research article ultrawideband noise radar tomography

Research ArticleUltrawideband Noise Radar TomographyPrinciples Simulation and Experimental Validation

Hee Jung Shin1 Ram M Narayanan1 Mark A Asmuth1 and Muralidhar Rangaswamy2

1Pennsylvania State University University Park PA 16802 USA2Air Force Research Laboratory WPAFB Dayton OH 45433 USA

Correspondence should be addressed to RamM Narayanan ramengrpsuedu

Received 2 November 2015 Accepted 15 March 2016

Academic Editor Walter De Raedt

Copyright copy 2016 Hee Jung Shin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The paper introduces the principles simulation results and hardware implementation of ultrawideband (UWB) noise radar forobtaining tomographic images of various scenarios of rotating cylindrical objects using independent and identically distributedUWB noise waveforms A UWB noise radar was designed to transmit multiple UWB random noise waveforms over the 3ndash5GHzfrequency range and tomeasure the backward scattering data for the validation of the theoretical analysis and numerical simulationresults The reconstructed tomographic images of the rotating cylindrical objects based on experimental results are seen to be ingood agreement with the simulation results which demonstrates the capability of UWB noise radar for complete two-dimensionaltomographic image reconstruction of various shaped metallic and dielectric target objects

1 Introduction

Noise radar has been developed and refined for covert detec-tion and imaging applications over the past few decades dueto several advantages such as low probability of interception(LPI) [1ndash3] electronic counter-countermeasure (ECCM) [4ndash6] and relatively simple hardware configurations [7ndash9]Further ultrawideband (UWB) noise radar has achievedhigh-resolution detection and imaging in foliage penetration(FOPEN) imaging [10 11] through-wall imaging (TWI) [12ndash14] and ground penetration radar (GPR) imaging [15 16] byemploying an ultrawide bandwidth For obtaining high-reso-lution images of various shaped targets tomographic radarimaging is emerging as a powerful imaging technique [17ndash19]In general radar imaging techniques tend to be formulatedin the time domain to use computationally efficient back-projection algorithms and to provide accurate object shapeand location results of the target objects [20ndash22]On the otherhand the objective of tomography-based radar imaging isto characterize the material property profiles of the targetobjects from the scattered fields and reconstruct specificscatterers within the interrogation medium by solving theinverse scattering problem [23ndash26]

Practical tomography systems have been developed andimplemented in a way that the multidimensional images ofthe target object are successfully obtained from electromag-netic scatteringwith variouswaveforms [27ndash29]The require-ment when using this method is the need for mechanicalrotation of either the body or the antenna in order to obtainmeasurements in different views [30ndash32] Every object wheninserted into an electromagnetic field causes a well-definedfield change and diffraction occurs when the wavelength ofthe radiation is of the order of the dimension of the objectA one-to-one relationship relating the scattered field to theobject complex permittivity can be obtained within the Bornapproximation via a Fourier transform using the so-calledFourier diffraction theorem [33ndash35]

This paper introduces the principle simulation andexperiment results of tomographic imaging of various targetscenarios using diffraction tomography for a bistatic UWBnoise radar Since the frequency behavior of the electricalparameters of the target objects due to the illuminating elec-tromagnetic fields depends on the frequency used in the sys-tem UWB imaging clearly provides advantages over single ornarrow band frequency operation in terms of resolution and

Hindawi Publishing CorporationInternational Journal of Microwave Science and TechnologyVolume 2016 Article ID 5787895 21 pageshttpdxdoiorg10115520165787895

2 International Journal of Microwave Science and Technology

x

Incidentplane wave

y

r

y

xz

x = minusd

1st Rx

2nd Rx

Δyn minus 1th Rx

nth Rx

Figure 1 Two-dimensional backward scattering geometry for a cylindrical object The 119911-polarized incident wave is illuminated from minus119909

direction and propagated in free space

accuracy Furthermore transmitting randomnoisewaveforminherits the aforementioned advantages of noise radar Thepaper is organized as follows In Section 2 theoretical analysisof the image reconstruction for a bistatic noise radar systemwith two-dimensional scattering geometry using Fourierdiffraction theorem under the assumption of plane waveillumination is presentedThenumerical simulation results ofdiffraction tomographyusingUWBrandomnoisewaveformsare presented in Section 3 Section 4 describes the RFhardware implementation and experimental results from thatnoise radar system Further we compare the images obtainedwith simulations and experiments Conclusions are drawn inSection 5

2 Theory and Formulation

The main advantage of transmitting a random noise wave-form is to covertly detect and image a target without alertingthe presence of radar system Such LPI characteristic of thenoise radar is achieved by using a random noise waveformwhich is constantly varying and never repeats itself exactly[36 37] The random noise waveform herein is mathemat-ically defined as discrete time wide-sense stationary (WSS)and ergodic random process and a sequence of independentand identically distributed (iid) random variable drawnfrom a normal distribution N(0 120590

2) The power spectral

density (PSD) of white Gaussian noise (WGN) waveform isideally a nonzero constant for all frequencies In practicalsituations however the PSD of the random noise waveformmay not be uniform across thewide frequency ranges becausea finite number of random noise amplitude samples mustbe chosen for WGN waveform generation In order tobypass such a shortcoming multiple sequences of iid noisewaveforms are transmitted to flatten the spectral densitywithout changing the mean and variance [38]

Figure 1 shows two-dimensional backward scatteringgeometry for a cylindrical target objectThe values of receiverspacing Δ119910 and the frequency sampling interval Δ119891 aredetermined based on the maximum operating frequency andthe size of the object respectively to ensure an image that isfree of false aliases [39ndash41]

The analysis starts from a single frequency and developsthe process for UWB by summing up the analysis results for119873 discrete frequencies As shown in Figure 1 the incident 119911-polarized plane wave of the WGN waveform for 119873 multiplefrequencies takes the form

119864119894(119896119899 119903)

= (1198641119890minus1198951198961sdot 119903

+ 1198641119890minus1198951198962sdot 119903

+ sdot sdot sdot + 119864119873119890minus119895119896119873sdot 119903)

=

119873

sum

119899=1

119864119899119890minus119895119896119899sdot 119903

119867119894(119896119899 119903) = minus

1

120578

times 119864119894(119896119899 119903)

(1)

where 119896119899

= 120596119899119888 is the wavenumber 120578 is the intrinsic

impedance in free space and 119864119899is the field amplitude of the

transmitted white Gaussian noise waveform at each discretefrequency of interest We start the analysis from a singlefrequency and develop the process for119873multiple frequenciesby summing up the analysis results for119873 The entire analysismust be repeated for 119870 times when 119870 multiple sequences ofiid noise waveforms are transmitted

Consider a dielectric target object illuminated by an inci-dent plane wave denoted in (1) which induces an equivalentelectric current distribution given by

119869eqdielectric (119896119899 119903) = 119895120596 [120576 ( 119903) minus 1205760] 119864 (119896119899 119903) (2)

where 120576( 119903) and 1205760denote the complex permittivity of the

object and the vacuum permittivity respectively 119864(119896119899 119903) in

(2) is the total field due to the presence of the object and isexpressed as the sum of the incident field 119864

119894(119896119899 119903) and the

scattered field 119864119904(119896119899 119903) that is

119864 (119896119899 119903) = 119864

119894(119896119899 119903) + 119864

119904(119896119899 119903) (3)

If the object is assumed to be a perfect electric conductor(PEC) the equivalent induced current distribution is calcu-lated by applying the physical optics approximation [42] andis given by

