A Fast Terahertz Imaging Method Using Sparse ... - Semantic Scholar

sensors Article

A Fast Terahertz Imaging Method Using Sparse Rotating Array Yanwen Jiang *, Bin Deng, Yuliang Qin, Hongqiang Wang

ID

and Kang Liu

College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China; [email protected] (B.D.); [email protected] (Y.Q.); [email protected] (H.W.); [email protected] (K.L.) * Correspondence: [email protected]; Tel.: +86-731-8457-4452 Received: 19 July 2017; Accepted: 24 September 2017; Published: 26 September 2017

Abstract: For fast and standoff personal screening, a novel terahertz imaging scheme using a sparse rotating array is developed in this paper. A linearly sparse array is designed to move along a circular path with respect to an axis perpendicular to the imaging scenario. For this new scheme, a modified imaging algorithm is proposed based on the frequency-domain reconstruction method in circular synthetic aperture radar. To achieve better imaging performance, an optimization method of the sparse array is also proposed, according to the distribution of the spectral support. Theoretical and numerical analysis of the point spread function (PSF) is provided to demonstrate the high-resolution imaging ability of the proposed scheme. Comprehensive simulations are carried out to validate the feasibility and effectiveness of the array optimization method. Finally, the imaging results of a human-scattering model are also obtained to further demonstrate the good performance of this new imaging scheme and the effectiveness of the array optimization approach. This work can facilitate the design and practice of terahertz imaging systems for security inspection. Keywords: sparse array optimization; spectral support; synthetic aperture radar; terahertz imaging

1. Introduction Due to the increasing threat of terrorism, security inspection has been becoming increasingly important at many high-security facilities, including airports and railway stations. Generally, effective detection instruments, like X-ray imagers, metal detecting gates and hand-held metal detectors, are widely applied for security inspection. However, for personal screening applications, the X-ray imager cannot be an acceptable choice because of its harmful effects on body health. Metal detectors are not suitable due to their dependence on human assistance, which leads to low efficiency. With their safety characteristics and short data acquisition time, terahertz (THz) and millimeter wave (MMW) technologies have been widely researched for security applications [1–4]. Moreover, THz waves and MMWs have penetration capability, and can achieve high spatial imaging resolution, which enables them to display good performance in the detection of concealed dangerous objects. Therefore, THz and MMW imaging is an alternative and effective means for personal screening. Hitherto, a number of THz and MMW imagers have been developed for personal screening, which can be divided into two types: mechanical scanning [5–8] and multistatic arrays [9–11]. The mechanical scanning architecture is usually implemented by a linearly moving process or fast rotating reflector. In particular, the linearly moving process requires either a single antenna scan, which lasts at least several minutes and results in low efficiency, or a linear array scan, which is very expensive [5]. The optical reflector used for fast rotating usually requires a high-precision manufacturing technique, and is also very expensive [6,7]. In addition, despite the very fast imaging speed, multistatic architectures based on thousands of antennas are bulky, complicated, and costly

Sensors 2017, 17, 2209; doi:10.3390/s17102209

www.mdpi.com/journal/sensors

Sensors 2017, 17, 2209

2 of 13

for practical implementation [9,11]. Recently, an imaging method has been proposed based on the mechanical scanning technique and multistatic arrays [12], which significantly reduces the time cost compared to the traditional mechanical scanning method, but still requires hundreds of antennas. Hence, to overcome the tradeoff between system cost and imaging speed, THz and MMW imagers still need further investigation for wide application under practical conditions. In this paper, a new terahertz imaging method for standoff personal screening is proposed based on the circular synthetic aperture radar (SAR) configuration and the sparse array technique. The circular scanning method ensures nonstop scanning with fast speed and high imaging resolution, and the sparse array technique, which only needs several antennas, reduces the system cost. The rest of this paper is organized as follows. In Section 2, the new terahertz imaging scheme is described in detail, and the spectral support and the point spread function (PSF) are analyzed. A modified imaging algorithm is developed based on the circular SAR imaging technique [13,14]. In Section 3, an optimization method for the sparse array based on the distribution of the spectral support is proposed, in order to achieve better imaging performance. Different from the existing array optimization method [15,16], the proposed array optimization method is based on the distribution of the spectral support and the imaging geometry. Simulations are performed to validate the effectiveness of this proposed method. In Section 4, simulations of the imaging of a human-scattering model are carried out to further demonstrate the good performance of the new imaging scheme. Results verify the effectiveness of the proposed imaging algorithm and the array optimization method. The conclusions are drawn in Section 5. 2. The Proposed Imaging Scheme and Algorithm 2.1. Description of the Imaging Model The observation geometry of the proposed imaging scheme is shown in Figure 1, where the front view displayed in Figure 1b is rotationally symmetric about the OZ axis. The target coordinate system OXYZ is fixed. The radar, consisting of m self-transceiver antennas, moves along a circular path on the vertical plane z = Zc , i.e., the X0 O0 Y 0 plane, where Zc is the range between the radar and the target in the horizontal direction. Thus, the radius of the circular path for each antenna is Ri ∈ [ Rm , R1 ], i = 1, . . . , m, and the coordinate of the ith antenna in the spatial domain can be denoted by ( Ri cos θ, Ri sin θ, Zc ), where θ ∈ [0, 2π ) is the azimuthal angle. It can be seen from Figure 1a that the circular synthetic aperture achieved by one antenna is similar to the synthetic aperture of the circular SAR [14,17]. In Figure 1b, αi represents the side angle of the ith antenna with respect to the origin O, which is equal to arctan ( Zc /Ri ). It should be noted that all the antennas rotate around the same center (0, 0, Zc ) and the same azimuthal angle θ, but with different radii Ri . As the radar moves along the circular path, the beams of all the antennas are spotlighted on a disk with radius W centered at the origin O on the XOY plane, where W indicates the radius of the imaging scenario. It can be seen from Figure 1b that the half-power beamwidth φi of the ith antenna can be denoted by φi = arctan [(W − Ri )/Zc ] + arctan [(W + Ri )/Zc ] [13]. Accordingly, the half-power beamwidth φ of all the antennas should satisfy the condition  φ ≥ max{φ1 , . . . , φm } = max arctan



W − Ri Zc





+ arctan

  W + Ri , i = 1, . . . , m Zc

(1)

Sensors 2017, 17, 2209 Sensors 2017, 17, 2209

3 of 13 3 of 13 Y

Y

W

W

Radar ..

P( x , y ,0)

1

R1

....

Rm 

X O

Y W

1  m

X

m

O

O

......

Y

R1 Rm

Zc Z

Z

Rm . . . .

..

R1



O

X

Target

Target

W

W

(a)

(b)

(c)

Figure 1. Observation geometry of the proposed imaging method: (a) Perspective view; (b) Front Figure 1. Observation geometry of the proposed imaging method: (a) Perspective view; (b) Front view; view; (c)side Right side view. (c) Right view.

