Single Point THz Imagery

Jaewook AhnKAIST - physics

Postech, March 2010

Thanks to collaborators• Kanghee Lee• Kyung Hwan Jin• Prof. Jong Ye (Kaist – biosystem)

Funding

Image encryption anddecryption through THz waveforms.

KAIST

Source: Terahertz waves

THz waves Pulsed

THzUltrafast

laser basedFEL

accelerator

THzRadio Microwave Infrared UV X-rays

Visible

Frequency (Hz)108 109 1010 1011 1012 1013 1014 1015 1016 1017

n = 1 THz

l = 300 mm

hn = 33 cm-1

T = 48 K

4.1 meVTHz ultrasonicBWOPhotomixingCO2 pumped FIRQCL ~100 fs

nW-mW10-100 kV/cm

What’s special about THz Optics ?

Wavelength = ~100 mm MEMS fabrication Laser micro-machining

Extremely broad bandwidth : df/f=1 Dispersion engineering Sub-diffraction limit optics ~ /100l

Coherent Emission and Detection Laser Induced Terahertz Emission Amplitude and Phase measurement

The First Terahertz Imaging

First THz imaging ???

Far-Infrared Imagery

T. S. Hartwick, D. T. Hodges, D. H. Barker, and F. B. Foote, Applied Optics 15, 1919 (1976).

Source: 0.3-1THz (Commercial HCN laser, etc) 1-10mWDetector: liquid helium –cooled GaAs. Future direction: coherent detection,

“Rapidly advancing FIR technology indicates that an FIR imaging system can be developed for industrial, military, law enforcement, and medical applications in the next few years.”

The First Terahertz Imaging

They predicted …

Hu and Nuss : Future Directions

“Imaging with Terahertz Waves”Hu and Nuss, OL 20, 1716 (1995).

1. “In future implementations, the THz beam could be scanned across the sample instead.”

2. “With current microelectronics fabrication technology, one should be able to fabricate a 100 x100 focal-plane array of photo-con-ducting dipole antennas to replace the single dipole detector that we used.”

3. “An obvious future improvement of the T-ray imaging technology will include the use of speech recognition algorithms for recogni-tion of the THz waveforms in amplitude and phase.”

THz beam over the sample …

Single-Pixel THz Camera

300번 (30%) 600번(60%)“A single-pixel THz imaging system based on compresssed sensing”

Chan, Charan, Takhar, Kelly, Baraniuk and Mittleman, APL 93, 121105 (2008)

Array detector imaging…

Real-Time THz Imaging : QCL

“Real-time terahertz imaging over a standoff distance”Lee, Qin, Kumar, Willams and Hu, APL 89, 11125 (2006).

Standoff operation (>25 m) Real-time operation

QCL 50 mW power : bright source uncooled microbolometer camera : low sensitivity

To use atmospheric windows at 4.9 THz, 1.5 THz, etc. Images taken with 1 s (20 frames) : Res. <0.75 mm

THz beam over the sample …

THz Reciprocal Imaging

“Terahertz wave reciprocal imaging”Xu and Zhang, APL 88, 151107 (2006).

Single detector to read out 2D target. 2D signals are separated in timed sequence. To avoid crosstalk : mod. freq. are prime numbers. Need source array with each modulated at a different frequency.

Still needs a lot of development …

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Fresnel Lens THz tomography

Targets are along the beam line. z= 3, 4, 7cm.Patterns are images at z’=6cm.

The corresponding focal lengths are achieved at 0.75, 1.24, and 1.57 THz.

Wang and Zhang (2002).

fzz

1

'

11

2

2p

v

rf

None of these have spectroscopic capability, and THz beams were used as a simple wave.

Image encryption anddecryption through THz waveforms ???

Here is how.

Simple wave Complex wave

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THz CDMA imaging…

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Image encryption and decryption through EM wave-forms.

+ =

Analog Optical Computing

Signal ProcessingDigital Image Recovery

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THz Single point Imagery : First Look

(a) Target(b) E(t, q)(c) E( , w q)(d) Sinogram(e) d = /10q p

(f) d = /15q p(g) d = /30q p

(h) Simulation

(a) (b)

(c) (d)

(e) (f)

(g) (h)

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(1) Fourier mask selects spatial frequencies of the object and maps into THz spectrum. E(kq) E(w)(2) Temporal waveforms deliver object function.

E(x,y) -> E(t, q)(3) Single waveforms for 2D imaging ?

Anatomy of the procedure…

(a) (b)

(c) (d)

Images Encrypted in Waveforms

(a) Target

(c) E( , w q)

(b) E(t, q)

(d) Sinogram

Sinogram : A visual representation of the raw data obtained in a computed axial tomography (CAT) scan. (wikipedia)

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(e) d = /10q p (f) d = /15q p(g) d = /30q p (h) Simulation

(e) (f)

(g)(h)

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(h)

Images Decrypted from Waveforms

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To understand how it works, we go back to the introductory optics textbook.

Abbe’s Theory of Image Formation

Double diffractions of the object at So do form a spatial-frequency filtered image at Si.

Fraunhoffer Formula

Spatial frequencies : (kx,ky)=k( /x f, h/f).

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f D

(x/f, h/f)

St SiSo

U(x,y)U’( ,x h)

V(x’,y’)S2

S1

S0

S-1

S-2

(x’/D, y’/D)

dxdyeyxUCUyf

xf

ik

),(),(' 1

Spatial filtering

THz Broadband ?