119869eqPEC (119896119899 119903) = 2 ( 119903) times 119867119894(119896119899 119903) (4)

International Journal of Microwave Science and Technology 3

Table 1 Target objects imaged by the numerical simulations

Object material Object description Dimension

PECCircular cylinder 20 cm diameter (7910158401015840 diameter)

Height of the objects is assumed to be infinitely longSquare box 20 cm times 20 cm (7910158401015840 times 7910158401015840)

Triangular prism 20 cm side (7910158401015840 side)

Dielectric 120576119903= 58 minus 119895075

Circular cylinder 16 cm diameter (6310158401015840 diameter)Square box 16 cm times 16 cm (6310158401015840 times 6310158401015840)

where ( 119903) is the outward unit normal vector to the boundaryof scatterer

The general form of the scattered field 119864119904(119896119899 119903) created by

the equivalent induced current is written as

119864119904(119896119899 119903) = minus119895120596120583

0int

119878

119869eq (119896119899 1199031015840) sdot 119866 ( 119903 minus 119903

1015840) 119889 1199031015840 (5)

where 119878 is the boundary of scatterer and 119866( 119903 minus 1199031015840) is the two-

dimensional Greenrsquos functionBased on [43] the 119911-polarized scattered field at the

receivers 119909 = minus119889 can be written as

119906119904(119896119899 119909 = minus119889 119910) = sdot 119864

119904(119896119899 119909 = minus119889 119910)

= 120595∬119900 ( 1199031015840) 119890minus119895119896119899sdot 1199031015840

119866( 119903 minus 1199031015840) 11988921199031015840

(6)

where 120595 = 1198962

119899119864119899for the dielectric object and 120595 = 119895119896

119899119864119899for

the PEC object case 119900( 1199031015840) is the scattering object functionwhich is related to the shape of the target object By usingthe plane wave expansion of Greenrsquos function the one-dimensional Fourier transform of the scattered field is givenby [44 45]

119904(119896119899 119909 = minus119889 119896

119910) =

minus119895120595

2120574

119890minus119895120574119889

(minus120574 minus 119896119899 119896119910) (7)

where

120574 =

radic119896119899

2minus 119896119910

2 as 10038161003816100381610038161003816119896119910

10038161003816100381610038161003816le 119896119899

minus119895radic119896119910

2minus 119896119899

2 as 10038161003816100381610038161003816119896119910

10038161003816100381610038161003816gt 119896119899

(8)

In deriving (7) the one-dimensional Fourier transform of119904in the 119910-direction is defined as

119904(119896119899 119909 = minus119889 119896

119910) = int119906

119904(119896119899 119909 = minus119889 119910) 119890

119895119896119910119910119889119910 (9)

If we define 119896119909= minus120574minus119896

119899 the scattering object function in

the Fourier domain (119896119909 119896119910) is the two-dimensional Fourier

transform of the scattering object function such that

(119896119909 119896119910) = ∬119900 (119909 119910) 119890

minus119895(119896119909119909+119896119910119910)119889119909 119889119910 (10)

The image of the target object is constructed by calculation ofthe magnitude of scattering object function 119900(119909 119910) in rectan-gular coordinate after performing two-dimensional inverseFourier transform of (10) By using119873 number of frequencies

the resolution and accuracy of the image can be enhancedAlso the variance of the frequency response in WGN isreduced by taking average of the frequency responses of 119870multiple transmissions of iid noise waveforms [46 47]

As the object is sequentially rotated with respect to therotational axis for the value of rotational step angle 120579 thecorresponding scattering object function at each angularincrement 120579 is obtained by rotating the obtained scatteringobject function 119900(119909 119910) with respect to the correspondingrotational step angle 120579 in 119909-119910 image coordinates A blockdiagram shown in Figure 2 displays the tomographic imagereconstruction procedure for 119870 multiple transmitted iidnoise waveforms for a sequentially rotated object usingdiffraction tomography

3 Numerical Simulation Results

As shown in Figure 2 the complete tomographic image of thetarget object is reconstructed based on the number of trans-mitted noise waveforms and angular stepsThe image qualityof UWB noise radar tomography has been quantitativelyanalyzed by calculating the cumulative mean squared error(MSE) between the corresponding pixels of the referenceimages and the reconstructed images [48 49]

For scattered field calculations and diffraction tomog-raphy simulations with multiple iid WGN waveforms10 bandlimited UWB noise waveforms over a frequencyrange from 3GHz to 5GHz are generated with 500 randomamplitude samples drawn fromN(0 120590

2) and are sequentially

transmitted for backward scattered field calculations Alsothe rotational step angle 120579 is set to 9∘ based on the mean-squared-error (MSE) analysis [50] For each transmittednoise waveform 40 discrete images are obtained after full360∘ rotation for each transmitted noise waveform and thecomplete tomographic image of the target is obtained bycombining these 40 discrete images into one single image

Table 1 is a list of target objects for the numerical simula-tionsThedielectric objects are assumed to be a homogeneousconcrete block the real and imaginary parts of complexrelative permittivity are assumed to be 58 and 075 respec-tively at the evaluation frequency of 3GHz [51]Themoisturecontents and surface roughness of the dielectric objects arenot considered for the simulations

Our simulation results below show cases wherein 1 3 7and 10 noise waveforms are averaged In an earlier paper [43]we compared the averaged image with that obtained usingthe commonly used first derivative Gaussian waveform anddetermined that the mean squared error (MSE) between theimages dropped off exponentially as the number of averages


Final target

Final target

Scattered field calculation


Diffraction tomography algorithm for


Target image1st UWBWGNwaveformtransmission

Kth UWBWGNwaveformtransmission

Target image







Target image

Complete target image

1205791

o(x y)

o11205791 (x y)for 1205791

for 1205791

1205791for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

120579rfor 120579rfor 120579r

120579rfor 120579rfor 120579r

o1120579r (x y)

oK1205791(x y)

oK120579r(x y)

image for 1205791ofinal1205791 (x y)

image for 120579rofinal120579119903 (x y)

sum

sum

sum

Figure 2 The image reconstruction procedure with 119870 multiple iid WGN transmitted waveforms for a sequentially rotated object usingdiffraction tomography

increasedTheMSE tended to level off after about 6 averagesafter which the drop in MSE was at a slower rate Thereforewe considered 10 averages to be adequate for generating thefinal image

31 Circular PEC Cylinder Figure 3 shows a bistatic noiseradar system with two-dimensional scattering geometry fora circular PEC cylinder The cylinder with a radius of 10 cmis located at (0 cm 0 cm) and its height is assumed to beinfinitely long along the 119911-axis A linear array of 55 receivers ispositioned 68 cm away from the center of the object with thereceiver spacing Δ119910 of 15 cm in order to avoid any aliasingThe scattered field is uniformly sampled at receiving array Rx1 through Rx 55 with frequency swept within the frequencyranges of 3ndash5GHz When the simulation is completed theobject is rotated in clockwise direction in steps of 9∘ withrespect to the origin (0 cm 0 cm) and the simulation processwas repeated until the object was fully rotated over 360∘

Four tomographic images of the circular PEC cylinderwith 10 transmitted iid bandlimited WGN waveforms areshown in Figures 4(a) 4(b) 4(c) and 4(d) when 1 3 7 and10 noise waveforms are transmitted respectively Completetomographic imaging of the cylinder is successfully achievedafter averaging all ten images by visual inspection of theformed images as shown in Figure 4(d) and increasing thenumber of transmissions of the iid UWB WGN waveformenhances the quality of final tomographic image of the objectby reducing the variance of the spectral response of WGN

