THz Wave 3D Imaging and Tomography

8/12/2019 THz Wave 3D Imaging and Tomography

1/22

Chapter 6

THz Wave 3D Imaging and Tomography

THz waves are transparent to most of the dry dielectric materials. This property

makes THz wave a promising candidate for nondestructive evaluation of the inter-nal structures of targets. THz wave time-of-flight imaging method is one of the

techniques to extract the information about the layered structures of a target. If there

is no layer structure within the target, or if the interesting features are not located on

those layer structures, one needs to use tomographic imaging techniques to extract

those interesting information [1].

T-Ray Computerized Tomography

Initially, Computerized tomography (CT) technique was developed for X-ray imag-

ing, and currently is used in medical diagnostics and other nondestructive evaluation

applications. Figure6.1illustrates the concept of CT. Collimated X-ray beam trans-

mits through the target and the transmitted intensity is recorded. The transmission

of the X-ray beam through different paths defined by lateral position and angles is

obtained by rotating and laterally shifting the target. For each beam path, the inten-

sity of transmitted beam is determined by the integral absorption along the optical

path. If the absorption distribution of the target is defined as f(x,y,z), then the total

absorption along the path with rotation angle , height z and lateral displacementlis described as

p(,l,z) =

L(,l,z)

f(x,y,z)dl (f(x,y,z), (1a)

where L(,l,z) denotes the beam path through the target. The transmission Tand

absorptionp of the beam path are defined as

T= exp

L(,l,z)

f(x,y,z)ds

exp[ p(,l,z)]. (1b)

127X.-C. Zhang, J. Xu,Introduction to THz Wave Photonics,

DOI 10.1007/978-1-4419-0978-7_6, C Springer Science+Business Media, LLC 2010


2/22

128 6 THz Wave 3D Imaging and Tomography

Fig. 6.1 Concept of

computerized tomography

(CT). Intensity of carrier

wave beam is recorded after

transmission through the

target with certain lateral

shifts and rotation angles.

Inverse Radon transform

of the recorded signal gives

3D information of the target

Equation (1) is known as the Radon transform [2]. The Fourier transform ofEquation (1) gives

P(,,z) = p(,l,z)exp( il)dl= exp[ i(x y)]f(x,y,z)dxdy. (2)

Here v is lateral spatial frequency, which indicates the spatial resolution of the

CT imaging process. = vsin()and= vcos()are spatial frequency componentsalong the xand ydirection, respectively. Equation (2) indicates that, Fourier trans-

form of the Radon transform is equivalent to 2D Fourier transform of the absorptiondistribution.

CT image directly measures transmission of the carrier wave corresponding to

each beam path. To get the 3D structure of the target, Equations (1) and (2) are used

to calculate the spatial distribution of the absorption, f(x,y,z), in the target

f(x,y,z) = P(,v,z) exp2 i(xcos +y sin ) dd=

P(,l,z)exp( il) exp

2 i(xcos +y sin )dldd.

(3)

This equation is called the reverse Radon transform. Reverse Radon transform of

the beam path absorptions at height zgives cross section image of the target at the

heightz. The above process is repeated for all different heights to obtain the cross

section images at the different heights. These different cross section images provide

the 3D structure of the target.

Unlike X-ray imaging, which provides only the intensity information, the THz

wave imaging provides both the intensity and the phase information. The THz CT

enables one to obtain the absorption and the refractive index information of the

target. An experimental setup of THz wave CT system is presented in Fig6.2.To

ensure the spatial resolution, THz beam is focused onto the target using either an

off-axis parabolic mirror or a lens. The focal spot size determines the spatial reso-

lution of the CT image, while its depth of focus should be at least as long as lateral

dimensions of the target. Therefore, the focusing conditions of THz beam needs to


3/22

T-Ray Computerized Tomography 129

Fig. 6.2 Experimental setup of THz wave CT. THz wave is focused with an off-axis parabolic mir-

ror onto the target. Temporal waveform of THz pulses transmitted through the target is recorded.

The target is driven by a rotation stage and a linear translation stage. THz waveform at each rotation

and lateral transition position is recorded

be well considered so that it provides sufficient depth of focus along with the high

spatial resolution. In order to obtain a tomographic image, the target is set on a rota-

tion stage which is able to rotate about the zaxis and the target moves along land

z directions by a 2D translation stage. Thus, the target is scanned in three dimen-

sions corresponding to variables of z, l and . Another off-axis parabolic mirror

collects the transmitted THz waves and a THz wave detector records its temporal

waveform.