It is assumed that the antennas transmit the linear frequency modulation (LFM) signal in time It is assumed that the signal antennas transmit the frequency modulation (LFM) itself signalisin time sequence. When the LFM is transmitted bylinear the ith antenna, the ith antenna used to sequence. When the LFM signal is transmitted by the ith antenna, the ith antenna itself is used to receive the echo signal, which can be defined by receive the echo signal, which can be defined by i i c si ( kZ,Z)   g( x, y)  eq dxdy − j2k ( x − Ri cos θ )2 +(y− Ri sin θ )2 + Zc2 dxdy si (k, θ ) = g( x, y) × e denotes the reflectivity function and k  2 f / c is the

 j 2 k ( x  R cos  )2 ( y  R sin  )2  Z2

where

g( x, y)

(2) (2) wavenumber.

c is the light f  [ fc g(B f c is the center  B / 2] , where frequency. bandwidth and wavenumber. where x,/y2,) fcdenotes the reflectivity function and kB is= the2π f /c is the the free space. fspeed ∈ [ f c in − B/2, fc + B/2], where f c is the center frequency. B is the bandwidth and c is the light speed in the free space. 2.2. Analysis of the Spectral Support and PSF 2.2. Analysis of the Spectral Support and PSF According to Equation (2) the phase trace of the ith antenna response is According tocosEquation the ith antenna response is    2q k (x  R  )2  ( y  (2) R sinthe  )2  phase Z 2 . Thetrace spatialoffrequency along the X and Y direction i

i

i

c

2 2 Ω −2k − Ri cos + (be y −defined Ri sin θ )by +the Zc2derivative . The spatial i = i , i.e., along the X and Y direction XOY( x plane on the canθ )then of frequency on the XOY plane can then be defined by the derivative of Ωi , i.e., i x  Ri cos kx   i  2k ∂Ω x− Ri cos θ q k xx= ∂x = −2k ( x  Ri cos )22  ( y  Ri sin  )2  Zc2 ( x − Ri cos θ ) +(y− Ri sin θ )2 + Zc2 (3) (3)  ∂Ω i sin Ri sin yy− R θ  ky  k y =i ∂yi =2 k−2k q 2 2 2 − Rcos +Z y i cos ( x ( xR θ))2 +(  y(−yRisinRθi )sin c)2  Zc2 i

ItItcan canbe beknown knownfrom fromEquation Equation(3) (3)that thatthe thespectral spectralsupport supportof ofthe theimaging imagingscheme schemeisisspatially spatially variant, the values valuesofof kk x and and kky are dependent on the the location locationofofthe thetarget targetP(Px(, yx,,0) y,.0In ). variant, because because the are dependent on x y In particular, for the target located at origin (0, 0, 0), the corresponding spatial frequency can be particular, for the target located at origin (0,0,0) , the corresponding spatial frequency can be written as written as k xk =2k2cos i cos k cosα cosθ (4) x i (4) k yk =2k2cos α sin θ k cosi i sin y q where cos αi = Ri / Zc22 + R22i . where cos i  Ri / Zc  Ri . q Denote the spatial wavenumber as ρi = k2x + k2y = 2k cos αi . When a signal with wide Denote the spatial wavenumber as i  kx2  ky2  2k cosi . When a signal with wide bandwidth is used and the condition θ ∈ [0, 2π ) is satisfied, the two-dimensional spectral support bandwidth is used imaging and the condition theradii two-dimensional spectral   [0,2  ) is satisfied, of the ith antenna is an annulus in Figure 2, and the are ρmin = 2k αi and min cossupport i max min ρof = 2k cos αi , respectively. To obtain a better visual onlyradii one are annulus an i isdisplayed 2 kmin cos as ithmaxantenna imaging is an annulus in Figure 2,effect, and the i the i and example in Figure 2, which represents the spectral support of one antenna. It can be noted that the max i  2 kmax cos i , respectively. To obtain a better visual effect, only one annulus is displayed as an spectral support of any other antenna is a similar annulus with a different radius. example in Figure 2, which represents the spectral support of one antenna. It can be noted that the spectral support of any other antenna is a similar annulus with a different radius.

Sensors 2017, 17, 2209 Sensors 2017, 17, 2209

4 of 13 4 of 13

ky

 im in O

kx

imax

Figure 2. 2. The The spectral spectral support support of of imaging imaging with with one one antenna. antenna. Figure

Accordingly, the PSF of the target located at the center point (0,0,0) in the spatial domain is Accordingly, the PSF of the target located at the center point (0,0,0) in the spatial domain is [13,18]: [13,18]: ρmax J1 (ρmax r ) − ρmin J (ρmin i  max i r r) ) J1 ( i imaxr )  i imin J11 ( imin psfpsf (5) i i ( x,( xy,)y= (5) )  r i r

p where r r=  xx2 2+y2y,2 J,1 isJ the orderorder BesselBessel function of the first kind. radial resolution becomes where is first the first function of the firstThe kind. The radial resolution 1 min = 0. Hence, the radial resolution is approximately a π/ρmax , π/ρmax under a limit condition ρ 0 i i i max imin of the 0 . Hence, becomes limit condition the imaging radial resolution is approximately where 1 ≤ /a0i ≤ 2under [14]. aThe spectral support proposed scheme with m antennas imax , where of1 m m  annuluses, a0  2 [14].shown The spectral support the the proposed imaging isa0a /combination in Figure 2, andofthus final PSF can bescheme writtenwith as the accumulation of Equation (5). antennas is a combination of m annuluses, shown in Figure 2, and thus the final PSF can be written

as the accumulation of Equation (5).