32 Square PEC Box Figure 5 shows a bistatic noise radarsystem with two-dimensional scattering geometry for asquare PEC box The length of each side of the square (119886) is20 cm and its height is assumed to be infinitely long alongthe 119911-axis Other simulation parameters such as the positionof receivers the parameters for receiver spacing and therotational angle are identical to the circular PEC cylindercase In order to generate the complete tomographic image ofthe square PEC box shown in Figure 5 10 iid random noisewaveforms are sequentially transmitted as well

Figures 6(a) 6(b) 6(c) and 6(d) display four tomo-graphic images of the square PEC box when 1 3 7 and10 noise waveforms are transmitted respectively As seen inFigure 6 four corners of the square box are not clearly imagedand fringes are observed at the sharp edges as expectedaffecting the image quality of the formed images Howeverthe approximate square shape can easily be inferred from theimage

33 Equilateral Triangular PEC Prism A bistatic noise radarsystem with two-dimensional scattering geometry for anequilateral triangular PEC prism is shown in Figure 7 Theprism is located at (0 cm 0 cm) and the length of each sideof the triangle (119886) is 20 cm Similarly the target object isconsidered as an infinitely long prism along the 119911-axis Allsimulation parameters remain unchanged

Four tomographic images of the triangular PEC prismwith 10 transmitted iid bandlimited WGN waveforms areshown in Figures 8(a) 8(b) 8(c) and 8(d) when 1 3 7


x

y

r = 10

Rx 1

Rx 55y

xz Rx 54

(0 0)

(minus68 minus405)

(minus68 405)

Incident noise waveform

Rx 2

x = minus68

Δy = 15

120579

Figure 3 A bistatic noise radar system with two-dimensional backward scattering geometry for a circular PEC cylinder The target object issurrounded by vacuum The rotational step angle is 9∘

minus04

minus04 minus03 minus02 minus01 0 01 02 03 04x (m)

y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)

Figure 4 Complete tomographic image of a PEC cylinder with a radius of 10 cm located at (0 cm 0 cm) after summing and averaging processbased on (a) one transmitted WGN waveform (b) three transmitted WGN waveforms (c) seven transmitted WGN waveforms and (d) allten transmitted WGN waveforms


x

y

Rx 1

Rx 55y

xz Rx 54

(minus68 405)


Rx 2

a = 20

a = 20

(0 0)

(minus68 minus405)

x = minus68

Δy = 15

120579

Figure 5 A bistatic noise radar system with two-dimensional backward scattering geometry for a square PEC box The target object issurrounded by vacuum The rotational step angle is 9∘

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)

Figure 6 Complete tomographic image of a square PEC box with a length of 20 cm located at (0 cm 0 cm) after summing and averagingprocess based on (a) one transmitted WGN waveform (b) three transmitted WGN waveforms (c) seven transmitted WGN waveforms and(d) all ten transmitted WGN waveforms


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 20 (0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579

Figure 7 A bistatic noise radar system with two-dimensional backward scattering geometry for an equilateral triangular PEC prism Thetarget object is surrounded by vacuum The rotational step angle is 9∘

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)

Figure 8 Complete tomographic image of an equilateral triangular PEC prism with a length of 20 cm located at (0 cm 0 cm) after summingand averaging process based on (a) one transmitted WGN waveform (b) three transmitted WGN waveforms (c) seven transmitted WGNwaveforms and (d) all ten transmitted WGN waveforms


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8


and 10 noise waveforms are transmitted respectively Theimage quality of complete tomographic image of the prismis enhanced as the number of transmitted noise waveformsincreases Although fringes are evident at the corners ofthe prism due to the scattering at the sharp edges theapproximate shape of the object is clearly observed

34 Circular Dielectric Cylinder Figure 9 shows a bistaticnoise radar system with two-dimensional scattering geome-try for a circular dielectric cylinder As previously discussedthe dielectric cylinder is assumed to be a homogeneousconcrete material with the real and imaginary parts ofcomplex relative permittivity set to 58 and 075 respectivelyThe aforementioned physical conditions of the object such asmoisture contents and surface roughness are not consideredfor the simulations

As shown in Figure 9 the dielectric cylinder with a radiusof 8 cm is located at (0 cm 0 cm) and the height of thecylinder is assumed to be infinitely long along the 119911-axis Alinear array of 55 receivers is positioned 68 cm away from thecenter of the object with the receiver spacing Δ119910 of 15 cm inorder to avoid any aliasing The scattered field is uniformlysampled at receiving array Rx 1 through Rx 55 with frequencyswept within the frequency ranges of 3ndash5GHz The generalsimulation procedure is identical to PEC object cases thecylinder is rotated in clockwise direction at 9∘ with respect tothe rotational axis that is (0 cm 0 cm) and the simulationsare repeated until the object is fully rotated

Four complete tomographic images of the dielectriccylinder based on 10 transmitted iid WGN waveforms areshown in Figures 10(a) 10(b) 10(c) and 10(d) when 1 3 7 and10 noise waveforms are sequentially transmitted respectivelySince the dielectric object is defined as a homogeneous con-crete object with perfectly smooth surface two-dimensionaltomographic image of the concrete cylinder is successfullyachieved

35 Square Dielectric Box Shown in Figure 11 is a bistaticnoise radar system with two-dimensional scattering geom-etry for a square dielectric box The length of each sideof the square (119886) is 16 cm and its height is assumed to beinfinitely long along the 119911-axis Other simulation parameters

such as the position of receivers the parameters for receiverspacing and the rotational angle remain unchanged Alsocomplex relative permittivity and physical conditions of theobject are identical to the previous simulation Similarly 10iid random noise waveforms are sequentially transmitted inorder to obtain the complete tomographic image of the box

Figures 12(a) 12(b) 12(c) and 12(d) show four tomo-graphic images of the dielectric box when 1 3 7 and 10 noisewaveforms are transmitted respectively As expected fringesare noted at the four corners of the box due to the physicalshape of the target Although the intensity of scattered fieldis relatively weak compared to PEC objects the shape of thedielectric objects can be clearly inferred because the signal-to-noise ratio (SNR) is infinity for all simulation cases

4 Implementation of UWB Noise Radar andExperimental Results

41 Hardware Implementation Figure 13 shows the blockdiagram of our hardware implementation of UWB noiseradar in a backward scattering arrangementThe entire exper-iment is sequentially controlled by a desktop computer Thecomputer is directly connected to the electrical componentsan arbitrary waveform generator (AWG) and a digital oscil-loscope The AWG is Agilent M8190A system mounted onM9602A chassis Before the data acquisition process beginsthe AWG at the transmitter side starts generating the randomwaveforms based on a given specification such as the numberof amplitude samples frequency bandwidth and samplingrate The AWG is designed to transmit the random noisewaveform continuously for the duration of the measurementAgilent DSO90804A digital oscilloscope is configured tocollect and save the scattering data at the receiver side

Also twomechanical components that is a turntable anda linear scanner are controlled by the desktop computerFor the data acquisition the target object is placed on theturntable and a stepper motor of the turntable rotates theobject a certain number of degrees The receiving antenna ismounted on the linear scanner the antenna moves along thelinear scanner and stops at the designated coordinate to col-lect the data at that pointThe receiving antenna is connectedto Agilent Infiniium DSO90804A for collecting scattering


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)