Refractive index of the materials can be approximately treated as 1 for almostall common materials when performing X-ray CT. As a result, X-ray beam can

be treated as a simple straight line without any beam bending in the CT process.

However, different materials may have different refractive index in THz band. For

example, refractive index of plastic is1.5, of glass is2, and of semiconductormaterials could be as high as 34. As a result, refractive behavior of THz wave may

not be negligible in CT process unless specific conditions are satisfied. Further, the

wavelength of THz wave is usually comparable to spatial features of the target, such

as textures, or microstructures, thus diffraction and scattering of the beams may also

affect propagation of THz wave through the target. To reconstruct the THz wavetomographic image using Equation (3), the materials refractive index should have

slow variation within a THz wavelength, otherwise, ray-tracing techniques need to

be used in order to correctly retrieve 3D image of the target. In pulsed THz wave

tomography, the entire THz waveform is recorded. Different physical quantities can

be used to represent different features of the target. For example, the amplitude of

transmission provides absorption coefficient, the phase delay represents refractive

index of the target and the spectroscopy provides the composition information of

the target.

Polystyrene foam material has very low absorption coefficient (


4/22


Fig. 6.3 Photo of a target

used in THz wave CT

imaging process. Cubic

polystyrene foam is carved

with THZ through its

height

wave CT process. Three letters T, H and Z were carved in the target. Since

there is no change in z direction, the cross section at z= z0 reflects the full 3Dinformation of the target. In order to obtain the image, the sample was driven along

the x-axis by a linear stage. For each xposition, the sample was rotated within a

range of= 0180 with an interval of 1.8. Imaging system recorded the THzwaveform for each x and . Figure 6.4 shows 3 THz waveforms recorded in the

experiment. Those waveforms were obtained for the lateral displacement x= 0,and rotation angles of 0, 60 and 120, respectively. Both amplitude and positionof peak in THz waveform vary for different beam paths. Figure 6.5ashows time

delay of THz pulses in the xspace. In the frequency domain, time delay of THz

pulses corresponds to the phase delay. Figure6.5bgives the phase distribution at 1

THz (the central frequency of THz pulses) in the x space. Using time delay to

replace absorption in Equation (3), the 3D image of the target can be reconstructed

according to its refractive index distribution. Figure6.6shows the retrieved cross

section image of the target of Fig.6.3.The profile of target and the carved letters are

reconstructed due to refractive index difference between air and polystyrene foam.Similarly, the phase distribution in the frequency domain can be used to retrieve 3D

image of the target and the result is very similar to Fig. 6.6. Further, one can also

use variation of THz amplitude to retrieve the absorption coefficient (or extinction

coefficient) distribution of the target. The image based on amplitude attenuation of

THz wave is less sharp due to scattering of the waves by the target.

When the sample is scanned in the vertical direction along with the lateral scan-

ning and rotation, the cross section of the target can be obtained for each height

that provides a true 3D image of the target. To save the scanning time, single pulse

detection method discussed in Chapter 3 can be used to record THz waveforms.

Figure6.7presents cross sections images of a ping-pong ball recorded by THz wave

CT at different heights. When all these cross sectional images are combined the

THz wave CT retrieves cavity structure of the ping-pong ball, which is presented

in Fig 6.8. The cavity structure of the ping-pong ball can be clearly seen in the


5/22

T-Ray Computerized Tomography 131

Fig. 6.4 Temporal waveforms of THz pulses transmitted through the target at 0, 60 and 120,respectively. THz pulse propagation through the target following different path does not only lead

to different absorption, but also gives different phase delay. The phase delay reflects refractiveindex distribution of the target

Fig. 6.5 The distribution of physical qualities in a THz wave CT measurement presented in x

space. (a) Distribution of THz peak timing, and (b). distribution of phase delay at 1 THz

THz wave CT; however, the thickness of the retrieved shell is much thicker than

the real one. This is due to the fact that the physical model of THz CT is based on

gradual change of refractive index; however, the real target has a sharp change at

boundaries of the shell. Further, the shell of the ping-pong ball has relatively high

refractive index and the Fresnel losses at its surface are not negligible. The Fresnel

losses also affect the image quality. Figure6.9shows an optical photo of a piece


6/22


Fig. 6.6 3D image of the

target reconstructed via

inverse Radon transform of

the peak timing distribution

in thexspace

of dry and defat turkey bone and the corresponding THz CT image [3]. The optical

photo only shows profile of the bone, while THz CT image shows the profile as wellas the central cavity structure. However, there are rich microstructures in the bone,

which are not retrieved in THz CT image. The inability of reconstruction to resolve

microstructure is because the CT algorithm requires that the target has low scattering

and absorption, which are not satisfied for the turkey bone. The heavy scatter-

ing by those complicated microstructures reduces image quality of the retrieved

image.

