T-Ray Reflection Computed Tomography

T-Ray Reflection Computed Tomography

Jeremy Pearce

Electrical & Computer Engineering

Imaging Throughout History

Daguerreotype (1839)

http://inventors.about.com/library/inventors/bldaguerreotype.htm

X-rays (1895)

http://inventors.about.com/library/inventors/blxray.htm

T-rays (1995)

B. B. Hu and M. C. Nuss, Opt. Lett., 20, 1716, 1995

Objectives

•Is easy to align and use

•Requires few measurements

•Generates “high” resolution pictures

Develop a T-ray imaging system that…

Outline

• T-Rays

• Principles of Tomography

• T-Ray Reflection Computed Tomography

• Discussion and Future Work

What Are T-Rays?

100 103 106 109 101

2

101

5

101

8

102

1

T-Rays

Radio Waves

Microwaves

X-Rays

Gamma Rays

Electronics Photonics

Visible Light

Hz

Why Can T-Rays Help?

0 20 40 60 80 100

Time (ps)

0.2 0.4 0.6 0.8 1.0

Frequency (THz)

0.2 0.4 0.6 0.8 1.0

Frequency (THz)

E(t) E(f) |E(f)|

•Measurement of E(t)

•Subpicosecond pulses

•Submillimeter Wavelengths

T-Rays Provide

•Depth Information

•High depth resolution

•High spatial resolution

Benefits to Imaging

Subpicosecond pulses Linear Phase Over 1 THz in Bandwidth

Material Responses to T-rays

Water

Metal

Plastics

Strongly Absorbing

Highly Reflective

Transparent

+ -

T-Ray System

THz Transmitter

Substrate LensFemtosecond Pulse

GaAs Substrate

DC Bias

Picometrix T-Ray Instrumentation System

Picometrix T-Ray Transmitter Module

Femtosecond Pulse

T-Ray System

T-Ray Control Box with Scanning Delay Line

Fiber Coupled Femtosecond Laser System

Sample

THz Transmitter THz Receiver

Optical Fiber

Summary of T-Rays

• Broad fractional bandwidth

• Direct measurement of E(t)

• Short wavelengths

• Unique material responses

Outline

• T-Rays




Tomography

v

x

y

2D Object Slice f(x,y)

u

1D Projection p(u)

Goal of Tomography: Reconstruct a 2D or 3D image from a set of 1D measurements at multiple viewing angles

f(x,y) can be an object’s absorption, velocity, reflectivity, etc.

p(u) can be fan beam or parallel beam, transmission or reflection measurements

Examples of Tomography in Medical Imaging

http://www.radiologyinfo.org (2004)

My brain (2003)

http://pregnancy.about.com (2004)

Magnetic Resonance Imaging

X-ray Computed Tomgraphy Scan

Ultrasound

Fourier Slice Theorem

v

x

y

Object

u

Projection

kx

ky

Fourier Transform

Space Domain

Fourier Domain

The Fourier Transform of a projection is a slice in the Fourier spatial domain

Filtered Backprojection Algorithm

Each slice shares some dependency with other slices at lower frequencies

kx

ky

Ramp Filter

FBP weights every slice to reduce the dependency at lower frequencies

x

y

Filtered Projection

The filtered projection is then backprojected over the image plane

Outline

• T-Rays




T-Ray Reflection Computed Tomography (TRCT)

Reflected Waves

Object Slice

Top View

Side View• Reconstruct reflectivity edge map of object’s thin tomographic slice

• Illuminate slice at multiple viewing angles and measure back reflected waveforms

• Apply filtered backprojection algorithm to retrieve image of object’s edge map

• Analagous to ultrasonic reflection computed tomography

Reflected waveforms are the convolution of the incident pulse with the projections of the object’s edge map

TRCT Imaging Setup

The object is rotated 360° in 1° increments. A measurement is made of the reflected wave at each angle.

f = 12 cm

THz Transceiver

ObjectCylindrical Lens

Tomographic Slice

Rotation Stage

Cross-Section of Test Object

Test Object: Metal Square Post

Dimensions: 1 in. x 1 in.