m m ρmax J ( ρmax r ) − ρmin J ( ρmin r ) 1 i 1 i i i PSF( x, y) = ∑ psf (6) m i ( x, y ) = ∑m imax J1 ( imaxr ) r imin J1( iminr ) 1 PSF( x , y) i= 1  psfi ( x, y) i= (6) r i 1 i 1 As cos αi is proportional to Ri , the best radial resolution depends on a0 π/ρmax 1 . The behavior of  /  max . Thesignal Ri , the  i isfunction As cos proportional best radial resolution depends on aof behavior 0 the1 radar the point spread and itstospatial resolution depends on the bandwidth and of the point spread function and its spatial resolution depends on the bandwidth of the radar signal the array configuration. Hence, the array optimization needs to be studied to further improve the and the array configuration. Hence, the array optimization needs to be studied to further improve imaging performance. the imaging performance. 2.3. Modified Imaging Algorithm 2.3. Modified Imaging Algorithm According to the array configuration, in order to meet the requirements of real-time imaging for personal screening, a modified imaging is proposed based onof the frequency-domain According to the array configuration, inalgorithm order to meet the requirements real-time imaging for reconstruction method describedimaging in [13,14]. The circular SAR reconstruction is based on personal screening, a modified algorithm is proposed based on themethod frequency-domain Fourier analysismethod and thedescribed slant plane which is reconstruction free of approximation. reconstruction in Green’s [13,14]. function, The circular SAR method Specifically, is based on the slantanalysis plane circular SAR phase history is firstly transmitted plane phase history, Fourier and the slant plane Green’s function, which isinto freethe of ground approximation. Specifically, and then plane the target areaSAR reconstruction based on the ground plane SARplane dataphase is conducted. the slant circular phase history is firstly transmitted into circular the ground history, Consequently, as thearea observation geometry thethe new THz plane imaging scheme is data vertical to that of and then the target reconstruction basedofon ground circular SAR is conducted. circular SAR, the imaginggeometry algorithmofinthe thisnew paper mainly includes twoissteps, i.e.,to thethat slant Consequently, asproposed the observation THz imaging scheme vertical of plane to SAR, vertical transformation and the vertical plane reconstruction. circular theplane proposed imaging algorithm in this paper mainly includes two steps, i.e., the slant interpolation process essential inplane the target reconstruction of the circular SAR, planeIntogeneral, verticalthe plane transformation andisthe vertical reconstruction. whichIntransforms target spectrum from polar coordinate form to rectilinear general, thethe interpolation process is essential in the target reconstruction of coordinate the circular form. SAR, However, the calculation volume and time consumption for the interpolation algorithm is enormous, which transforms the target spectrum from polar coordinate form to rectilinear coordinate form. and this would be multiplied withand thetime array configuration the proposed imaging scheme. Hence, However, the calculation volume consumption forinthe interpolation algorithm is enormous, to meet real-time requirement screening, the Fast Fourier Transform and thisthe would be multiplied with of thepersonal array configuration in Non-Uniform the proposed imaging scheme. Hence, to meet the real-time of personal screening, the Non-Uniform Fast Fourier Transform (NUFFT) is used in therequirement proposed imaging algorithm. The NUFFT algorithm possesses a particularly (NUFFT) is usedimplementation in the proposed[19,20], imagingwhich algorithm. The NUFFT possesses a particularly fast and simple can substitute the algorithm interpolation processing and the fast and simple implementation [19,20], which substitute the interpolation processing and the two-dimensional inverse Fourier transform. The can imaging procedure is described in detail as follows. two-dimensional inverse Fourier transform. The imaging procedure is described in detail as follows.

Sensors 17, 2209 2209 Sensors 2017, 2017, 17,

55 of of 13 13

Firstly, the slant plane to vertical plane transformation is performed on the echo of each antenna ith antennaiscan separately. particular, thetoprocessing of the be achieved by echo of each antenna Firstly,In the slant plane vertical plane transformation performed on the separately. In particular, the processing of the ith antenna can be achieved by siv ( i , )   * ( i , k)si ( k , )dk (7) k Z

Λ∗ (ρi , k)si (k, θ )dk

where

siv (ρi , θ ) =

where

( i , k) = Wf ( i , k)  e

k

(7)

 j 4 k 2 ( i )2 Zc

(8) (8) Λ ( ρi , k ) = W f ( ρi , k ) × e Different from the target reconstruction approach in circular SAR, the proposed imaging method Differenton from the target reconstruction approach circular SAR,function the proposed method Wf ( iimaging , k) in the concentrates a fixed scenario with constant radius.inThe window polar concentrates on a fixed scenario with constant radius. The window function W f (ρi , k) in the polar spatial frequency domain is defined as spatial frequency domain is defined as max  i  2 k cos imin ( 1 2 k cos i W f ( i , k )   (9) 1 2k cos αmax ≤ ρi ≤ 2k cos αmin i i W f (ρi , k) =  0 otherwise (9) 0 otherwise where  imax  arctan [Zc / ( Ri  W )] and  imin  arctan [Zc / ( Ri  W )] are the maximum and where αmax = arctan ( Ri − )] and αmin = respect arctan [ Z ( Ri + W )]of are thescenario, maximum and minimum ithWantenna minimum angles[ Zofc /the toc /each edge the respectively. i side i with side angles of thestep, ith antenna respect each edge of the scenario, respectively. The second i.e., the with vertical planetoreconstruction, is performed by The second step, i.e., the vertical plane reconstruction, is performed by Fi ( i , )  Siv ( i , )i* ( i , ) (10) q − j 4k2 −(ρi )2 Zc

Fi (ρi , ξ ) = Siv (ρi , ξ )Γi∗ (ρi , ξ ) where  is the Fourier counterpart domain of  (Fourier series domain) and

( )

(10) [ ] denotes one-

where ξ is the Fourier counterpart and F*i ((θ)i[,]) denotes dimensional Fourier transform withdomain respect ofto θ (Fourier . Siv ( i ,series .  is the  )  domain) [sv ( i , )] ( ) i one-dimensional Fourier transform with to θ. Siv (ρi , ξ ) = F(θ ) [siv (ρi , θ )]. Γi∗ (ρi , ξ ) is the  j  R cosrespect  ]. conjugate of i ( i , ) , i ( i , ) = ( )[e − jρ R cos conjugate of Γi (ρi , ξ ), Γi (ρi , ξ ) = F(θ ) [e i i θ ]. Therefore, polar spatial spatial frequency Therefore, the the target target function function in in the the polar frequency domain domain can can be be obtained obtained from from the the 1 − 1F (  , )] . Then, the imaging result with high resolution can be inverse transformation F (  ,  ) = [ inverse transformation Fi (i ρi ,i θ ) = F((θ) ) [iFi (iρi , ξ )]. Then, the imaging result with high resolution can be achieved through the joint the the flowchart of the joint NUFFT NUFFT processing processingof of FF11((ρ11,,θ),),..., ..F . m, (Fmm(,ρ)m.,Moreover, θ ). Moreover, flowchart of the modified imaging algorithm for the proposed imaging method is illustrated in Figure 3. modified imaging algorithm for the proposed imaging method is illustrated in Figure 3. i

i

Raw Data s1 ( k , ),..., sm ( k , )

 * ( 1 , k )

 * ( m , k)

Vertical plane data s1v ( 1 , )

Vertical plane data smv (  m , ) ......

Perform

( )

Perform

[]

( )

1* ( 1 ,  )

Perform

-1 ( )

[]

 *m (  m ,  ) Perform

[]

-1 ( )

[]

JOINT 2-D NUFFT ( 1 , ),...,(  m , )

2-D Imaging results

Figure 3. Flowchart of the proposed imaging algorithm. Figure 3. Flowchart of the proposed imaging algorithm.