Spatial resolution is the most important feature for an imaging system. The def-

inition of spatial resolution may vary from one imaging system to anther system.

If the imaging system is diffractive limited, the Rayleigh criteria is the most com-monly used definition. For THz CT imaging, however, structure or composition of

the target may become a dominant factor affecting the spatial resolution. As a result,

a more practical definition of spatial resolution is commonly used in study of THz

wave CT. It is defined as the smallest distance between two spots that can be dis-

tinguished in the retrieved image. Figure6.10shows photos of a cylindrical sample

made using polystyrene foam. The sample contains eight holes with a diameter of

2.5 mm each and two slots with 2.5 mm width. The smallest distance between two

holes lying on the line AA is 0.5 mm. Figure16.11agives the reconstructed crosssection image of the sample using THz CT. The image indicates that THz CT pro-

vides a spatial resolution of at least 0.5 mm, because even the closest holes are

distinguishable in the image. Ray approximation used in the reconstruction does

not consider the diffractive behavior of THz wave limited by the imaging system

aperture. In reality, the measured phase change is an involution between the sample


7/22

T-Ray Diffraction Tomography 133

Fig. 6.7 THz wave CT images of a ping-pong ball

caused phase delay and the diffraction effect. Using Wiener filter, the diffraction

induced phase change can be removed from the THz CT image to obtain the pure

sample information. Figure6.11bshows the enhancement in the sharpness of the

structure of the target obtained by applying Weiner filter on the image in Fig.6.11a.

T-Ray Diffraction Tomography

Diffraction phenomenon plays a strong role in THz wave imaging due to the rela-

tively long wavelength of THz waves. Interaction between THz wave and the target

can be described by the following Maxwell equation[4]:


8/22


Fig. 6.8 3D image of the

ping-pong ball cavity

Fig. 6.9 Photo of a turkey bone (left) and its THz wave CT image (right)

2E+ (r)(r)c2

2

t2E+ [ln (r)] ( E) + [E ln (r)] = 0, (4)

where r denotes a position in space, c is the speed of light, (r) and (r) are

the complex permittivity and permeability of the material, respectively. If the

variation of both and is small within a wavelength, the above equation can

be simplified to


9/22


Fig. 6.10 Side view and top view of a target used in THz wave CT. The target is made of

polystyrene foam

Fig. 6.11 (a) THz wave CT cross section image of the target shown in Fig. 6.10(b) the cross

section image with Wiener filter applied

2E+ n(,r)2

c2

2

t2E= 0 (5)

.

Here n = is the complex refractive index of the target. If polarization effectsof the EM wave are negligible, the vector equation can be further simplified to the

Helmholtz scalar equation:


10/22


2u(r) + k20n(,r)2u(r) = 0, (6)

wherek0= 2/is the wave number of EM wave in vacuum and u(r)is the complexamplitude function of the electric field. In an imaging process,u(r)can be described

as the sum of two components: u(r)= u0(r) + us(r), where the former is electricfield of EM wave which does not penetrate through the target or is a solution to the

equation

2 + k20

u0(r) = 0, (7)

while the later is the electric field of EM wave after transmission through the target.

If the target modulates only phase of the EM wave, the electric field can be

written as

u(r) = exp [(r)] = exp[0(r) + s(r)], (8)

where is the complex phase of the electric field. Assuming that the scattering

induced phase shift changes slowly, Equation (7) can be further simplified using the

first order Rytov approximation to

s(r) = 1u0(r)

G(r r)V(r)u0(r)dr, (9a)

whereG(rr)is a Green function [5]and is described as

G(r r) = exp

ik0r r

4r r (9b)

andV(r) is defined as

V(r) = k20[n2(,r) 1]. (9c)