Figure 10 Complete tomographic image of a dielectric cylinder with a radius of 8 cm located at (0 cm 0 cm) after summing and averagingprocess based on (a) one transmitted WGN waveform (b) three transmitted WGN waveforms (c) seven transmitted WGN waveforms and(d) all ten transmitted WGN waveforms

x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579

Figure 11 A bistatic noise radar system with two-dimensional backward scattering geometry for a square dielectric box The target object issurrounded by vacuum The rotational step angle is 9∘


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


data and then sends it to the computer for tomographic imageprocessing

For transmitted noise waveforms the AWG generatesa bandlimited random noise waveform of 3ndash5GHz at anoutput power of 0 dBmThegenerated noisewaveform is thenamplified through a Mini-Circuits ZVE-8G+ amplifier andthe measured output power of the transmitted bandlimitednoise waveform for 3ndash5GHz after ZVE-8G+ with 12V DCinput bias is approximately 35 dBm

As shown in Figure 13 the amplified noise waveformis transmitted through an A-Info dual-polarization hornantenna (LB-SJ-20180) The dual-polarized horn antennaoperates over the frequency range of 2ndash18GHz and theantenna has a gain of approximately 10 dB over 3ndash5GHzfrequency range The position of the transmitting antenna is

fixed at the center of the backward scattering geometry butthe receiving antenna is designed to move along the linearscanner to collect the scattering dataThe receiving side of thesystem uses an identical antenna for data collection and bothtransmitting and receiving antenna are installed to measureonly vertically polarized scattering data

The data collection system is controlled using a singlecomputer The computer is connected to four devices Thecomputer directly controls two Arduinos the AWG and theoscilloscope Before the data collection process begins thecomputer uploads the noise waveform to the AWG using aMATLAB code The AWG continuously transmits that noisewaveform for the duration of the test One Arduino controlsthe position of the turntable on which the test object isplaced The second Arduino controls a linear scanner that


y

x

z

Rx Tx

Turntable with stepping motor

Rx scanning direction

Microwave absorber

Linear scanner

Power amplifier

Arbitrary waveform generator

(AWG)

Desktop computer

Digital oscilloscope

120579

Figure 13 UWB noise tomography radar system block diagram

has the receiving antenna mounted on it The scanner stopsat each point that is designated in MATLAB so data can becollected at that pointThe oscilloscope collects time-domaindata and then passes that data back to the computer forstorage and further processing

42 Data Acquisition and Image Processing Figure 14 shows apicture of actual experimental hardware implementationThetransmitted noise waveforms are not identical between eachmeasurement however the iid white Gaussian noise wave-forms are generated and transmitted for the experimentsEach time the linear scanner stops DSO90804A collects atotal of 363000 amplitude samples As previously describedthe turntable rotates in steps of 9∘ after a single line scan hasbeen completed and the data acquisition process repeats untilthe object has fully rotated for 360∘ The total data stored ofa single target object with complete 360∘ rotation are in 40 times363000 matrix array for tomographic image processing at alater point in time

The spectral response of the transmitted random noisewaveform is directly related to the image quality If the insuf-ficient amount of scattering data is collected an unrecog-nizable image of the target may be formed due to the fluctua-tion of the spectrum response Although a long sample lengthor the averaging of multiple samples is necessary to achieve aflat frequency spectrum the data size of 40 times 363000 matrix

array may not be processed at the same time due to the com-putational limitations of the desktop computer For the com-putational efficiency each of the 363000 point samples is splitinto119873 segments for processing and then summed and aver-aged to create an image A total of119873 images are reconstructedfor each rotational angle where the turntable stops and thefinal tomographic image is generated via sum and average of119873 images After measurement with complete 360∘ rotationsa total of 40 times119873 final tomographic images are created Usingimage processing these 40 times 119873 images are combined intoone complete tomographic image [52] For this paper allcollected data samples are split into 200 segments such thatthe complete tomographic image of each target object shownin this chapter is reconstructed based on 40times 200 imagesThegeneral experiment process is identical to Figure 2

Both metallic and dielectric cylinders with differentshapes are measured for tomographic image reconstructionsThe metallic objects are constructed from sheets of alu-minum For the dielectric target objects they are concreteblocks The test objects are placed on the center of theturntable one at a time Table 2 shows the actual target objectsfor which the tomographic images are presented herein andcompared with the simulation results

43 Circular Metallic Cylinder Top view and side view ofexperiment configuration for a circular metallic cylinder areshown in Figure 15 The measured radius (119903) and height (ℎ)


Table 2 Target objects imaged by the tomographic noise radar


MetalCircular cylinder 203 cm diameter times 406 cm height (810158401015840 diameter times 1610158401015840 height)

Square box 203 cm times 203 cm times 61 cm height (810158401015840 times 810158401015840 times 2410158401015840)Triangular prism 203 cm side times 305 cm height (810158401015840 side times 1210158401015840 height)

ConcreteCircular cylinder 152 cm diameter times 305 cm height (610158401015840 diameter times 1210158401015840 height)Square block 152 cm times 152 cm times 28 cm height (610158401015840 times 610158401015840 times 1110158401015840)

Semicircular cylinder 76 cm radius times 305 cm height (310158401015840 radius times 1210158401015840 height)

Figure 14 A metal cylinder placed on the turntable Also shown are the transmitting and receiving antenna and microwave absorber behindthe target to minimize reflections from the back as well as the test equipment and the scanner [52]

z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm

Figure 15 Top and side view of experiment configuration for a circular metallic cylinderThe cylinder is placed on the turntable for rotationAlso the microwave absorber behind the target is shown to minimize reflections from the back The rotational step angle is 9∘

of the cylinder are approximately 102 cm and 406 cmrespectively and the measured distance (119889) from the centerof the cylinder to the edge of a transmitting antenna isapproximately 66 cmA complete viewof the circularmetalliccylinder is shown in Figure 16The transmitting antenna (Tx)is fixed at the center of the object and the receiving antenna(Rx) is moving along the 119910-axis to collect the scattering dataMoving interval (Δ119910) for Rx is 15 cm that is scattering dataare measured and recorded for 55 different positions along119910-axis from (minus66 cm minus405 cm) and (minus66 cm 405 cm)

Figure 17 shows the final tomographic image of thecircular metallic cylinder based on the measured scatteringdata The tomographic image of the cylinder is correctlyreconstructed however the image quality is not as goodwhencompared to the simulated images displayed in Figure 4Since the experiment is performed in the room surroundedby concrete walls the image is contaminated by the addi-tional scattering due to concrete walls where no microwaveabsorbers are present Also unwanted noise from activeRF components and equipment degrades the image quality


Figure 16 The metallic cylinder used for the experiment Measured dimensions are in inches

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

Figure 17 Tomographic image of the metallic cylinder based on the measured data

a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm

Figure 18 Top and side view of experiment configuration for a square metallic box The box is placed on the turntable for rotation Therotational step angle is 9∘

However despite these unwanted reflections the cylindricalshape is well recognized

44 Square Metallic Box Top view and side view of experi-ment configuration for a square metallic cylinder are shownin Figure 18 The dimension of the box is 203 times 203 times 61 cmand themeasured distance (119889) from the center of the cylinderto the edge of a transmitting antenna is approximately 66 cmOther experimental configuration remains unchanged Acomplete view of the square metallic box is shown inFigure 19

As shown in Figure 20 the tomographic image of the boxis correctly reconstructed and the shape can be recognized

Similarly fringes are imaged due to the sharp corners of theboxAs before the image quality is degraded by the additionalscattering data due to concrete walls and unwanted noisefrom active RF components