Sensors 2017, 17, 2209 Sensors 2017, 17, 2209

6 of 13 6 of 13

3. OptimizationMethod MethodofofSparse SparseArray Array 3. Optimization Array OptimizationMethod Method 3.1.3.1. Array Optimization According analysis of PSF in Section 2.2,spatial the spatial resolution the proposed new According to to thethe analysis of PSF in Section 2.2, the resolution of theof proposed new imaging imaging method is dependent on the array configuration. Hence, the optimization method of the method is dependent on the array configuration. Hence, the optimization method of the sparse sparse array is studied here to achieve better imaging performance. The spectral support of the array is studied here to achieve better imaging performance. The spectral support of the proposed proposed imaging scheme is the combination of m annuluses shown in Figure 2, and the radii are imaging scheme is the combination of m annuluses shown in Figure 2, and the radii are decided by the decided by the parameters R1 , ..., Rm . Generally, the spatial distribution of the two antennas’ spectral parameters R1 , . . . , Rm . Generally, the spatial distribution of the two antennas’ spectral supports have supports have three types of relationships, i.e., separate, adjacent and overlapping, shown in Figure 4 three types of relationships, i.e., separate, adjacent and overlapping, shown in Figure 4 (each color (each color region indicates the spectral support of one antenna). The values of R of the outside region indicates the spectral support of one antenna). The values of Ri of the outside iannuluses remain Ri +1 of theincreases annuluses invariant and have the same value. However, the inside invariant andremain have the same value. However, the corresponding Ri+corresponding 1 of the inside annulus annulusfrom increases gradually gradually Figure 4a–c. from Figure 4a–c. ky

ky

O

ky

O

kx

(a)

kx

(b)

O

kx

(c)

Figure 4. The distribution of two antennas’ spectral supports: (a) Separate; (b) Adjacent; (c) Figure 4. The distribution of two antennas’ spectral supports: (a) Separate; (b) Adjacent; Overlapping. (c) Overlapping. 2 cos2 2α R Basedonongeometric geometricknowledge, knowledge, the the area area of of annulus ), i Based annulus isis proportional proportionaltotocos cos2 iαi( (cos i ∝i Ri ), R which indicates that the area of the spectral support increases with an increase of . Hence, the which indicates that the area of the spectral support increases with an increase of Ri . Hence, the second i second of the spatial distribution Figure 4b largest has the area. largest area. type of thetype spatial distribution in Figurein4b has the Accordingtotothe theproperties propertiesof of Fourier Fourier transform, transform, the with thethe According the imaging imagingresolution resolutionincreases increases with R increase of the width of the spectral support [21]. With the same value of , the imaging resolutions i i , the imaging resolutions increase of the width of the spectral support [21]. With the same value of R correspondingtotoFigure Figure4a–c 4a–care arethe thesame same in in theory. However, the spectral corresponding However,the thedensity densityand andgap gapofof the spectral support are associated with the side-lobe level, and a lower side-lobe can be obtained when the support are associated with the side-lobe level, and a lower side-lobe can be obtained when the gap gap is is smaller. Therefore, the array configuration corresponding to the second type spatial distributioncan smaller. Therefore, the array configuration corresponding to the second type of of spatial distribution beto used to achieve imaging performance. be can used achieve betterbetter imaging performance. 2k cos 2 kmin cos  , and the radii of  i and In Figure 4, the radii of the outside annuluses are In Figure 4, the radii of the outside annuluses are 2k max cosi αi , and the radii of min cos α i and 2kmax 2 2 k k cos cos   the inside annuluses are and . Therefore, the spatial distribution of two max cos αi +1 the inside annuluses are 2kminmincos αi+i +11 and 2kmax i +1 . Therefore, the spatial distribution of two antennas’ spectral supportininFigure Figure4b 4bcan canbe be expressed expressed by: antennas’ spectral support by:

2kmin cos i = 2kmax cos i +1 (11) 2kmin cos αi = 2kmax cos αi+1 (11) Substitute  i with arctan (Zc / Ri ) and replace  i +1 with arctan (Zc / Ri +1 ) . Then, the Substitute αi with arctan with arctan ( Zc /Ri+1 ). Then, the relationship Ri 1 ( Zc /R R ) and replace α relationship between and i ican be given by:i+1 between Ri+1 and Ri can be given by: R

R

i +1 i  fmin (12) RRi+ 2 1 2 2 R i2  Z R  Zc q q f max (12) i +1 c = f min i 2 2 Ri+1 + Zc2 Ri + Zc2 The value of Ri +1 is decided by the parameters Ri , f and Zc , which indicate that the optimization of Rthe sparse array should be conducted with the constraints of system parameters. The value of i +1 is decided by the parameters Ri , f and Zc , which indicate that the optimization When the system parameters are fixed, the value of Ri +1 should be accurately obtained according to of the sparse array should be conducted with the constraints of system parameters. When the system Equation (12), which the willvalue lead toofbetter parameters are fixed, Ri+1 imaging should performance. be accurately obtained according to Equation (12),

fmax

which will lead to better imaging performance.

Sensors 2017, 17, 2209

7 of 13

Sensors 2017, 17, 2209

7 of 13

3.2. Simulation Results for Array Design

In this section, simulations are performed to show the advantage and effectiveness of the 3.2. Simulation Results for Arraymethod. Design According to the current device level of the terahertz radar, proposed array optimization theInfrequency of the transmitted signal istofrom to 230 GHz. The radius ofofthe this section, simulations areLFM performed show210 theGHz advantage and effectiveness theimaging proposed scenario is set as 1 m, which is fit for a human being’s height. The radar system works at a standoff array optimization method. According to the current device level of the terahertz radar, the frequency 3 m from LFM the imaging According theGHz. theoretical analysis above, the best spatial of range the transmitted signal isscene. from 210 GHz toto 230 The radius of the imaging scenario is set max a  /  resolution is determined by the maximum value of the antenna rotation radius. Thus, 1 as 1 m, which 0is fit 1for a human being’s height. The radar system works at a standoff range 3 m Rfrom set as 0.6scene. m to achieve the theoretical imaginganalysis resolution 0.0017 m. The main simulation theisimaging According to the theoretical above, them~0.0034 best spatial resolution a0 π/ρmax is 1 parameters are listed in Table 1. determined by the maximum value of the antenna rotation radius. Thus, R1 is set as 0.6 m to achieve the

theoretical imaging resolution 0.0017 m~0.0034 m. The main simulation parameters are listed in Table 1. Table 1. Simulation parameters.

Table 1. Simulation parameters.Numerical Value Parameters Center frequency f c 220 GHz

Parameters

Numerical Value

Bandwidth B Center frequency f c antenna R Maximum radius of 1

20 GHz

2200.6 GHz m 20 GHz 0.63mm 1m 3m 1 mGHz 0.01 0.01 GHz 0.1° 0.1◦ 2001 2001 3600 3600

Bandwidth B Horizontal range Z Maximum radius of antenna R1c W Imaging scene Z radius Horizontal range c Imaging scene radius W of f Sampling interval Sampling interval of f of  Sampling interval Sampling interval of θ Sampling numbers of frequency N f Sampling numbers of frequency N f Sampling numbers of azimuthal angle angle Nθ N Sampling numbers of azimuthal

ToTo simplify radial direction directionare areused usedininthe thesimulations, simulations, and simplifythe theanalysis, analysis,two two antennas antennas in in radial and thethe setup of rotation radii is displayed in Table 2. The values of R are set differently for comparison, setup of rotation radii is displayed Table 2. The values of R2 2are set differently for comparison, resulting the spectral spectralsupport supportcorresponding corresponding to the three types of relationship resultinginina adistribution distribution of of the to the three types of relationship in in Figure Figure4.4.The Theradius radius RR2 2 ==0.546 0.546mmofofType TypeIV IVisiscalculated calculatedaccording according to Equation (12). Additionally, to Equation (12). Additionally, a simulation using 0.6 m m is is also alsoperformed. performed. a simulation usinga asingle singleantenna antennawith with radius radius 0.6 Table array configurations. configurations. Table 2. 2. Different Different array