Material: Aluminum

Measured Waveforms

0 100 200-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Ele

ctric

Fie

ld (

Arb

. Uni

ts)

Delay (ps)

Measured Waveforms s(,t)Reference Pulse r(t)

duupcutrts )()/2(),(

Measured waveform is the convolution of the reference pulse with the projection

Measured Waveform

Reference Pulse

Projection

Round Trip Travel Time

Image Retrieval Procedure

Step 1: Deconvolve projections p(u) from measurements s(,t)

Step 2: Retrieve reflectivity map f(x,y) from p(u)

Fourier-Wavelet Regularized Deconvolution (ForWaRD)

1. Estimate p(u) through direct Fourier inversion

2. Apply some Fourier shrinkage to reduce the amplified noise from the inversion

3. Shrink the wavelet coefficients to retrieve final estimate of p(u)

Filtered Backprojection Algorithm (FBP)

1. Filter p(u) with ramp filter

2. Backproject filtered projections across image plane

Step 1: Retrieval of p(u)

Measured Waveforms s(,t)

Projections p(u)

Step 2: Reconstruct Image

T-ray Image of Test Object

Photograph of Test Object

Successful recovery of object’s edges!

Dependence on Number of Viewing Angles

Dependence on Number of Viewing Angles

“Ideal” Image

0 50 100 150 200 250 300 3500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

% C

orre

latio

n

Number of Angles

Correlation of “Ideal” Image with Reconstructed Estimate

kj kj

kjkjperfect

kj

kjkjperfect

II

II

, ,

2,2,

,

,,

%

Circular Post



Plastic with Metal Posts



Plastic with Holes



Outline

• T-Rays




Does TRCT Meet Objectives

•Is easy to align and useUses single transceiver

•Requires few measurements

360 waveforms or less

•Generates “high” resolution pictures

Resolution 100 m

Develop a T-ray imaging system that…

Possible Applications

Zandonella, C. Nature 424, 721–722 (2003).

Wallace, V. P., et. al. Faraday Discuss. 126, 255 - 263 (2004).

Medical Imaging Security

Safety

Zandonella, C. Nature 424, 721–722 (2003).

Space Shuttle Foam

Diseased Tissue

Concealed Weapon

Can TRCT Compete with X-rays?

TRCT X-rays

100 m spatial resolution

• Low health risk

• High contrast

• Spectroscopic information

• Potential Uses: Security, quality control, medical imaging

• < 10 m spatial resolution

• Potential health risks

• Lower contrast

• Narrow bandwidth

• Current Uses: Medical imaging, security

Answer: Application dependent

Future System Improvements

• Actual Transceiver Module

• Increase Signal to Noise Ratio

• Acquisition Speed: – 5-6 sec./meas. 100 msec./meas.

• 3-D Imaging

• Automated Software

Future Algorithm Improvements

Inhomogeneous Velocity Incomplete Angle Data

Distortion of aluminum rods from incorrect velocity model

Reconstruction artifacts from incomplete data

Other Improvements

• Computational time

• Deconvolution method

• Velocity estimation

Summary

• Developed a new reflection mode T-ray imaging system

• Tested system’s capabilities on a diverse set of objects

• Compared TRCT to other commercially available imaging systems

• Suggested improvements for imaging system and reconstruction algorithm

Other Work

THz detector

THz transmitter

Sample cell

-8 -6 -4 -2 0 2 4 6 81E-6

1E-5

1E-4

1E-3

0.01

0.1

P(E

r/),

P(E

i/)

E/

NO free parameters!

The Multiple Scattering of Broadband Terahertz Pulses

THz Circular Synthetic Aperture Radar

Publications

1. J. Pearce, Z. Jian and D. M. Mittleman, “Spectral shifts as a signature of

the onset of diffusion of broadband terahertz pulses,” Optics Letters,

accepted (2004).

2. J. Pearce, Z. Jian, and D. Mittleman, “Propagation of terahertz pulses in

random media,” Philosophical Transactions A, 362, 301 (2004).

3. J. Pearce, Z. Jian, and D. Mittleman, “Statistics of multiply scattered

broadband terahertz pulses,” Physical Review Letters, 91, 043903 (2003).

4. J. Pearce and D. Mittleman, “Scale model experimentation: Using

terahertz pulses to study light scattering,” Physics in Medicine and

Biology, 47, 3823 (2002).

5. J. Pearce and D. Mittleman, “Definition of the Fresnel zone for broadband

radiation,” Physical Review E, 66, 056602 (2002).

6. J. Pearce and D. Mittleman, “The propagation of single-cycle THz pulses

in random media,” Optics Letters, 26, 2002 (2001).

Documents

T-Ray Reflection Computed Tomography