S' Wang, H' Zhong, B' Ferguson, M' Cheneya, B' Roysamb, and X'C' Zhang

1
High Resolution T-ray CT
S. Wang, H. Zhong, B. Ferguson, M. Cheneya, B.
Roysamb, and X.-C. Zhang Center for Teraherz
Research, Rensselaer Polytechnic Institute, Troy,
New York
Introduction THz wave, or T-ray, is an
electromagnetic radiation between microwave and
infrared waves. Its frequency is within 0.1 THz
to 10 THz,. Many molecular fundamentals can be
found in this frequency range 1.
Solution
Imaging reconstruction
The spatial resolution curve along A-A line for
the reconstructed slice images, without
WIF and with WIF
respectively.
T-ray CT system and sample
1. Develop a more accurate mathematical model for
the T-ray CT optical system.
The reconstructed refractive index distribution,
an accuracy better than 0.001 has been obtained.
Terahertz time-domain spectroscopy has been used
to determine the samples complex dielectric
function, and the complex dielectric function in
THz spectrum can be used to sense different
materials.
Methmetical model
Discussion and conclusion
T-ray wave scalar Helmholtz equation 4
A
( 1 )

• 1. This T-ray CT mathematical model has more
  accurately described our imaging system.
• 2. In present T-ray imaging system with this
  reconstruction algorithm, the spatial resolution
  is limited by SNR.
• 3. Good tomographic imaging system
• A. The mathematical model describes the
  optoelectronic T-ray CT imaging system
  accurately.
• B. High SNR.
• Future work
• Improve reconstruction algorithm.
• Modify imaging optics to enhance SNR.
• Acknowledgment

where
A
( 2 )
Under Rytov first approximation, the measured THz
wave can be written as
Polystyrene sample with hole pattern.
The optical image of the samples slice.
T-ray spectroscopic tomography has potential
applications in many fields such as security
screening and nondestructive inspection 2.
Borrowing the tomographic modality from X-ray CT,
we have demonstrated T-ray CT3 .
( 3 )
For T-ray optical imaging system, the phase term
in Eq. (3) can be approximated
Promised imaging
Mathematics

Problems with T-ray CT
( 4 )
Optics
1. In T-ray CT, T-ray propagation can not be
correctly described by a geometrical ray line
which is valid in X-ray CT,
The reconstructed slice image of the sample
without using Wiener inverse filter
The reconstructed image using Wiener inverse
filter.
( 5 )
The phase measurement is a convolution between
the object function and the beam distribution
function. The object can be recovered by an
inverse filter.
Reference 1. T. G. Philips and J. Keene, Proc.
IEEE, 80, 1662 (1992) 2. S. Wang et al, CLEO
2002, Post conference Edition p. 132 (Optical
Society of America, Washington DC, 2002). 3. B.
Ferguson et al, Optics Letters 4. A. C. Kak et
al, Principles of ComputerizedTomographic Imaging
(Society of Industrial and AppliedMathematics,
Philadelphia, 2001). 5. T. S. Huang, Picture
Processing and Digital Filtering
(Springer-Verlag, Berlin, 1979)

( 6 )
X-ray (0.25 Å) Tray (0.3 mm)
When noise has to be considered, a Wiener inverse
filter (WIF) 5 can be designed to extract
blurred image.
Contact zhangxc_at_rpi.edu
Beam waist 1 µ
3 mm Rayleigh Range 6 cm
5 cm
a Electrical, Computer and Systems Engineering
Department, Rensselaer Polytechnic Institute,
Troy, NewYork. b Department of mathematical
Science, Rensselaer Polytechnic Institute, Troy,
New York.
2. Build T-ray imaging system according to the
Mathematical model.
2. The T-ray CT, in general, does not satisfy
short wavelength limit assumption that is well
satisfied for x-ray CT, Diffraction or scattering
effects blur or deform the reconstructed image .