No. No. R1 (m) R1 (m) R2 R(m) 2 (m)

Type TypeI I

Type TypeIIII

Type Type III III

0.6

0.6

0.6

0.6

0.6

0.3 0.3

0.4 0.4

0.5 0.5

0.546 0.546

0.6

0.6

Type IV Type IV 0.6

TypeVV Type 0.6

0.6 0.57 0.57

TypeVIVI Type 0.6

0.6

The spectralsupports supportsof ofthe thedifferent different array configurations Figure 5. To compare The spectral configurationsare aredisplayed displayedinin Figure 5. To compare imagingperformance performanceof ofdifferent different array configurations imaging thethe imaging configurationssufficiently, sufficiently,the thetwo-dimensional two-dimensional imaging results at (0,0) and the one-dimensional imaging results are also shown in Figures 6 and 7, results at (0,0) and the one-dimensional imaging results are also shown in Figures 6 and 7, respectively. respectively. Furthermore, quantitative analysis of the imaging performance is performed, and is 3. Furthermore, quantitative analysis of the imaging performance is performed, and is listed in Table listed in Table 3. definition The meaning and definition parameter in Table 3 is explained below. The meaning and of each parameterofineach Table 3 is explained below.

(a)

(b) Figure 5. Cont.

(c)

Sensors2017, 2017,17, 17,2209 2209 Sensors Sensors 2017, 17,17, 2209 Sensors 2017, 2209

of13 13 88of

8 of813of 13

(d) (d) (d)

(e) (e)

(e)

(f)(f)

(f)

Figure5.5.The Thespectral spectral support support of two antennas: (a) I;I;(b) Type II;II; (c)(c) Type III;III; (d)(d) Type IV; IV; (e) (e) Figure antennas: (a)Type Type (b) Type Type Type Figure 5. Thespectral spectralsupport supportofoftwo twoantennas: antennas: Type I; (b) Type II; (c) Type Type Figure 5. The (a)(a) Type I; (b) Type II; (c) Type III; III; (d) (d) Type IV; IV; (e) TypeV;V; (f)Type TypeVI. VI. Type (f) (e) Type Type Type V; V; (f) (f) Type VI.VI.

(a) (a) (a)

(b)

(c)

(d)

(e)

(f)

(b) (b)

(c) (c)

(e)at (0, 0): (a) Type I; (b) Type II; (c) Type (f)III; (d) Type Figure 6.(d) The two-dimensional imaging results (d) (e) (f) IV; (e) Type V; (f) Type VI. Figure 6. The The two-dimensionalimaging imaging resultsatat(0,(0,0):0):(a)(a)Type Type I; (b) Type II; (c) Type III; (d) Type Figure I; I; (b) Type II; II; (c)(c) Type III;III; (d) (d) Type IV; Figure 6. 6. The two-dimensional two-dimensional imagingresults results at (0, 0): (a) Type (b) Type Type Type IV; (e) Type V; (f) Type VI. (e) V; (f)V;Type VI. VI. IV;Type (e) Type (f) Type

(a)

(a) (a)

(b)

(b) (b) Figure 7. Cont.

(c)

(c) (c)

Sensors 2017, 17, 2209 Sensors 2017, 17, 2209

9 of 13 9 of 13

(d)

(e)

(f)

Figure 7. 7. Comparison simulated PSF: (a)(a) Type I; (b) Type II; (c) III; (d) Figure Comparisonofofthe thetheoretical theoreticaland and simulated PSF: Type I; (b) Type II; Type (c) Type III; Type IV; (e) Type V; (f) Type VI. (d) Type IV; (e) Type V; (f) Type VI. Table 3. Quantitative comparison of the different distribution antennas. Table 3. Quantitative comparison of the different distribution antennas.

No. Type I Type II No. Type I Type II Area percentage 16.43% 18.99% Area percentage 16.43% 7.5736 18.99% ISLR (dB) 9.0674 ISLR (dB) 9.0674 7.5736 Image entropy 12.8088 12.0532 Image entropy 12.8088 12.0532 IRW (m)(m) 0.0019 IRW 0.0019 0.0017 0.0017

Type III Type III 22.24% 22.24% 7.3180 7.3180 11.3908 11.3908 0.0015 0.0015

Type IV Type IV 23.95% 23.95% 6.7343 6.7343 10.5492 10.5492 0.0013 0.0013

Type V 19.22% 19.22% 8.4933 8.4933 11.1750 11.1750 0.0013 0.0013

Type V

Type VI 13.06% 13.06% 9.9953 9.9953 11.7455 11.7455 0.0013 0.0013

Type VI

The area percentage is defined as the ratio of the area of array’s spectral support to the area Theby area percentage ratio of the area of array’s spectral support to the area kx  [2k cos1 ,isdefined 2k cos1as ] , the defined ky  [2k cos1 ,  2k cos1 ] , i.e., the ratio of the area in white defined by k x ∈ [−2k cos α1 , −2k cos α1 ], k y ∈ [−2k cos α1 , −2k cos α1 ], i.e., the ratio of the area in color to the area in area blackincolor incolor Figure Obviously, the area percentage is associated with the image white color to the black in5.Figure 5. Obviously, the area percentage is associated with side-lobe level. The two-dimensional integral side-lobe ratio (ISLR) is defined as the the the image side-lobe level. The two-dimensional integral side-lobe ratio (ISLR) is defined ratio as theofratio power of the side-lobe to that of the main lobe, which reflects the focusing performance of the image of the power of the side-lobe to that of the main lobe, which reflects the focusing performance of the and theand lower the better Image entropy has beenhas successfully applied image the value lowerrepresents value represents theperformance. better performance. Image entropy been successfully to evaluate the quality of SAR or inverse SAR (ISAR) images [22,23]. A canonical definition of the applied to evaluate the quality of SAR or inverse SAR (ISAR) images [22,23]. A canonical definition of image entropy is [24] the image entropy is [24] 2

h( x , y) 2 Enx  H( x, y)  ln H( x, y)dxdy , H( x, y)  |h( x, y)| En = − H ( x, y) × ln H ( x, y)dxdy, H ( x, y) = s h( x, y) 2 dxdy  |h(x, y)|2 dxdy

(13) (13)

where H( x, y) is the normalized image power density, h( x, y) depicts the reconstructed reflectivity where H ( x, y) is the normalized image power density, h( x, y) depicts the reconstructed reflectivity function of of target. target. However, paper are are discretized discretized images images function However, the the imaging imaging results results obtained obtained in in this this paper composed of discrete grids; thus, the discretized expression of Equation (13) can be written as composed of discrete grids; thus, the discretized expression of Equation (13) can be written as 2

h( p , q) En   H( p , q)  ln H( p, q), H( p, q)  P Q| h( p, q)|2 2 En = − ∑ ∑ p 1 qH 1 ( p, q ) × ln H ( p, q ), H ( p, q ) = P Qh( p , q)  2 p =1 q =1 p ∑1 q 1∑ |h( p, q)| P