45 Equilateral Triangular Metallic Prism Figure 21 showstop view and side view of experiment configuration for anequilateral triangular metallic prism The length of all sidesof the triangle is 203 cm and the height (ℎ) of the prism is305 cm The measured distance (119889) from the center of theprism to the edge of a transmitting antenna is approximately66 cm Figures 22 and 23 depict the actual triangular prismand the complete tomographic image with a full 360∘ rotation


Figure 19 The metallic square box used for the experiment Measured dimensions are in inches

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

Figure 20 Tomographic image of the metallic box based on the measured data

z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm

Figure 21 Top and side view of experiment configuration for an equilateral triangular metallic prism The rotational step angle is 9∘

Figure 22 The metallic prism used for the experiment Measured dimensions are in inches


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

Figure 23 Tomographic image of the metallic prism based on the measured data

z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm

Figure 24 Top and side view of experiment configuration for a circular concrete cylinder The rotational step angle is 9∘

of the object respectively The cross-section image of theprism can be clearly inferred in Figure 23

46 Circular Concrete Cylinder Figure 24 shows top view andside view of experiment configuration for a circular concretecylinder The measured radius (119903) and height (ℎ) of thecylinder are approximately 76 cm and 305 cm respectivelyand themeasured distance (119889) from the center of the cylinderto the edge of a transmitting antenna is approximately 66 cmA view of the concrete cylinder is shown in Figure 25 For theconcrete cylinder measurement moving interval (Δ119910) for Rxis 3 cm that is scattering data are measured and recorded for29 different positions along 119910-axis from (minus66 cm minus405 cm)and (minus66 cm 405 cm)

Figure 26 shows the complete tomographic image of thecircular concrete cylinder based on the measured scatteringdata Although the tomographic image of the dielectriccylinder is successfully obtained the image is not truly vividcompared to the metallic circular cylinder as expected Themeasured scattering field intensity of concrete object is not asstrong as the metallic object case Also the surface roughnessand the composition of concrete cylinder affect the scatteringbehavior which degrades the image quality compared to themetallic cylinder case

47 Square Concrete Block Top view and side view ofexperiment configuration for a square concrete block are

shown in Figure 27 The dimension of the block is 152 times

152 times 28 cm The measured distance (119889) from the centerof the cylinder to the edge of a transmitting antenna isapproximately 66 cm For the concrete block measurementthe transmitting antenna (Tx) is fixed at the center of theobject and only receiving antenna (Rx) is moving along the119910-axis to collect the scattering data for 29 different scanningpoints that is Δ119910 = 3 cm from (minus66 cm minus405 cm) and(minus66 cm 405 cm) The turntable is configured to rotate 9∘after a single line scan and the scattering data is measured for40 different angles Figures 28 and 29 show the actual concreteblock and the complete tomographic image with a full 360∘rotation of the object respectively The image of the concreteblock is affected by the measured field intensity Since thesurface of the concrete block is rough the image quality is notcomparable to metallic box case However the experimentalresults are in good agreement with the simulation resultsshown in the previous section

48 Semicircular Concrete Cylinder Top view and side viewof experiment configuration for a semicircular concretecylinder are shown in Figure 30 The measured radius (119903)and height (ℎ) of the cylinder are approximately 76 cm and305 cm respectively and the measured distance (119889) from thecenter of the cylinder to the edge of a transmitting antennais approximately 66 cm A view of the concrete cylinder is


Figure 25 The concrete cylinder used for the experiment Measured dimensions are in inches

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

Figure 26 Tomographic image of the concrete cylinder based on the measured data

a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm

Figure 27 Top and side view of experiment configuration for a square concrete block The rotational step angle is 9∘

Figure 28 The concrete block used for the experiment Measured dimensions are in inches


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

Figure 29 Tomographic image of the concrete block based on the measured data

z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm

Figure 30 Top and side view of experiment configuration for a semicircular concrete cylinder The rotational step angle is 9∘

shown in Figure 31 For the semicircular concrete cylindermeasurement moving interval (Δ119910) for Rx is changed to15 cm that is scattering data are measured and recorded for55 different positions along 119910-axis from (minus66 cm minus405 cm)and (minus66 cm 405 cm) As seen in Figure 31 the surface of thesemicircular concrete cylinder is not perfectly smooth andhomogeneous

Figure 32 shows the complete tomographic image ofthe semicircular concrete cylinder based on the measuredscattering data Since the object has two sharp edges at theback side the fringes are observed around the corners ofthe flat side The surface roughness and the composition ofconcrete cylinder definitely degrade the image quality whichis similar to the previous concrete object cases

49 Imaging through Barriers A few of the targets wereplaced within optically opaque containers such as a card-board box and a wooden box and tomographic images wereproduced

The size of the cardboard box was 508 cm times 406 cm times

541 cm and its wall thickness was 4mm Figure 33 showsthe complete tomographic images of the circular metalliccylinder (Figure 16) and the equilateral triangular metallicprism (Figure 22) By comparing Figures 33(a) and 17 and

also Figures 33(b) and 23 it can be observed that while thecardboard adds a small amount of noise the target object isstill clearly visible and discernible

Objects were also concealed within a wooden box ofsize 381 cm times 381 cm times 381 cm and 127 cm wall thicknessFigure 34 shows the complete tomographic images of thecircular metallic cylinder (Figure 16) the square metallic box(Figure 19) the circular concrete cylinder (Figure 25) andthe square concrete block (Figure 28) The wooden box addsmore noise to the images when compared to the correspond-ing images obtained in the free space environment but thetarget objects are still visible and their shapes recognizableObjects having a square cross section are imaged well whileimages of objects with a circular cross section are somewhatdistorted

5 Conclusions

Radar tomography using UWB random noise waveformsis accomplished while maintaining the advantages of UWBnoise radar such as LPI and high-resolution imaging capa-bility Theoretical analysis numerical simulation results andhardware implementation of the bistatic UWB noise tomog-raphy radar are presented in this paper We conclude that thetomographic images of various target scenarios are correctly


Figure 31 The semicircular concrete cylinder used for the experiment Measured dimensions are in inches


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

Figure 32 Tomographic image of the semicircular concrete cylinder based on the measured data


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)

Figure 33 Tomographic images of (a) the circularmetallic cylinder and (b) equilateral triangularmetallic prism concealedwithin a cardboardbox based on the measured data



y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)

Figure 34 Tomographic images of (a) the circular metallic cylinder (b) the square metallic box (c) the circular concrete cylinder and(d) the square concrete block concealed within a wooden box based on the measured data

formedwithUWB randomnoise waveforms showing a goodagreement between simulation and experiment results forboth metallic and dielectric target object cases Based onthe comparison of simulation and experimental results thepresence of unwanted noise truly degrades the image qualityhowever the suppression of unwanted noise contributions bycontrolling SNR can help to enhance the image quality oftomographic images in practical radar imaging

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by the Air Force Office of ScientificResearch (AFOSR) Contract no FA9550-12-1-0164

References

[1] E KWalton ldquoUse of fixed-range noise radar formoving-vehicleidentificationrdquo in Proceedings of the ARL (Army Research Labo-ratory) Symposium on Sensors and Electron Devices SymposiumCollege Park Md USA January 1997

[2] H Sun Y Lu and G Liu ldquoUltra-wideband technology andrandom signal radar an ideal combinationrdquo IEEE Aerospaceand Electronic Systems Magazine vol 18 no 11 pp 3ndash7 2003