E( )w

E(x)

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dxxUexV f

xxik

)()'('

(a) Conventional imaging (b) Broadband imaging

dxxUeV f

xx

ci

x )()('

'

Broadband nature may allow single point imagery.

The question is how.

Coherent Optical Computer TM

)}],({),([)','( 1 yxUMyxV FF

f

(x/f, h/f)

SiSt

U(x,y) M( ,x h) V(x’,y’)

f f f

So

Lt Li

Tricks:

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Coherent Optical Computer

)}],({),([)','( 1 yxUMyxV FF

f

(x/f, h/f)

SiSt

U(x,y) M( ,x h) V(x’,y’)

f f f

So

Lt Li

M( ,x h)

ddxdydeyxUMCVyf

xf

ik

),(),()0,0( 1

ddxdydeyxUCVy

f

dx

f

d

ci

sincos

1 ),(),(

Spectrum at the image plane delivers the object shape.

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Image encrypted in THz waveform

ddxdydeyxUCVy

f

dx

f

d

ci

sincos

1 ),()(),(

dxdytd

fcyxyxUtV )sincos(),(),(

~

(c) E( , w q)(b) E(t, q)

(b)

(c)

(c)

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Single-Point THz Imagery

(a) Target(b) E(t, q)(c) E( , w q)(d) Sinogram(e) d = /10q p

(f) d = /15q p(g) d = /30q p

(h) Simulation

(a) (b)

(c) (d)

(e) (f)

(g) (h)

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(1) Fourier mask selects spatial frequencies of the object and maps into THz spectrum. E(kq) E(w)(2) Temporal waveforms deliver object function.

E(x,y) -> E(t, q)(3) Single waveforms for 2D imaging ?

“Coherent Optical Computing for T-ray Imaging”K.Lee et al, submitted (2009).

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Decryption of Image from Waveform

Angular resolution / =1,3,5, ... ,120p Dq

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Target Images are reconstructed byInverse Radon transformation

E’(x,y)Sinogram

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Field of View

dxdyeyxUCVy

f

dx

f

d

ci

sincos

1 ),()(),(

ddxdydeyxUMCVyf

xf

ik

),(),()0,0( 1(a)

(b)

(b’) , where fka

fkaJyxUayxU

/

)/(2),(),(' 12

22 yx

maxmax

/215.2

afc

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THz Bandwidth & Image Resolution

Inverse Radon Transformation is used to reconstruct the image.

Terahertz Bandwidth: wmax=0-1.8 THz

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fc

d

f

dk maxmax

Image Resolution

THz C(F?)DMA Imaging : proposal

Simple mask CDMA mask

N sets of spectral combs for diff. angular measurements.

S1=Dw{1, Nq+1, 2Nq+1, 3Nq+1, ...}

S2=Dw{2, Nq+2, 2Nq+2, 3Nq+2, ...}

S3=Dw{3, Nq+3, 2Nq+3, 3Nq+3, ...}…

SNq=Dw{Nq, 2Nq, 3Nq, 4Nq, ...}

Total # of combs = wmax/(Dw) # of combs In each set = MT

: Dw frequency comb widthNq : Dw comb width in each set

NqDw

wmax

Dq

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Using frequency: up to 1.8 THzFrequency resolution: 10GHz

one set of combsWith 45waveforms

object 3 sets of combsWith 15waveforms

5 sets of combsWith 9waveforms

15 sets of combsWith 3waveforms

45 sets of combsWith 1 waveform

~4cm

THz CDMA Imaging : SimulationK

AIS

T -

Ph

ys

ics

Using frequency: up to 1.8 THzFrequency resolution: 1GHz

one set of combsWith 45waveforms

object 3 sets of combsWith 15waveforms

5 sets of combsWith 9waveforms

15 sets of combsWith 3waveforms

45 sets of combsWith 1 waveform

~4cm

THz CDMA Imaging : SimulationK

AIS

T -

Ph

ys

ics

Using frequency: up to 1.8 THzFrequency resolution: 100MHz

one set of combsWith 45waveforms

object 3 sets of combsWith 15waveforms

5 sets of combsWith 9waveforms

15 sets of combsWith 3waveforms

45 sets of combsWith 1 waveform

~4cm

THz CDMA Imaging : SimulationK

AIS

T -

Ph

ys

ics

Simulation : Field of View

= / =45N p Dq

=M wmax/

(NDw)=401GHz combs

object50 x 50 pixels

~4cm

= / =45N p Dq

=M wmax/

(NDw)=400100MHz combs

Nyquist-Shannon sampling theorem limits the field of view.

)number pixel(max

NM

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Simpler variations

(a) Waveforms could measured at once by (a-1) time separation with dense materials (a-2) frequency separation with multi-layers or modulations(b) Integrated array detector

(a-1) (a-2)

(b)

THz CDMA Imaging

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Summary

/ =10p Dq / =15p Dq / =30p Dq

1. Single-pixel THz imagery has been demonstrated.

2. THz waves finds new applicationsin broadband coherent optical computing.

3. Code division multiple access protocol for “real” single-point THz imagery is under development.

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Thanks to collaborators and students

THz System Development Prof. Jong C. Ye (Kaist-biosystem) Prof. Kihoon Jeong (Kaist-biosystem) Dr. D.S. Yi (KRISS)

Laser Terahertz Emission Microscope Prof. Y. D. Cho (Gist-IC)

Students 이강희 , THz CDMA imaging 이민우 , LTEM 한대훈 , THz metamaterials

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