Compared to optical waves, diffraction of THz pulses shows its unique prop-

erties. The THz pulse contains broadband spectrum and its interference pattern is

generated by sum of all frequency components. Figure6.12 illustrates an experi-

mental setup of Youngs double slit interference measurement for THz wave. In this

experiment, the sample was a 0.17 mm thick aluminum foil with double slits of

width 1 mm each and the distance between those two slits being 6 mm. The dis-

tance from the double slits plane to the THz wave detector was 48 mm. Since THz

pulse has a short pulse width, its interference pattern also varies in time. The num-

ber of peaks and valleys in the interference pattern increases with time delay. This


11/22


Fig. 6.12 Experimental setup of THz wave Youngs double slit measurement. The double slits are

carved on 0.17 mm thick aluminum foil with width of 1 mm each. The distance between those two

slits isd= 6 mm the distance between the double slit and the detection crystal is D = 48 mm

phenomenon indicates that, after THz pulse pass through the double slits, lower fre-

quency components propagate faster than the higher frequency components. Figure

6.13ashows the evolution of THz wave interference pattern along the direction per-

pendicular to the double slits. Figure 6.13b shows position of peak and valley in

Fig. 6.13a, which presents the wavefront propagation of THz wave starting from

each slit.

a b

Fig. 6.13 The temporal evolution of THz field along xaxis. (a) experimental result, and (b) the

normalized electric field (according to peak of THz waveform)


12/22


Fig. 6.14 The concept of

diffraction tomography (DT).

The carrier wave in DT

measurement is a plane wave.

Wavefront of the carrier wave

is recorded after propagation

through the target, and which

is used to retrieve 3D image

of the target

In THz diffraction tomography, a planar THz wave is used to illuminate a target

and the targets structural information is extracted by measuring and processing the

diffracted THz distribution by the target. Figure 6.14shows the concept of diffrac-

tion tomography using a monochromatic wave. The light source in a diffraction

tomography is a plane wave. The THz wave is detected in a detection plane per-

pendicular to its propagation direction after transmission through the target. The

Fourier transform of the forward scattered electric field of the THz wave on the

detection plane is proportional to 3D Fourier transform of the object function in adisplaced hemisphere in the frequency domain. The displacement value equals to

a negative incident wave number along the incident wave direction. Consequently,

reverse Fourier transform of the measurement result leads to the object function. In

THz CT, one needs to record THz field of an entire beam; however, in THz DT, THz

wave distribution in the detection plane needs to be resolved. This can be achieved

by using the 2D imaging technique discussed in Chapter 3. In THz DT set up, THz

waves are generated from a point emitter via optical rectification process excited

by high intensity fs laser pulses. The generated THz beam is collimated by a off-

axis parabolic mirror and illuminates the entire target which is placed on a rotationstage. The forward scattered THz beam from the sample and the optical probe beam

propogate collinearly through the EO crystal. This probe beam records the 2D dis-

tribution of the THz diffraction formed on the EO crystal. The 2D image of the

target is obtained for each rotation angle by recording the forward scattered wave

detected using a large aperture EO crystal. Figure6.15shows a target made of three

plastic rectangular bars used in THz DT. If the target modulates only the phase of

THz wave, the first order Rytov approximation can be used to reconstruct the 3D

image:

u = u0ln

us

uo+ 1

(10)

.


13/22

3Dimensional Imaging Using Fresnel Lens 139

Fig. 6.15 Photo of the target in THz wave DT (left) and its top view illustration (right). The target

consists of 3 plastic bars

Figure 6.16a gives a reconstructed refractive index distribution of the sample

shown in Fig.6.15and the Fig.6.16bshows the reconstructed image presented in

3D. The image is reconstructed based on 0.2 THz component.

The purpose of imaging is to obtain an image that closely resembles the target and

provides the maximum structural information of the target. Therefore, the quality of

image is evaluated by calculating similarity between the target and its reconstructedimage. The imaging quality of THz wave tomography is defined as a normalized

cross correlation function between a target and its image [6, 7]:

Q =M,N

i,j=0[O(i,j) O][I(i,j) I]M,Ni,j=0

O(i,j) OM,Ni,j=0 I(i,j) I , (11)where i,j are the pixel index, O is the object function of the target, O is mean of

O,Iis the reconstructed image function and Iis its mean value. Figure6.17shows

image quality of THz DT image presented in Fig.6.16as a function of the THz wave

frequency. For low frequency wave ( 0.45

THz), the imaging quality is limited by the lower Signal to noise ratio. Thus, the

imaging quality of the THz wave diffraction tomography increases with frequency

until 0.2 THz and has a plateau between 0.2 and 0.45 THz and further decreases

with the frequency.