P

Q

Q

(14) (14)

p =1 q =1

Where p and q are the discretized pixels of the imaging result, and P and Q represent the total where p and q are the discretized pixels the imaging and P and Qimage represent the total numberthe of number of pixels in each row and eachofcolumn. The result, two-dimensional entropy represents pixels in each row and each column. The two-dimensional image entropy represents the quality of the quality of the imaging result, and a smaller value corresponds to a better imaging performance. The imaging andimage a smaller valuecan corresponds to abased better on imaging of ISLR values ofresult, ISLR and entropy be calculated Figureperformance. 6. Moreover, The the 3values dB resolution and image entropy can be calculated based on Figure 6. Moreover, the 3 dB resolution of the imaging of the imaging results can be represented by the impulse response width (IRW), which can be results canfrom be represented obtained Figure 7. by the impulse response width (IRW), which can be obtained from Figure 7. It can be seen fromfrom Figure 5a–c that spectral the previous third array configurations It can be seen Figure 5a–cthethat the support spectralofsupport of the previous third array have a separated distribution relationship, and the width of the gap in each annulus decreases from configurations have a separated distribution relationship, and the width of the gap in each annulus Figure 5a–c. In Table 3, the IRWs of Type Type II and Type I, IIIType are larger those of the last three array decreases from Figure 5a–c. In Table 3, I,the IRWs of Type II andthan Type III are larger than those configurations, which indicates that the gap in the spatial frequency domain may degrade the imaging of the last three array configurations, which indicates that the gap in the spatial frequency domain may degrade the imaging resolution. According to the quantitative analysis of the array configurations of Type I, Type II and Type III, the values of ISLR, image entropy and IRW decrease,

Sensors 2017, 17, 2209

10 of 13

resolution. According to the quantitative analysis of the array configurations of Type I, Type II and Type III, the values of ISLR, image entropy and IRW decrease, which demonstrates that the quality of the imaging results gradually improves from Type I to Type III. Hence, it can be concluded that the narrower the gap in the spatial frequency domain, the better the imaging performance that can be achieved. Figure 5d represents the adjacent distribution of the spectral support, which corresponds to Sensors 2017, 17, 2209 10 of 13 the optimized array configuration (Type IV). In Figure 5e, the overlapped distribution of spectral support is displayed with to ofType V. Theresults spectral support of imaging with one antenna which demonstrates thatrespect the quality the imaging gradually improves from Type I to Type it can be depicted concludedin that the narrower the gap in the the spatial frequency the types better of array locatedIII. atHence, R1 = 0.6 m is Figure 5f. Comparing imaging resultsdomain, of the six the imaging thatVI canhas be achieved. configurations, theperformance ISLR of Type the largest value, which indicates that the obtained image using Figure 5d represents the adjacent distribution of the spectral support, which corresponds to the single antenna has poor imaging performance with higher side-lobe level and lower image-focusing optimized array configuration (Type IV). In Figure 5e, the overlapped distribution of spectral support ability.isThe image entropy of Type I and Type II is larger than that of Type VI, which is caused by the displayed with respect to Type V. The spectral support of imaging with one antenna located at R1 lower IRWs of Type I and Type II. The more antennas that are used, the better the imaging performance = 0.6 m is depicted in Figure 5f. Comparing the imaging results of the six types of array that can be achieved. the advantages of the array configuration proposed configurations, theHence, ISLR of Type VI has the largest value, which indicates thatfor thethe obtained imageimaging schemeusing can be recognized. single antenna has poor imaging performance with higher side-lobe level and lower imagefocusing ability. imageofentropy of percentage Type I and Type II is thatthe of Type VI, which is shown According to theThe results the area listed inlarger Tablethan 3 and spectral support caused by the lower IRWs of Type I and Type II. The more antennas that are used, the better the in Figure 5, the spectral support of the optimized array (Type IV) has the maximum area among the imaging performance that can be achieved. Hence, the advantages of the array configuration for the six array configurations. Moreover, the ISLR, image entropy and IRW of the optimized array’s imaging proposed imaging scheme can be recognized. result haveAccording the minimum values in area all imaging indicates thatsupport the optimized array to the results of the percentageresults, listed in which Table 3 and the spectral shown configuration bespectral used to achieve theoptimized best imaging performance with lowerarea andamong fewerthe side-lobes. in Figurecan 5, the support of the array (Type IV) has the maximum six array Moreover, the of ISLR, entropy andconfiguration IRW of the optimized In addition, the configurations. best imaging performance the image optimized array can alsoarray’s be recognized imaging the minimum in all imaging which a indicates that thethat optimized with the best result visualhave effect in Figurevalues 6. Therefore, weresults, can draw conclusion the proposed array configuration can be used to achieve the best imaging performance with lower and fewer sideoptimization method is feasible and effective. lobes. In addition, the best imaging performance of the optimized array configuration can also be In addition, the theoretical PSF according to Equation (6) is also calculated, and is shown recognized with the best visual effect in Figure 6. Therefore, we can draw a conclusion that the in Figure 7. It can be seen from Figure 7 that main-lobes of the simulated PSF and the theoretical proposed optimization method is feasible andthe effective. PSF almostInhave the the same width, PSF despite the different distribution of the antennas. Additionally, addition, theoretical according to Equation (6) is also calculated, and is shown in Figure 7.of It the can simulated be seen fromPSF Figure thattheoretical the main-lobes themore simulated PSFwhen and the the side-lobes and7the PSFofare similar thetheoretical spectral support almost Thus, have the same width, despite distribution the antennas. Additionally, the is morePSF intense. the effectiveness of the thedifferent proposed imagingofalgorithm is validated. side-lobes of the simulated PSF and the theoretical PSF are more similar when the spectral support is more intense. effectiveness of the proposed imaging algorithm is validated. 4. Imaging ResultsThus, and the Analysis

4. Imaging Results and Analysis Based on the proposed array optimization method, the imaging results of the human-scattering model are provided toproposed show the advantages of method, the proposed imaging scheme for personal screening. Based on the array optimization the imaging results of the human-scattering modeltoare provided(12), to show advantages ofof thesix proposed imaging schemem, for0.413 personal According Equation thethe rotation radii antennas are 0.377 m, screening. 0.453 m, 0.497 m, According to Equation (12), the rotation radii of six antennas are 0.377 m, 0.413 m, 0.453 m, 0.497denoted m, 0.546 m, and 0.6 m. Two uniform array configurations are considered for comparison, by 0.546 m, and 0.6 m. Two uniform array configurations are considered for comparison, denoted bym, 0.4 m, uniform array 1 and uniform array 2. The rotation radii of uniform array 1 are 0.1 m, 0.2 m, 0.3 uniform array 1 and uniform array 2. The rotation radii of uniform array 1 are 0.1 m, 0.2 m, 0.3 m, 0.4 0.5 m and 0.6 m, and the rotation radii of uniform array 2 are 0.45 m 0.48 m, 0.51 m, 0.54 m, 0.57 m and m, 0.5 m and 0.6 m, and the rotation radii of uniform array 2 are 0.45 m 0.48 m, 0.51 m, 0.54 m, 0.57 0.6 m. m The supports of the three configurations areareshown Figure8.8.It can It can andspectral 0.6 m. The spectral supports of thearray three array configurations shown in in Figure be be seen from Figure 8b,c that8b, thec that spectral supports of the array configurations possess separated seen from Figure the spectral supports of thetwo twouniform uniform array configurations possess separated and overlapped distribution relationships, respectively. TheThe areaarea percentages of Figure 8 are 52.03%, and overlapped distribution relationships, respectively. percentages of Figure 8 are 52.03%, and 41.07%, which indicate that that the array has the largest area of spectral support. 33.39%33.39% and 41.07%, which indicate theoptimized optimized array has the largest area of spectral support.

