caps that may be theresult of global warming. In addition, space borne synthetic apertureradar (SAR) imagery can monitor tropical hurricanes and cyclones,produce high spatial resolution ocean surface wind maps, monitorice sheets and glaciers threatening ocean navigation and monitorthe ordinance of man-made structures [3].

The major types of imaging radar methods are SAR [1,2,4], inversesynthetic aperture radar (ISAR) [5,6], interferometric synthetic aperture(InSAR) [7], software-defined radar sensors (SDRS) [8], and softwareand moving target indicator (MTI) [9,10].

As mentioned before, the spatial resolution of radar mainly dependson the size of its antenna. The larger the antenna the better is the reso-lution. Another factor that limits the performance of radar is the numberof detection channels that are connected to a given antenna. The largerthe number of such channels the better is the obtainable spatial

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discrimination along the given field of view. However, large antennaand large number of detection channels increase the cost, weight andvolume of a given radar system.

In optics many super resolving approaches were developed in thelast 15 years. Those techniques aim to overcome the diffraction limi-tation caused by the limited size of the imaging lens [11-14] as well asthe geometric limit of the detection array [15,16]. The size of the im-aging lens in optics is equivalent to the size of the antenna in radars.The number of pixels in the optical sensor is equivalent to the numberof detection channels in radar systems.

The aim of this paper is to propose a super resolving technique,coming from the world of optics, which improves the resolution of asingle detection channel radar having limited antenna size. The ideais to incorporate time shifting projected grating combined togetherwith spectral scanning in order to image the inspected object [14].Luckily, although the fundamental concept is coming from theworld of optics, the proposed configuration cannot be realized inoptics since it requires wide bandwidth spectral scanning (scanningof the projected and detected microwave frequency) which is notpossible in optics but feasible in the world of radars.

The paper is constructed in the following way: in Section 2 we pre-sent the mathematical overview of the proposed concept. In Section 3we show simulation results done to establish the accuracy of the pro-posed method. Section 4 presents preliminary experimental resultstaken under lab conditions and in Section 5 we conclude the paper.

2. Mathematical analysis

The general operating principle is based upon a system in whichseveral sources illuminate the object with a grating like pattern. A

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single detector collects the information. The projected pattern variesas multiple radio frequencies (RF) illuminate the object. The averageover all frequencies and over time provides a high resolution recon-struction of the inspected object.

The projection sources generate in far field a grating like structure.This structure will be shifted over the object by linearly modifying therelative phase between the RF sources. We assume we have N sources(N can even be 2 as we have in our simulation and experiment).Therefore, the transverse dependence of the projected far field (i.e.after neglecting the quadratic term of x2) pattern g(x) is:

g xð Þ ¼ ∑nan exp 2πi

nΔμ⋅xλRFZ

� �ð1Þ

where Δμ is the spatial separation between two adjacent sources, λRF istheir RF wavelength and an is the field amplitude of each source (theydo not have to be equal in power). Note that an can be a complex coef-ficient. Z is the distance to the object. x is spatial transverse coordinate inthe object plane.

The projected pattern is shifted in timewith a velocity V by applyinga timedependent phaseϕ to all sources of the formφ∝nVt, resulting in:

g x−Vtð Þ ¼ ∑nan exp 2πi

nΔμ⋅ x−Vtð ÞλRFZ

� �ð2Þ

This projection is multiplied by the object's pattern s(x) and cap-tured by the mono detector. The fact that we have a mono detectoris represented by spatial averaging (integration over x). We denoteby D(t,λRF) the signal detected at the mono detector versus timeand for a given RF wavelength as:

D t;λRFð Þ ¼ ∫∞

−∞s xð Þ∑

nan exp 2πi

nΔμ⋅ x−Vtð ÞλRFZ

� �dx ð3Þ

Our decoding process includes multiplication of the captured fieldD(t,λRF) by the projected reference grating-like pattern and then inte-grating over time:

r x;λRFð Þ ¼ ∫Δt

D t;λRFð Þ⋅∑nan exp 2πi

nΔμ⋅ x−Vtð ÞλRFZ

� �dt ð4Þ

where Δt is the time integration range. In order to obtain the superresolved image we repeat the above mentioned procedure for manyRF frequencies (we vary the RF frequency) and we average:

r̂ x; vRFð Þ ¼ ∫r x;cvRF

� �dvRF ð5Þ

Note that λRF=c/vRF where c is the speed of light. By substitutingEq. (3) into Eq. (4) one obtains the following relation:

r x;λRFð Þ ¼ ∑n1

∑n2

an1an2∫Δt

exp −2πiVtΔu⋅ n1 þ n2ð Þ

λRFZ

� �dt

!