3Dimensional Imaging Using Fresnel Lens

A Fresnel lens is a Fresnel zone plate with phase or amplitude patterns formed

by series of concentric circles. The Fresnel lens manipulates the optical wave via


14/22


Fig.

6.1

6

Th

ereconstructedTHzwaveDTimageofthetargetshowsinFig

.6.1

5(a)refractiveindexdistributionofthetarget,and(b)3D

imageofthe

refractiveindexdistribution


15/22


Fig. 6.17 The image quality

of THz wave DT as a function

of THz wave frequency

diffraction and interference. Fresnel lens can be considered as an example of diffrac-

tion optical components. Compared to traditional optical lens, Fresnel lens is more

flexible in design and fabrication. Further, it can be much thinner than refractive

lens with same aperture and focal length and thus can replace large aperture lens

in order to reduce the weight. Binary Fresnel lens are fabricated by photolithogra-

phy and etching on a transparent disk to make phase modulation features.Ncircles

of photolithography and etching gives L= 2 N levels of phase modulation depth.Figure6.18shows pictures of three THz wave binary Fresnel lens fabricated on an

intrinsic silicon wafer. Levels of those lenses are 2, 4, and 8, respectively. Figure

6.18illustrates the diffraction patterns of THz pulses focused by these three lenses.

Diffraction of THz wave by Fresnel lens along z-axis (normal of the lens) is [8]

u(z)

= nAn expi2

n

r

2

p +

1

2z (x2 +

y2) dxdy, (12)where n= 1,2,. . .., An= sin c(n/L). r2p is Fresnel zone of the lens with thedimensions of area and indicates a zone area where the phase delay is constant. For

an incident plane wave, its focal spot is located at

zn= r2p

2n, n = 1,2,...... . (13)

Equation (13) indicates that Fresnel lens has a very high chromatic dispersion and

its focal length is inversely proportional to the wavelength of the incident wave.

Equation (13) also shows that a Fresnel lens has multiple orders of focal spots for

a monochromatic plane wave. The diffraction efficiency for its focal point of each

order is


16/22


Fig. 6.18 THz wave Fresnel lenses made on silicon wafer with a level of 2 (a), 4 (c), and 8 (e),

respectively. The corresponding THz wave intensity distribution at the focal plane ( b,d, andf)

(n) |An|2 = sin c2(n/L). (14)

Equation (14) indicates that the lower order of focal spot gives the higher diffraction

efficiency. Table6.1summarizes the diffraction efficiency for the first order focal

spot of those three silicon based Fresnel lenses. An aluminum zone plate is used as

comparison.


17/22


18/22


Fig. 6.19 The first order

focal length of a Fresnel lens

as a function of THz

frequency

Fig. 6.20 The axial evolution of THz amplitude focused by a Fresnel lens

length of 2.6 cm at 1 THz. By scanning the time delay between the THz and opti-

cal probe beam, a temporal waveform of the THz wave at each pixel on the image

plane was recorded using a CCD camera. Fourier transformation of the temporal

waveforms provides the THz field amplitude (or intensity) distribution on the image

plane at each frequency. The measured two-dimensional THz field distribution at

each frequency provides images of the THz field transmission of a target at each

corresponding position along the z-axis. Figure6.21a, b, and c show illustration of


19/22


Fig. 6.21 Illustrations of three targets used in Fresnel lens based THz wave tomographic imaging

(a), (b), and (c). Their images made with THz wave at different frequencies (d), (e), and (f)

three objects used in the pulsed THz wave tomographic imaging system. The three

targets (OU, OC and OT) were made from 2 mm thick polyethylene sheet with the

dimensions of 60 by 40 mm with three different shapes carved on these three sam-

ples. These targets were placed along the THz beam path with their distances tothe lens, corresponding to d0 in Equation (15), being 3, 7 and 14 cm, respectively.

Images of patterns on the sensor plane at distance d1= 6 cm are measured at fre-quencies of 0.74, 1.24, and 1.57 THz, respectively. The corresponding images are

shown in Fig.6.21d, e, and f. At each frequency, a Fresnel lens images a different

plane section of a target object while images from other depths remain blurred. Each

point in the different object planes along the z-axis is mapped onto a correspond-

ing point on the image plane (sensor plane) with the magnification factor d1/d0 at

their corresponding frequencies. Table6.2summarizes the properties of those three

objects and their images.