(a)

(b)

(c)

Figure 8. The spectral supports of different array configuration: (a) Optimized array; (b) Uniform

Figure 8. The spectral supports of different array configuration: array 1; (c) Uniform array 2. (b) Uniform array 1; (c) Uniform array 2.

(a) Optimized array;

Sensors 2017, 17, 2209 Sensors 2017, 17,17, 2209 Sensors 2017, 2209

11 of 13 11 of 11 13 of 13

The reflection distribution of of the human-scattering model used is displayed in in Figure which The reflection distribution human-scattering model used is displayed Figure 9, which The reflection distribution ofthe the human-scattering model used is displayed in 9,Figure 9, contains 3453 scatters with 0.005 m spacing. The imaging results of the three arrays are achieved contains 3453 scatters with 0.005 spacing. The imaging of results the three are achieved in which contains 3453 scatters withm0.005 m spacing. The results imaging ofarrays the three arrays in are Figure 10. The image entropy of the three sub-images in Figure 10 are 11.7326, 12.9384 and 11.9848, Figure 10. The image entropy of the three sub-images in Figure 10 are 11.7326, 12.9384 and 11.9848, achieved in Figure 10. The image entropy of the three sub-images in Figure 10 are 11.7326, 12.9384 and which indicate thethe array optimization procedure leads to to better image quality. Moreover, it can which indicate that array optimization procedure leads better image quality. Moreover, it can 11.9848, whichthat indicate that the array optimization procedure leads to better image quality. Moreover, beitbe seen from the imaging result in Figure 10a that the profiles and details of the human model areare seen fromfrom the imaging result in Figure 10a 10a thatthat the the profiles andand details of the human model can be seen the imaging result in Figure profiles details of the human model quite clear. Thus, thethe proposed new imaging scheme can be used forfor security inspection. quite clear. Thus, proposed new imaging scheme can be used security inspection. are quite clear. Thus, the proposed new imaging scheme can be used for security inspection.

Figure 9. Scattering model of human. Figure Scattering model human. Figure 9.9.Scattering model ofofhuman.

(a)(a)

(b)(b)

(c)(c)

Figure 10.10. Imaging results of of thethe human-scattering model: (a)(a) Optimized array; (b)(b) Uniform array 1; 1; Figure Imaging results human-scattering model: Optimized array; Uniform array Figure 10. Imaging results of the human-scattering model: (a) Optimized array; (b) Uniform array 1; (c)(c) Uniform array 2. Uniform array 2. (c) Uniform array 2.

In In this paper, a desktop computer with Intel(R) Core(TM) i5-4460U CPU @ 3.2 GHz and 8 GB this paper, a desktop computer with Intel(R) Core(TM) i5-4460U CPU @ 3.2 GHz and 8 GB In this paper, a desktop computer with Intel(R) Core(TM) i5-4460U CPU @ 3.2 GHz and RAM is is used forfor thethe imaging simulation. Through thethe processing of of thethe 3D3D data RAM used imaging simulation. Through processing dataN fNf N  N m m 8 GB RAM is used for the imaging simulation. Through the processing of the 3D data 2 with (2001 × 3600 × 6), imaging results of of 2 ×22×m with 0.001 mm spacing can bebe achieved in in 3030 s. Accordingly, × 3600 × 6), imaging results 2 2m 0.001 spacing can achieved s. Accordingly, 2 N(2001 f × Nθ × m (2001 × 3600 × 6), imaging results of 2 × 2 m with 0.001 m spacing can be achieved in thethe time consumption of of thethe imaging processing can bebe reduced to to several seconds with advanced time consumption imaging processing can reduced several seconds with 30 s. Accordingly, the time consumption of the imaging processing can be reduced to severaladvanced seconds computer technology, which meets the requirements of the real-time imaging. Hence, the proposed computer technology, which meets the requirements of the real-time Hence, the proposed with advanced computer technology, which meets the requirements of imaging. the real-time imaging. Hence, new imaging scheme is suitable forfor standoff personal screening. new imaging scheme is suitable standoff personal screening. the proposed new imaging scheme is suitable for standoff personal screening. 5.5.Conclusions 5.Conclusions Conclusions To conclude, a afast terahertz imaging method based on a asparse rotating array has been proposed To conclude, afast fast terahertz imaging method based on asparse sparse rotating array has been proposed To conclude, terahertz imaging method based on rotating array has been proposed ininin this paper. This new imaging scheme can be used to achieve high imaging resolution, fast imaging thispaper. paper.This Thisnew newimaging imagingscheme schemecan canbe beused usedto toachieve achievehigh highimaging imagingresolution, resolution,fast fastimaging imaging this speed and low system cost, which is is an effective acceptable terahertz forfor standoff speed and low system cost, which an effective and acceptable terahertz imager standoff speed and low system cost, which is an effective and and acceptable terahertz imagerimager for standoff personal personal screening. A modified imaging algorithm oncircular thethe circular reconstruction method personal screening. A modified imaging algorithm based on circular SAR reconstruction method screening. A modified imaging algorithm basedbased on the SARSAR reconstruction method was was developed for this new imaging scheme, which was validated by analyzing the PSF. Moreover, was developed for new this new imaging scheme, which was validated analyzingthe thePSF. PSF. Moreover, Moreover, developed for this imaging scheme, which was validated bybyanalyzing anan optimization method ofofof the sparse array was proposed. Based onon the proposed optimization an optimization method the sparse array was proposed. Based on the proposed optimization optimization method the sparse array was proposed. Based the proposed optimization method, a sparse array was obtained and the imaging results of a human-scattering model were method, a sparse array was obtained and the imaging results of a human-scattering model were method, a sparse array was obtained and the imaging results of a human-scattering model were achieved, which validated the good performance and merits of the proposed imaging scheme. achieved,which whichvalidated validatedthe thegood goodperformance performanceand andmerits meritsofofthe theproposed proposedimaging imagingscheme. scheme. achieved, Acknowledgments: This work was supported byby thethe National Natural Science Foundation of China under Grant Acknowledgments: This work was supported National Natural Science Foundation of China under Grant No.No. 61571011. 61571011.

