T-Ray Reflection Computed Tomography

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

Imaging Throughout History Daguerreotype (1839) X-rays (1895) T-rays (1995) http://inventors.about.com/library/inventors/bldaguerreotype.htm http://inventors.about.com/library/inventors/blxray.htm 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

T-Rays Electronics Photonics X-Rays Radio Waves 103 100 106 109 1015 1012 1018 1021 Hz Visible Light Microwaves Gamma Rays What Are T-Rays?

E(t) E(f) |E(f)| Why Can T-Rays Help? Subpicosecond pulses Linear Phase Over 1 THz in Bandwidth T-Rays Provide Benefits to Imaging • Depth Information • High depth resolution • High spatial resolution • Measurement of E(t) • Subpicosecond pulses • Submillimeter Wavelengths

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

- + T-Ray System THz Transmitter Femtosecond Pulse Substrate Lens GaAs Substrate Picometrix T-Ray Instrumentation System Picometrix T-Ray Transmitter Module Femtosecond Pulse DC Bias

T-Ray System Sample THz Transmitter THz Receiver Optical Fiber T-Ray Control Box with Scanning Delay Line Fiber Coupled Femtosecond Laser System

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

Tomography y 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 v 2D Object Slice f(x,y) x  u 1D Projection p(u)

Examples of Tomography in Medical Imaging Magnetic Resonance Imaging X-ray Computed Tomgraphy Scan Ultrasound My brain (2003) http://www.radiologyinfo.org (2004) http://pregnancy.about.com (2004)

y ky v Fourier Domain Object x kx   Fourier Transform Space Domain u The Fourier Transform of a projection is a slice in the Fourier spatial domain Projection Fourier Slice Theorem

Filtered Backprojection Algorithm ky y kx  x Ramp Filter Filtered Projection Each slice shares some dependency with other slices at lower frequencies FBP weights every slice to reduce the dependency at lower frequencies The filtered projection is then backprojected over the image plane

Object Slice T-Ray Reflection Computed Tomography (TRCT) 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 Top View Reflected Waves Reflected waveforms are the convolution of the incident pulse with the projections of the object’s edge map

TRCT Imaging Setup Cylindrical Lens Object Tomographic Slice THz Transceiver f = 12 cm Rotation Stage The object is rotated 360° in 1° increments. A measurement is made of the reflected wave at each angle.

Cross-Section of Test Object Test Object: Metal Square Post Dimensions: 1 in. x 1 in. Material: Aluminum

Measured Waveforms Reference Pulse r(t) Measured Waveforms s(,t) Measured Waveform Projection Reference Pulse Round Trip Travel Time Measured waveform is the convolution of the reference pulse with the projection

Image Retrieval Procedure Step 1: Deconvolve projections p(u) from measurements s(,t) • Fourier-Wavelet Regularized Deconvolution (ForWaRD) • Estimate p(u) through direct Fourier inversion • Apply some Fourier shrinkage to reduce the amplified noise from the inversion • Shrink the wavelet coefficients to retrieve final estimate of p(u) Step 2: Retrieve reflectivity map f(x,y) from p(u) • Filtered Backprojection Algorithm (FBP) • Filter p(u) with ramp filter • 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 Correlation of “Ideal” Image with Reconstructed Estimate

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

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

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

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 Medical Imaging Security Concealed Weapon Wallace, V. P., et. al. Faraday Discuss.126, 255 - 263 (2004). Safety Diseased Tissue Zandonella, C. Nature 424, 721–722 (2003). Space Shuttle Foam Zandonella, C. Nature 424, 721–722 (2003).

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 • Other Improvements • Computational time • Deconvolution method • Velocity estimation Reconstruction artifacts from incomplete data Distortion of aluminum rods from incorrect velocity model

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

THz detector Sample cell NO free parameters! THz transmitter Other Work The Multiple Scattering of Broadband Terahertz Pulses THz Circular Synthetic Aperture Radar

Publications • 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). • J. Pearce, Z. Jian, and D. Mittleman, “Propagation of terahertz pulses in random media,” Philosophical Transactions A, 362, 301 (2004). • J. Pearce, Z. Jian, and D. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Physical Review Letters, 91, 043903 (2003). • J. Pearce and D. Mittleman, “Scale model experimentation: Using terahertz pulses to study light scattering,” Physics in Medicine and Biology, 47, 3823 (2002). • J. Pearce and D. Mittleman, “Definition of the Fresnel zone for broadband radiation,” Physical Review E, 66, 056602 (2002). • J. Pearce and D. Mittleman, “The propagation of single-cycle THz pulses in random media,” Optics Letters, 26, 2002 (2001).

T-Ray Reflection Computed Tomography