T-Ray Reflection Computed Tomography Jeremy Pearce Electrical & Computer Engineering

Imaging Throughout History Daguerreotype (1839) inventors/bldaguerreotype.htm X-rays (1895) 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? T-Rays Radio Waves Microwaves X-Rays Gamma Rays ElectronicsPhotonics Visible Light Hz

Why Can T-Rays Help? 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 pulsesLinear PhaseOver 1 THz in Bandwidth

Material Responses to T-rays Water Metal Plastics Strongly Absorbing Highly Reflective Transparent

+ - T-Ray System THz Transmitter Substrate Lens Femtosecond 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 TransmitterTHz Receiver Optical Fiber

Summary of T-Rays Broad fractional bandwidth Direct measurement of E(t) Short wavelengths Unique material responses

Outline T-Rays Principles of Tomography T-Ray Reflection Computed Tomography Discussion and Future Work

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 (2004)My brain (2003) (2004) Magnetic Resonance Imaging X-ray Computed Tomgraphy Scan Ultrasound

Fourier Slice Theorem v x y  Object u Projection kxkx kyky  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 kxkx kyky  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 Principles of Tomography T-Ray Reflection Computed Tomography Discussion and Future Work

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 Measured Waveforms s( ,t) Reference Pulse r(t) 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 ObjectPhotograph of Test Object Successful recovery of object’s edges!

Dependence on Number of Viewing Angles

“Ideal” ImageCorrelation of “Ideal” Image with Reconstructed Estimate

Circular Post T-ray Image of Test ObjectPhotograph of Test Object

Plastic with Metal Posts T-ray Image of Test ObjectPhotograph of Test Object

Plastic with Holes T-ray Image of Test ObjectPhotograph of Test Object

Outline T-Rays Principles of Tomography T-Ray Reflection Computed Tomography Discussion and Future Work

Does TRCT Meet Objectives Is easy to align and use Uses 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, (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? TRCTX-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 VelocityIncomplete 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 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, (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, (2002). 6.J. Pearce and D. Mittleman, “The propagation of single-cycle THz pulses in random media,” Optics Letters, 26, 2002 (2001).