Sensors 2017, 17, 2209

12 of 13

Acknowledgments: This work was supported by the National Natural Science Foundation of China under Grant No. 61571011. Author Contributions: Y.J., B.D. and Y.Q. proposed the terahertz imaging scheme, Y.J. proposed the imaging algorithm and optimization method, conducted the theoretical analysis and simulations, and wrote the paper, H.W. and K.L. revised the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

References 1.

2. 3. 4.

5. 6. 7.

8. 9.

10. 11.

12.

13. 14. 15.

16.

17.

Friederich, F.; Spiegel, W.; Bauer, M.; Meng, F.; Thomson, M.; Boppel, S.; Lisauskas, A.; Hils, B.; Krozer, V.; Keil, A.; et al. THz active imaging systems with real-time capabilities. IEEE Trans. Terahertz Sci. Technol. 2011, 1, 183–200. [CrossRef] Siegel, P. THz for space: The Golden Age. In Proceedings of the 2010 IEEE MTT-S International Microwave Symposium, Anaheim, CA, USA, 23–28 May 2010; pp. 816–819. Appleby, R.; Wallace, H. Standoff detection of weapons and contraband in the 100 GHz to 1 THz region. IEEE Trans. Antennas Propag. 2007, 55, 2944–2956. [CrossRef] Gollub, J.; Yurduseven, O.; Trofatter, K.; Arnitz, D.; Imani, M.; Sleasman, T.; Boyarsky, M.; Rose, A.; Pedross-Engel, A.; Odabasi, H.; et al. Large metasurface aperture for millimeter wave computational imaging at the human-scale. Sci. Rep. 2017, 20, 42650. [CrossRef] [PubMed] Sheen, D.; Mcmakin, D.; Hall, T. Three-dimensional millimeter-wave imaging for concealed weapon detection. IEEE Trans. Microw. Theory Tech. 2001, 49, 1581–1592. [CrossRef] Cooper, K.; Dengler, R.; Llombart, N.; Thomas, B.; Chattopadhyay, G.; Siegel, P. THz imaging radar for standoff personnel screening. IEEE Trans. Terahertz Sci. Technol. 2011, 1, 169–182. [CrossRef] Alexander, N.; Alderman, B.; Allona, F.; Frijlink, P.; Gonzalo, R.; Hägelen, M.; Ibáñez, A.; Krozer, V.; Langford, M.L.; Limiti, E.; et al. TeraSCREEN: Multi-frequency multi-mode Terahertz screening for border checks. Proc. SPIE 2014, 9078. [CrossRef] Venkatesh, S.; Viswanathan, N.; Schurig, D. W-band sparse synthetic aperture for computational imaging. Opt. Express 2016, 24, 8317–8331. [CrossRef] [PubMed] Ahmed, S.; Genghammer, A.; Schiessl, A.; Schmidt, L. Fully electronic active E-band personnel imager with 2 m2 aperture based on a multistatic architecture. IEEE Trans. Microw. Theory Tech. 2013, 61, 651–657. [CrossRef] Ahmed, S.; Schiessl, A.; Gumbmann, F.; Tiebout, M.; Methfessel, S.; Schmidt, L. Advanced microwave imaging. IEEE Microw. Mag. 2012, 13, 26–43. [CrossRef] Gonzalez-Valdes, B.; Alvarez, Y.; Mantzavinos, S.; Rappaport, C.; Las-Heras, F.; Martinez-Lorenzo, J. Improving security screening: A comparison of multistatic radar configurations for human body imaging. IEEE Antennas Propag. Mag. 2016, 58, 35–47. [CrossRef] Moulder, W.; Krieger, J.; Majewski, J.; Coldwell, C.; Nguyen, H.; Maurais-Galejs, D.; Anderson, T.; Dufilie, P.; Herd, J. Development of a high-throughput microwave imaging system for concealed weapons detection. In Proceedings of the 2016 IEEE International Symposium on Phased Array Systems and Technology (PAST), Waltham, MA, USA, 18–21 October 2016; pp. 1–6. Soumekh, M. Synthetic Aperture Radar Signal Processing with MATLAB Algorithms; Wiley-Interscience: Malden, MA, USA, 1999. Soumekh, M. Reconnaissance with slant plane circular SAR imaging. IEEE Trans. Image Proc. 1996, 5, 1252–1265. [CrossRef] [PubMed] Rappaport, C.; Gonzalez-Valdes, B.; Allan, G.; Martinez-Lorenzo, J. Optimizing Element Positioning in Sparse Arrays for Near Field MM-Wave Imaging. In Proceedings of the 2013 IEEE International Symposium on Phased Array Systems & Technology, Waltham, MA, USA, 15–18 October 2013; pp. 333–335. Baccouche, B.; Agostini, P.; Mohammadzadeh, S.; Kahl, M.; Weisenstein, C.; Jonuscheit, J.; Keil, A.; Loffler, T.; Sauer-Greff, W.; Urbansky, R.; et al. Three-dimensional Terahertz imaging with sparse multistatic line arrays. IEEE J. Sel. Top. Quant. 2017, 23, 1–11. [CrossRef] Bryant, M.; Gostin, L.; Soumekh, M. 3-D E-CSAR imaging of a T-72 tank and synthesis of its SAR reconstructions. IEEE Trans. Aerosp. Electron. Syst. 2003, 39, 211–227. [CrossRef]

Sensors 2017, 17, 2209

18.

19. 20. 21. 22. 23. 24.

13 of 13

Ponce, O.; Prats-Iraola, P.; Pinheiro, M.; Rodriguez-Cassola, M.; Scheiber, R.; Reigber, A.; Moreira, A. Fully polarimetric high-resolution 3-D imaging with circular SAR at L-band. IEEE Trans. Geosci. Remote Sens. 2014, 52, 3074–3090. [CrossRef] Greengard, L.; Lee, J. Accelerating the nonuniform fast Fourier transform. SIAM Rev. 2004, 46, 443–454. [CrossRef] Gao, J.; Deng, B.; Qin, Y.; Wang, H.; Li, X. Efficient Terahertz wide-angle NUFFT-based inverse synthetic aperture Imaging considering spherical wavefront. Sensors 2016, 16, 2120. [CrossRef] [PubMed] Cumming, I.; Wong, F. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implimentation; Artech House Publishers: London, UK, 2005. Li, X.; Liu, G.; Ni, J. Autofocusing of ISAR images based on entropy minimization. IEEE Trans. Aerosp. Electron. Syst. 1999, 35, 1240–1252. [CrossRef] Yang, L.; Xing, M.; Zhang, L.; Sheng, J.; Bao, Z. Entropy-based motion error correction for high-resolution spotlight SAR imagery. IET Radar Sonar Navig. 2012, 6, 627–637. [CrossRef] Sun, Z.; Li, C.; Gao, X.; Fang, G. Minimum-entropy-based adaptive focusing algorithm for image reconstruction of terahertz single-frequency holography with improved depth of focus. IEEE Trans. Geosci. Remote Sens. 2015, 53, 519–526. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).