[3] R M Narayanan and X Xu ldquoPrinciples and applications ofcoherent random noise radar technologyrdquo in Noise in Devicesand Circuits vol 5113 of Proceedings of SPIE pp 503ndash514 SantaFe NM USA June 2003

[4] G Liu X Shi and J Lu ldquoRandom FM-CW radar and itsECCMrdquo in Proceedings of the Record of the Chinese Institute ofElectronics International Conference on Radar (CIE ICR rsquo86) pp155ndash160 Nanjing China November 1986


[5] N Gonget P Y Arques and L Martinet ldquoSurveillanceradar waveform fitted for antistealthness and for counter-countermeasures evaluationrdquo in Proceedings of the 8th Euro-pean Signal Processing Conference (EUSIPCO rsquo96) Paper noPSO10 Trieste Italy September 1996

[6] D S Garmatyuk and R M Narayanan ldquoECCM capabilities ofan ultrawideband bandlimited random noise imaging radarrdquoIEEE Transactions on Aerospace and Electronic Systems vol 38no 4 pp 1243ndash1255 2002

[7] J R Forrest and J P Meeson ldquoSolid-state microwave noiseradarrdquo Electronics Letters vol 12 no 15 pp 365ndash366 1976

[8] L Guosui G U Hong and S U Weimin ldquoThe developmentof random signal radarsrdquo IEEE Transactions on Aerospace andElectronic Systems vol 35 no 3 pp 770ndash777 1999

[9] J SachsM Kmec H C Fritsch et al ldquoUltra-wideband pseudo-noise sensorsrdquoApplied Radio Electronics vol 12 no 1 pp 79ndash882013

[10] X Xu and R M Narayanan ldquoFOPEN SAR imaging usingUWB step-frequency and random noise waveformsrdquo IEEETransactions on Aerospace and Electronic Systems vol 37 no 4pp 1287ndash1300 2001

[11] R M Narayanan X Xu and J A Henning ldquoRadar pene-tration imaging using ultra-wideband (UWB) random noisewaveformsrdquo IEE Proceedings-Radar Sonar and Navigation vol151 no 3 pp 143ndash148 2004

[12] K Lukin and V Konovalov ldquoThrough wall detection andrecognition of human beings using noise radar sensorsrdquo inProceedings of the NATO RTO SET Symposium on TargetIdentification and Recognition Using RF Systems pp P151ndashP1512 Oslo Norway October 2004

[13] J Sachs M Aftanas S Crabbe et al ldquoDetection and trackingof moving or trapped people hidden by obstacles using ultra-wideband pseudo-noise radarrdquo in Proceedings of the 5th Euro-pean Radar Conference pp 408ndash411 IEEE Amsterdam TheNetherlands October 2008

[14] R M Narayanan ldquoThrough-wall radar imaging using UWBnoise waveformsrdquo Journal of the Franklin Institute vol 345 no6 pp 659ndash678 2008

[15] E K Walton ldquoGround penetrating radar using ultra-widebandnoiserdquo in Proceedings of the Second Government Workshop onGround Penetrating Radar (GPR rsquo93) p 121 Columbus OhioUSA October 1993

[16] E K Walton and L Cai ldquoSignatures of surrogate mines usingnoise radarrdquo in Detection and Remediation Technologies forMines and Minelike Targets III vol 3392 of Proceedings of SPIEpp 615ndash626 Orlando Fla USA September 1998

[17] C K Chan and N H Farhat ldquoFrequency swept tomographicimaging of three-dimensional perfectly conducting objectsrdquoIEEE Transactions on Antennas and Propagation vol 29 no 2pp 312ndash319 1981

[18] K K Knaell and G P Cardillo ldquoRadar tomography for the gen-eration of three-dimensional imagesrdquo IEE Proceedings RadarSonar and Navigation vol 142 no 2 pp 54ndash60 1995

[19] L Jofre A Broquetas J Romeu et al ldquoUWB tomographic radarimaging of penetrable and impenetrable objectsrdquo Proceedings ofthe IEEE vol 97 no 2 pp 451ndash464 2009

[20] W C Chew W H Weedon and M Moghaddam ldquoInversescattering and imaging using broadband time-domain datardquo inUltra-Wideband Short-Pulse Electromagnetics 2 L Carin andL B Felsen Eds vol 2 pp 549ndash562 Springer New York NYUSA 1995

[21] E Porter A Santorelli M Coates and M Popovic ldquoAn experi-mental system for time-domain microwave breast imagingrdquo inProceedings of the 5th European Conference on Antennas andPropagation (EUCAP rsquo11) pp 2906ndash2910 IEEE Rome ItalyApril 2011

[22] H J Shin R M Narayanan and M Rangaswamy ldquoTomo-graphic imaging with ultra-wideband noise radar using time-domain datardquo in Radar Sensor Technology XVII vol 8714 ofProceedings of SPIE pp 1ndash9 Baltimore Md USA May 2013

[23] A C Kak ldquoComputerized tomography with X-ray emissionand ultrasound sourcesrdquo Proceedings of the IEEE vol 67 no 9pp 1245ndash1272 1979

[24] L Garnero A Franchois J-P Hugonin C Pichot andN Joachimowicz ldquoMicrowave imagingmdashcomplex permittivityreconstruction by simulated annealingrdquo IEEE Transactions onMicrowave Theory and Techniques vol 39 no 11 pp 1801ndash18071991

[25] S Valle L Zanzi and F Rocca ldquoRadar tomography for NDTcomparison of techniquesrdquo Journal of Applied Geophysics vol41 no 2-3 pp 259ndash269 1999

[26] R Ciocan and H B Jiang ldquoModel-based microwave imagereconstruction simulations and experimentsrdquoMedical Physicsvol 31 no 12 pp 3231ndash3241 2004

[27] L Huang and Y Lu ldquoThrough-the-wall tomographic imagingusing chirp signalsrdquo in Proceedings of the IEEE InternationalSymposium on Antennas and Propagation pp 2091ndash2094Spokane Wash USA July 2011

[28] K A Lukin P L Vyplavin V V Kudriashov V P PalamarchukP G Sushenko and N K Zaets ldquoRadar tomography usingnoise waveform antenna with beam synthesis and MIMOprinciplerdquo in Proceedings of the 9th International Conferenceon Antenna Theory and Techniques (ICATT rsquo13) pp 190ndash192Odessa Ukraine September 2013

[29] G FornaroA PauciulloD Reale and SVerde ldquoMultilook SARtomography for sensing built structures with very high reso-lution spaceborne sensorsrdquo in Proceedings of the 11th EuropeanRadarConference (EuRad rsquo14) pp 221ndash224 Rome ItalyOctober2014

[30] A Broquetas R Jordi J M Rius A R Elias-Fuste A Cardamaand L Jofre ldquoCylindrical geometry a further step in activemicrowave tomographyrdquo IEEE Transactions on Microwave The-ory and Techniques vol 39 no 5 pp 836ndash844 1991

[31] H C Rhim and O Buyukozturk ldquoWideband microwave imag-ing of concrete for nondestructive testingrdquo Journal of StructuralEngineering vol 126 no 12 pp 1451ndash1457 2000

[32] P Mojabi and J LoVetri ldquoA prescaled multiplicative regularizedGauss-Newton inversionrdquo IEEE Transactions on Antennas andPropagation vol 59 no 8 pp 2954ndash2963 2011

[33] A J Devaney ldquoInversion formula for inverse scattering withinthe Born approximationrdquoOptics Letters vol 7 no 3 pp 111ndash1121982