Figure6.22 shows target distance d0 as function of TLHz wave frequency for

three different image distances of d1 equal to 4.6, 5.6 and 7.4 cm respectively

and shows a strong agreement between the experimental (points) and the mea-

sured (curves) values. Lateral spatial resolution of THz wave image created by a


20/22


Table 6.2 Characters of 3 targets and their images

Object (Fig.6.22)

Size (mm) 5 10 14

Object distance (cm) 3 7 14Carrier frequency (THz) 0.75 1.24 1.57

Image size (mm) 10 8 6

Magnification (experimental) 2 0.8 4.2

Magnification (calculation) 2 0.85 4.3

Fig. 6.22 The object distance in Fresnel lens based THz wave tomographic imaging system as

functions of THz frequency for three different image distances

Fresnel lens is limited by diffraction of the imaging system. The longitudinal spatial

resolution is determined by the spectral resolution of the THz wave detector. The

relationship between longitudinal range of the object plane and the bandwidth of

THz wave can be derived from Equation (16) as

d0=

d20

z

. (17)

Equation (17) shows that the longitudinal resolution increases with higher THz wave

frequency. The longitudinal resolution also quickly decays with the object distance.

Figure 6.23 shows longitudinal spatial resolution in Fresnel lens induced tomo-

graphic image as a function of THz frequency. The depth of field of the imaging


21/22


Fig. 6.23 The longitudinal

resolution in Fresnel lens

based THz wave tomographic

imaging system as a function

of THz wave frequency

(corresponding to the object

distance)

system, provided by Equation (21) of Chapter 3 also affects the longitudinal reso-

lution of the system The distance between the two distinguishable planes should be

larger than the depth of field for a better resolution.. If the spatial resolution on the

imaging plane equals to the Airy disk size and is much smaller than aperture of the

lens, depth of field of the imager is defined as

L = 2.44 l2

D2. (18)

Equation (18) indicates that the depth of field is also proportional to square of the

object distance and inversely proportional to the carrier wave frequency.

Similar to THz DT, image quality of Fresnel lens induced THz tomographic

imaging is also related to frequency of THz wave. The image quality is best between

Fig. 6.24 Photo (a) and cw

THz wave CT image of an air

freshener


22/22


0.5 and 1.25 THz and reduces at higher and lower frequency ends. At the lower fre-

quency end, the lateral resolution is limited by diffraction of the carrier while the

longitudinal resolution is limited according to Equation (17). It is also worth notic-

ing that, since Fresnel lens creates image following the imaging formula in Equation

(15), the magnification factors will be different for targets with different object dis-tances. This needs to be taken into account in order to correctly retrieve the 3D

image.

Above discussions are focused on THz wave tomography techniques utilizing

pulsed THz wave. THz wave tomographic images can also be obtained using cw

THz. Figure6.24shows a tomographic image (displayed in 2D) of an air freshner

case obtained by using the CW Gas Laser at 1.63 THz with a power of 180 mW. The

case is made of plastic, which is transparent to THz wave. The THz wave tomog-

raphy image shows both the external pattern of the shell profile and the internal

structure of the case.

References

1. S. Wang, and X.-C. Zhang, Pulsed terahertz tomography, J. Phys. D: Appl. Phys. 37, R1

(2004).

2. S. R. Deans,The Radon Transform and Some of its Applications. New York, John Wiley &

Sons (1983).

3. B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, T-ray computed tomography,

Opt. Lett.27, 1312 (2002).4. M. Born, and E. Wolf,Principles of Optics. Cambridge, Cambridge University Press (1997).

5. P. M. Morse, and H. Feshbach, Methods of Theoretical Physics. New York, McGraw-Hill

(1953).

6. J. C. Russ,The Image Processing Handbook. Michigan, CRC Press (1992).

7. D. N. Bhat, and S. Nayar, Ordinal measures for image correspondence,IEEE Trans. Pattern

Anal. Mach. Intell.20, 415 (1998).

8. G. B. Jin, Y. B. Yang, and M. X. Wu,Binary Optics. Beijing, National Defense Industry Press

(1998).

9. S. Wang, T. Yuan, E. D. Walsby, R. J. Blaikie, S. M. Durbin, D. R. S. Cumming, J. Xu, and

X. C. Zhang, Characterization of T-ray binary lenses, Opt. Lett.27, 1183 (2002).

THz Wave 3D Imaging and Tomography

Documents

Transcript of THz Wave 3D Imaging and Tomography