� ∫∞

−∞s x1ð Þ exp 2πi

Δμ n1x1 þ n2xð ÞλRFZ

� �dx1

! ð6Þ

The integral over time, up to a proportion factor, equals to:

∫Δt

exp −2πiVtΔμ⋅ n1 þ n2ð Þ

λRFZ

� �dt≈δ n1 þ n2½ � ð7Þ

This is true for integration period which is long enough:

Δt >>λRFZVΔμ

ð8Þ

Therefore substituting Eq. (7) into Eq. (6) yields:

r x;λRFð Þ≈∑nana−n ∫

∞

−∞s x1ð Þ exp 2πi

vRFΔμn x1−xð ÞcZ

� �dx1 ð9Þ

and therefore

r̂ x; vRFð Þ≈∑nana−n ∫

∞

−∞s x1ð Þ ∫ exp 2πi

vRFΔμn x1−xð ÞcZ

� �dvRF

� �dx1 ð10Þ

Note that up to a constant we also have,

∫ exp 2πivRFΔμn x1−xð Þ

cZ

� �dvRF≈δ x1−xð Þ ð11Þ

This is an approximation since in real-life the bandwidth is not in-finite. The reconstruction obtained in Eq. (10) equals to:

r̂ x; vRFð Þ≈s xð Þ⋅ηn≡ ∑n ana−nð Þ ð12Þ

which means that a super resolved RF image is obtained and it con-tains all the spatial features of the original object s(x). η is a constant.

3. Simulation results

In order to confirm our theory and also to prepare the reconstructioncode, we designed a MATLAB simulation that mimics the experimentalsystem. The first simulations were preformed in order to check the the-ory as described in the mathematical section. Two kinds of syntheticradar cross-section were tested: a series of rectangular bars, mimickingmetal strips, and a sinusoidal one. The results gained by the simulationof Fig. 1, indeed confirm the theory. The conditions of the simulation in-cluded frequency range of 4–14 GHz, distance between antennas andtarget was 3 m, distance between projecting antennas was 30 m.5 mmwas the simulated resolution in x-axis and the frequency scanningresolution was 0.1 GHz.

We then adjusted the simulation program to meet the conditionsof the experimental scenario. The simulation must be fed by two dif-ferent data streams; one comes from the single receiving antenna, asseen in Fig. 2 and the other is the interference grating generated bythe antenna sources on the target. The interference grating patterndepends on several parameters: (i) d which is the distance betweenthe illuminating sources; (ii) Z is the distance to the target; and (iii)v is the frequency of the transmitted signal. For the calculationsbelow we used the following parameters: the span of x (lateral axis)was 80 cm, frequency range was 2–12 GHz and the projected gratingwas shifted along lateral distance of 80 cm.

For good results the illuminating and reconstructing gratings mustbe aligned in phase. Therefore, the illuminating grating was measuredby scanning the target plane with a special conic antenna, Fig. 3.

By having this result we can now calibrate the reconstruction gratingin the simulation as can be seen in Fig. 4. In the upper part of Fig. 4(a)weshow thenormalized results obtained from the network analyzer and onthe lower part, the result coming fromour simulation. Note that the cen-ters of both graphs are not aligned and this was due to impedance mis-match between the antennas arms. After the extra phase induced by thismismatch has been added in the simulation, full alignment has beenachieved, as seen in Fig. 4(b). This real calibrated grating was nextused for the processing of the measured data.