[34] T H Chu and K Y Lee ldquoWide-band microwave diffractiontomography under Born approximationrdquo IEEE Transactions onAntennas and Propagation vol 37 no 4 pp 515ndash519 1989

[35] B S Robinson and J F Greenleaf ldquoAn experimental studyof diffraction tomography under the Born approximationrdquoin Acoustical Imaging H Lee and G Wade Eds vol 18 ofAcoustical Imaging pp 391ndash400 Springer New York NY USA1990


[36] L Turner ldquoThe evolution of featureless waveforms for LPI com-municationsrdquo in Proceedings of the IEEENational Aerospace andElectronics Conference (NAECON rsquo91) pp 1325ndash1331 DaytonOhio USA May 1991

[37] C-P Lai and R M Narayanan ldquoUltrawideband random noiseradar design for through-wall surveillancerdquo IEEE Transactionson Aerospace and Electronic Systems vol 46 no 4 pp 1716ndash1730 2010

[38] H J Shin R M Narayanan andM Rangaswamy ldquoSimulationsof tomographic imaging of various target scenarios using noisewaveformsrdquo in Proceedings of the IEEE International RadarConference pp 963ndash968 IEEE Arlington Va USA May 2015

[39] L Jofre A P Toda J M J Montana et al ldquoUWB short-range bifocusing tomographic imagingrdquo IEEE Transactions onInstrumentation andMeasurement vol 57 no 11 pp 2414ndash24202008

[40] D Sheen D McMakin and T Hall ldquoNear-field three-dimensional radar imaging techniques and applicationsrdquoApplied Optics vol 49 no 19 pp E83ndashE93 2010

[41] S Gu C Li X Gao Z Sun and G Fang ldquoTerahertz aperturesynthesized imaging with fan-beam scanning for personnelscreeningrdquo IEEE Transactions on Microwave Theory and Tech-niques vol 60 no 12 pp 3877ndash3885 2012

[42] R F Harrington ldquoOn scattering by large conducting bodiesrdquoIRE Transactions on Antennas and Propagation vol 7 no 2 pp150ndash153 1959

[43] H J Shin R M Narayanan and M Rangaswamy ldquoUltra-wideband noise radar imaging of impenetrable cylindricalobjects using diffraction tomographyrdquo International Journal ofMicrowave Science and Technology vol 2014 Article ID 60165922 pages 2014

[44] W Tabbara B Duchene C Pichot D Lesselier L Chom-meloux and N Joachimowicz ldquoDiffraction tomography con-tribution to the analysis of some applications inmicrowaves andultrasonicsrdquo Inverse Problems vol 4 no 2 pp 305ndash331 1988

[45] J C Bolomey and C Pichot ldquoMicrowave tomography fromtheory to practical imaging systemsrdquo International Journal ofImaging Systems and Technology vol 2 no 2 pp 144ndash156 1990

[46] H J Shin R M Narayanan and M Rangaswamy ldquoDiffrac-tion tomography for ultra-wideband noise radar and imagingquality measure of a cylindrical perfectly conducting objectrdquo inProceedings of the IEEE Radar Conference (RadarCon rsquo14) pp702ndash707 Cincinnati Ohio USA May 2014

[47] H J Shin R M Narayanan and M Rangaswamy ldquoUltra-wideband noise radar imaging of cylindrical PEC objects usingdiffraction tomographyrdquo in Radar Sensor Technology XVIII vol9077 of Proceedings of SPIE pp 1ndash10 Baltimore Md USA May2014

[48] A M Eskicioglu and P S Fisher ldquoImage quality measures andtheir performancerdquo IEEE Transactions on Communications vol43 no 12 pp 2959ndash2965 1995

[49] I Avcibas B Sankur and K Sayood ldquoStatistical evaluation ofimage quality measuresrdquo Journal of Electronic Imaging vol 11no 2 pp 206ndash223 2002

[50] H J Shin M A Asmuth R M Narayanan and MRangaswamy ldquoPrinciple and experimental results of ultra-wideband noise radar imaging of a cylindrical conductingobject using diffraction tomographyrdquo in Radar Sensor Tech-nology XIX and Active and Passive Signatures VI vol 9461 ofProceedings of SPIE pp 1ndash11 Baltimore Md USA April 2015

[51] M G AminThrough-the-Wall Radar Imaging CRC Press BocaRaton Fla USA 2010

[52] M A Asmuth H J Shin R M Narayanan and M Ran-gaswamy ldquoDesign and implementation of a noise radar tomo-graphic systemrdquo in Radar Sensor Technology XIX vol 9461 ofProceedings of SPIE pp 1ndash9 Baltimore Md USA April 2015

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



x

Incidentplane wave

y

r

y

xz

x = minusd

1st Rx

2nd Rx

Δyn minus 1th Rx

nth Rx

Figure 1 Two-dimensional backward scattering geometry for a cylindrical object The 119911-polarized incident wave is illuminated from minus119909

direction and propagated in free space

accuracy Furthermore transmitting randomnoisewaveforminherits the aforementioned advantages of noise radar Thepaper is organized as follows In Section 2 theoretical analysisof the image reconstruction for a bistatic noise radar systemwith two-dimensional scattering geometry using Fourierdiffraction theorem under the assumption of plane waveillumination is presentedThenumerical simulation results ofdiffraction tomographyusingUWBrandomnoisewaveformsare presented in Section 3 Section 4 describes the RFhardware implementation and experimental results from thatnoise radar system Further we compare the images obtainedwith simulations and experiments Conclusions are drawn inSection 5

2 Theory and Formulation

The main advantage of transmitting a random noise wave-form is to covertly detect and image a target without alertingthe presence of radar system Such LPI characteristic of thenoise radar is achieved by using a random noise waveformwhich is constantly varying and never repeats itself exactly[36 37] The random noise waveform herein is mathemat-ically defined as discrete time wide-sense stationary (WSS)and ergodic random process and a sequence of independentand identically distributed (iid) random variable drawnfrom a normal distribution N(0 120590

2) The power spectral

density (PSD) of white Gaussian noise (WGN) waveform isideally a nonzero constant for all frequencies In practicalsituations however the PSD of the random noise waveformmay not be uniform across thewide frequency ranges becausea finite number of random noise amplitude samples mustbe chosen for WGN waveform generation In order tobypass such a shortcoming multiple sequences of iid noisewaveforms are transmitted to flatten the spectral densitywithout changing the mean and variance [38]

Figure 1 shows two-dimensional backward scatteringgeometry for a cylindrical target objectThe values of receiverspacing Δ119910 and the frequency sampling interval Δ119891 aredetermined based on the maximum operating frequency andthe size of the object respectively to ensure an image that isfree of false aliases [39ndash41]

The analysis starts from a single frequency and developsthe process for UWB by summing up the analysis results for119873 discrete frequencies As shown in Figure 1 the incident 119911-polarized plane wave of the WGN waveform for 119873 multiplefrequencies takes the form

119864119894(119896119899 119903)

= (1198641119890minus1198951198961sdot 119903

+ 1198641119890minus1198951198962sdot 119903

+ sdot sdot sdot + 119864119873119890minus119895119896119873sdot 119903)

=

119873

sum

119899=1

119864119899119890minus119895119896119899sdot 119903

119867119894(119896119899 119903) = minus

1

120578

times 119864119894(119896119899 119903)

