T-rays: appropriateness for imaging applications Terahertz rays (T-rays) are pulses of sub- picosecond duration of electromagnetic radiation. They lie in the region on the electromagnetic spectrum between what is traditionally considered electronics and photonics. In practical implementations, picosecond bursts may be artificially generated in such a way so that they attain near linear phase and a broad fractional bandwidth in the Terahertz (THz) frequency range. Accordingly, it is possible to directly measure the temporal electric field using T- rays in a similar way that this is done for rays that lie in other regions on the electromagnetic spectrum. This allows probing depths of materials by looking at the arrival time of transmitted or reflected pulses. Note that one THz is equal to 1012 Hertz which corresponds to sub millimeter wavelengths in free space. Indeed, the wavelengths within the bandwidth of a typical T-ray are between 1 mm at 0.3 THz and 0.3 mm at 1 THz and evidently this can be translated into high temporal resolution (.3 mm in transmission and .15 in reflection), in imaging and detection applications.

In addition, T-rays have a number of unique material responses. On the one hand, plastics, papers, and many packaging materials are virtually transparent to T-rays. In fact, plastics work with T-rays similarly to glass with visible light. As an example, all of the lenses that are used in practice to suitably focus T-rays are made out of plastic and thus they can be readily machined. On the other hand, metals, such as Aluminum, are highly reflective. Water is strongly absorbing and T-rays cannot penetrate it, rendering biomedical imaging using T-rays of limited interest. However, T-rays can be used in package inspection or for manufacturing quality control. In 1995, Hu and Nuss took the first T-ray pictures of a semiconductor (see references). This work fueled interest in using T-rays for imaging in a number of applications and in a variety of configurations. NASA is using T-rays to inspect the foam on the shuttle tanks for defects, which is believed to have caused the Columbia accident.

Experimental setup that provided the data used in this project The present project uses experimental data obtained by a reflection computed tomography method utilizing T-rays (TRCT), proposed by J. Pearce, H. Choi, D. Mittleman, J. White, D. Zimdars (see references). In TRCT, the objective is to reconstruct the reflectivity edge map of an object’s thin tomographic slice. The setup of the TRCT imaging system is shown in the next figure. A THz transceiver is used in order to generate T-ray pulses and measure the back-reflected waveforms. A lens is placed in front of the transceiver to collimate the beam and then the cylindrical lens of focal length 12 cm focuses the beam in the vertical direction, confining it to a horizontal plane. The generated T-rays illuminate a thin cross-sectional slice of the object of interest. The object is placed on a rotation stage. It is rotated in 1 degree increments for 360 degrees and a measurement is taken at each viewing angle.

The available experimental data for the purposes of this project concern the metal square post shown in the next picture. It is a square inch in dimensions and made of aluminum. The reason for the choice of this test object is that it contains both large and small features. The dents in the metal are less than 1 mm across and it is interesting to verify the spatial resolution capabilities of the T-rays to resolve these features. Aluminum is a strong reflector so the measured reflected waveform is substantial. Since aluminum is opaque, it is not expected that the screw hole will be resolved because none of the T-rays will reach it.

Two main steps for imaging the test object: I) Deconvolution, II) Reconstruction The techniques and signal processing algorithms that are used are completely analogous to reflection computed tomography used with ultrasonic rays (see references). It is evident from the experimental setup that reflections from points that lie on the wavefront will sum together. This corresponds to a parallel beam projection. Each reflected waveform is the convolution of the incident T-ray pulse with the projections of the object’s edge map. The plan of attack for image retrieval consists of 2 steps. First, the projections have to be deconvolved from the measured waveforms. Second, the reflectivity map of the object is obtained from the projections. Herein, in order to deconvolve the projections from measurements, two methods were attempted: Regularized inverse filtering and Wiener filtering. Next, the image retrieval procedure is accomplished by application of the Filtered Backprojection Algorithm. FBP filters each projection with a ramp filter and then backproject the filtered projections across image plane.