4. Experimental system and preliminary results

The experimental setup appears in Fig. 2. An RF signal generator(PNA Network Analyzer Model E8362B) was delivering a signal intotwo horn polarized antennas (20 cm in diameter, 2–18 GHz, vertical

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Fig. 1. Simulation results: (a). The original and the reconstructed RECT shape function. (b). The original and the reconstructed mono frequency function.

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polarization), separated by a center to center distance of d=50 cm.The distance to the target, Z, was set to be 3 m at about 1.45 meterabove the floor. A picture of the setup sitting in an anechoic chamberappears in Fig. 5 showing the two radiating sources (B1) (two horn

Recan

Interference grating sampling the target

Fig. 2. Schematic ske

antennas placed on a computer controlled rail) and the receiving(B2) and calibration (B3) antennas.

Moving the projected grating across the target can be implemen-ted not only by changing the relative phase between the sources

d

Two beaming antennas

eiving tenna

Function generator 2-12 GHz

πDynamic phase

tch of the setup.

Fig. 3. The special conic antenna used for the sampling of the generated RF interferencegrating.

2522 A. Shemer et al. / Optics Communications 285 (2012) 2519–2524

(e.g., by a phase shifter or an adjustable delay line), but also by later-ally moving the pair of source antennas across the radiating plane.This was accomplished by the computer control stage which could

Fig. 4. The RF interference grating (a). Upper part: The normalized network analyzerresults, Lower part: Simulation results. (b). Upper part: The normalized network ana-lyzer results, Lower part: Simulation results after mismatch phase adaptation.

Fig. 5. The RF system and the echo free room (a). The two radiating sources (B1) (twohorn antennas placed on computer controlled rail) (b). The receiving (B2) and calibra-tion (B3) antennas.

move the antennas by up to 48 cm off center to both sides, so thatthe required field of view could be properly covered.

In the first experiment we took 100 samples along the X axis witha 5 mm step between recordings and 100 samples in the frequencydomain, which was set to be between 2 and 12 GHz, with 0.1 GHz fre-quency sweeping step. During each step along the X axis, the networkanalyzer made a sweep of frequencies and grabbed the response fromthe receiving antenna. Therefore, the array of collected data containedmore than 10,000 samples, which were stored in dB format. Systemnoise was evaluated by operating the setup without the target. Theresults were then subtracted from the data received with the target pre-sent, thereby achieving the benefits of noise reduction.

For clarity in Fig. 6 we present experimental results obtained forthe projected interference grating as function of its spatial positionsand of the radiated radio frequency.

Our first target was a metallic rod, 1.2 cm wide and 10 cm long.Such a rod has a cylindrically symmetric cross-section. We expectthe reconstructed image of the rod to follow any lateral displacementof the rod (shift invariance). Fig. 7(a) shows illustrative rod target,while the reconstructions for two different lateral positions of the tar-get, 3 cm apart are depicted in Fig. 7(b). Clearly, the peak of thereconstructed image follows the target displacement. The recon-structed image itself does notmatch exactly the cross section of the tar-get due to sensitivity to noises thatwe have in our experimental systemand due to the low SNR in certain frequencies that affect the final recon-struction in a way that is equivalent to applying a low pass filter. Thepresented reconstructedwas obtained after applying properWiener fil-tering processing.

Fig. 6. The experimental results of the projected interference grating as function of itsspatial positions and of the radiated radio frequency.

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To demonstrate the spatially super-resolving characteristics of thesetup, a second experiment with two-nail target was constructed,with an inter-nail separation of 20 cm. The spectral span range was4–14 GHz, sampled at 101 points. Fig. 8(a) presents the recordedlow resolution information (without reconstruction. The datapresented there does not resemble the original object (with the twonails positioned 20 cm apart). Fig. 8(b) shows the obtained recon-struction with the proposed configuration and decoding. Now, one

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may clearly see two targets separated by the right distance of about20 cm, appearing in their true and real positions.

5. Summary

In this paper we presented a novel microwave method for superresolved imaging. The mathematically supported concept is basedon the projection of a grating pattern on the surface of the inspectedtarget and using frequency sweeping, as well as spatial scanning ofthe projected pattern, to super resolve the target. Simulations andpreliminary experimental results, involving only two projecting andsingle receiving small size antennas, demonstrated the validity ofthe proposed concept.

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