(1)

where 119896119899

= 120596119899119888 is the wavenumber 120578 is the intrinsic

impedance in free space and 119864119899is the field amplitude of the

transmitted white Gaussian noise waveform at each discretefrequency of interest We start the analysis from a singlefrequency and develop the process for119873multiple frequenciesby summing up the analysis results for119873 The entire analysismust be repeated for 119870 times when 119870 multiple sequences ofiid noise waveforms are transmitted

Consider a dielectric target object illuminated by an inci-dent plane wave denoted in (1) which induces an equivalentelectric current distribution given by

119869eqdielectric (119896119899 119903) = 119895120596 [120576 ( 119903) minus 1205760] 119864 (119896119899 119903) (2)

where 120576( 119903) and 1205760denote the complex permittivity of the

object and the vacuum permittivity respectively 119864(119896119899 119903) in

(2) is the total field due to the presence of the object and isexpressed as the sum of the incident field 119864

119894(119896119899 119903) and the

scattered field 119864119904(119896119899 119903) that is

119864 (119896119899 119903) = 119864

119894(119896119899 119903) + 119864

119904(119896119899 119903) (3)

If the object is assumed to be a perfect electric conductor(PEC) the equivalent induced current distribution is calcu-lated by applying the physical optics approximation [42] andis given by

119869eqPEC (119896119899 119903) = 2 ( 119903) times 119867119894(119896119899 119903) (4)












119864119904(119896119899 119903) = minus119895120596120583

0int

119878

119869eq (119896119899 1199031015840) sdot 119866 ( 119903 minus 119903

1015840) 119889 1199031015840 (5)




119906119904(119896119899 119909 = minus119889 119910) = sdot 119864

119904(119896119899 119909 = minus119889 119910)

= 120595∬119900 ( 1199031015840) 119890minus119895119896119899sdot 1199031015840

119866( 119903 minus 1199031015840) 11988921199031015840

(6)

where 120595 = 1198962


119899119864119899for


119904(119896119899 119909 = minus119889 119896

119910) =

minus119895120595

2120574

119890minus119895120574119889

(minus120574 minus 119896119899 119896119910) (7)

where

120574 =

radic119896119899

2minus 119896119910

2 as 10038161003816100381610038161003816119896119910

10038161003816100381610038161003816le 119896119899

minus119895radic119896119910

2minus 119896119899

2 as 10038161003816100381610038161003816119896119910

10038161003816100381610038161003816gt 119896119899

(8)


119904(119896119899 119909 = minus119889 119896

119910) = int119906

119904(119896119899 119909 = minus119889 119910) 119890

119895119896119910119910119889119910 (9)





(119896119909 119896119910) = ∬119900 (119909 119910) 119890

minus119895(119896119909119909+119896119910119910)119889119909 119889119910 (10)












Final target

Final target







Target image







Target image


1205791

o(x y)

o11205791 (x y)for 1205791

for 1205791

1205791for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

120579rfor 120579rfor 120579r

120579rfor 120579rfor 120579r

o1120579r (x y)

oK1205791(x y)

oK120579r(x y)



sum

sum

sum










x

y

r = 10

Rx 1

Rx 55y

xz Rx 54

(0 0)

(minus68 minus405)

(minus68 405)


Rx 2

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54

(minus68 405)


Rx 2

a = 20

a = 20

(0 0)

(minus68 minus405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 20 (0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8













minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















119864119904(119896119899 119903) = minus119895120596120583

0int

119878

119869eq (119896119899 1199031015840) sdot 119866 ( 119903 minus 119903

1015840) 119889 1199031015840 (5)




119906119904(119896119899 119909 = minus119889 119910) = sdot 119864

119904(119896119899 119909 = minus119889 119910)

= 120595∬119900 ( 1199031015840) 119890minus119895119896119899sdot 1199031015840

119866( 119903 minus 1199031015840) 11988921199031015840

(6)

where 120595 = 1198962


119899119864119899for


119904(119896119899 119909 = minus119889 119896

119910) =

minus119895120595

2120574

119890minus119895120574119889

(minus120574 minus 119896119899 119896119910) (7)

where

120574 =

radic119896119899

2minus 119896119910

2 as 10038161003816100381610038161003816119896119910

10038161003816100381610038161003816le 119896119899

minus119895radic119896119910

2minus 119896119899

2 as 10038161003816100381610038161003816119896119910

10038161003816100381610038161003816gt 119896119899

(8)


119904(119896119899 119909 = minus119889 119896

119910) = int119906

119904(119896119899 119909 = minus119889 119910) 119890

119895119896119910119910119889119910 (9)





(119896119909 119896119910) = ∬119900 (119909 119910) 119890

minus119895(119896119909119909+119896119910119910)119889119909 119889119910 (10)












Final target

Final target







Target image







Target image


1205791

o(x y)

o11205791 (x y)for 1205791

for 1205791

1205791for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

120579rfor 120579rfor 120579r

120579rfor 120579rfor 120579r

o1120579r (x y)

oK1205791(x y)

oK120579r(x y)



sum

sum

sum










x

y

r = 10

Rx 1

Rx 55y

xz Rx 54

(0 0)

(minus68 minus405)

(minus68 405)


Rx 2

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54

(minus68 405)


Rx 2

a = 20

a = 20

(0 0)

(minus68 minus405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 20 (0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8













minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Final target

Final target







Target image







Target image


1205791

o(x y)

o11205791 (x y)for 1205791

for 1205791

1205791for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

for 1205791

120579rfor 120579rfor 120579r

120579rfor 120579rfor 120579r

o1120579r (x y)

oK1205791(x y)

oK120579r(x y)



sum

sum

sum










x

y

r = 10

Rx 1

Rx 55y

xz Rx 54

(0 0)

(minus68 minus405)

(minus68 405)


Rx 2

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54

(minus68 405)


Rx 2

a = 20

a = 20

(0 0)

(minus68 minus405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 20 (0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8













minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x

y

r = 10

Rx 1

Rx 55y

xz Rx 54

(0 0)

(minus68 minus405)

(minus68 405)


Rx 2

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54

(minus68 405)


Rx 2

a = 20

a = 20

(0 0)

(minus68 minus405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 20 (0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8













minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x

y

Rx 1

Rx 55y

xz Rx 54

(minus68 405)


Rx 2

a = 20

a = 20

(0 0)

(minus68 minus405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 20 (0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8













minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 20 (0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579


minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)



x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8













minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579r = 8













minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)


x

y

Rx 1

Rx 55y

xz Rx 54


Rx 2

a = 16

a = 16

(0 0)

(minus68 minus405)

(minus68 405)

x = minus68

Δy = 15

120579



minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(a)

minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(b)minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(c)

minus04


y (m

)minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0

(d)








y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










y

x

z

Rx Tx



Microwave absorber

Linear scanner

Power amplifier


(AWG)

Desktop computer


120579
















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm






minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm









minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z a

d

dRx Tx

Rx

TxhaΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

Txh

Δy

120579

81 cm











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


a

a

z

xy

y

x

z a

d

dRx Tx

Rx

TxhΔy

120579

81 cm




minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus04


y (m

)

minus03

minus02

minus01

0

01

02

03

04

1

09

08

07

06

05

04

03

02

01

0


z

xy

y

x

z

r

r

d

dRx Tx

Rx

TxhΔy

120579

81 cm









5 Conclusions





y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04



y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)




y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











y (m

)1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(a)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(b)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(c)


y (m

)

1

09

08

07

06

05

04

03

02

01

0

04

03

02

01

0

minus01

minus02

minus03

minus04

(d)



Competing Interests


Acknowledgments


References

























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article ultrawideband noise radar tomography

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