Electromagnetic waves in terahertz frequency range (T-rays) enable non-invasive, non-contact and non-ionizing inspection of dielectric materials and semiconductors. T-rays are sensitive to complex permittivity changes, therefore any defect or structure detail causing its noticeable disturbance can be detected. The most common method of defects localization is transmission or reflection imaging based on pulsed terahertz Time Domain Spectroscopy (THz TDS) [1,2,3,4,5].

Tomography is defined as the cross-sectional imaging of an object under test (OUT) by measuring scattered wave (rays). There are several terahertz imaging techniques [6,7,8,9,10]:

time of flight reflection tomography (THz ToFRT),

digital holography,

diffraction tomography (THz DT),

tomography with binary lens,

computed tomography (THz CT).

Terahertz CT enables analogous to conventional x-ray CT reconstruction of the objects physical properties distribution based on sectional slices (Figure 1). However, in case of terahertz tomography both amplitude and phase data are collected (opposite to intensity of radiation for x-ray CT). The above fact causes that THz CT provides more information about the examined object [1]. For each slice object under test is rotated by angle *Θ* and shifted by distance *r*. The terahertz radiation passing through the object is recorded in the measuring plane, where the projection *R* (*Θ*, *r*) is obtained. In Ref. [7] it has been shown that the change in phase of the electromagnetic wave in the measuring plane can be used to determine the distribution of the refractive index *n* (and consequently permittivity ∊) in the cross-section of the object. Forward problem (projection *R* (*Θ*, *r*) calculation) mathematically is described by Radon transform [7, 9, 11]:

Figure 1 Simplified scheme of THz CT principle of operation

$$\begin{array}{}{\displaystyle R\left(\mathit{\Theta},r\right)=\underset{-\mathrm{\infty}}{\overset{\mathrm{\infty}}{\int}}\underset{-\mathrm{\infty}}{\overset{\mathrm{\infty}}{\int}}g\left(x,y\right)\phantom{\rule{thinmathspace}{0ex}}\delta \left(r-x\mathrm{cos}\mathit{\Theta}-y\mathrm{sin}\mathit{\Theta}\right)\phantom{\rule{thinmathspace}{0ex}}dx\phantom{\rule{thinmathspace}{0ex}}dy}\end{array}$$(1)

where: *g*(*x*,*y*) – spatial distribution of
the selected electromagnetic parameter of the imaged object, e.g. refractive index *n*(*x*, *y*), *δ* (•) – Dirac delta function, *Θ* – projection angle, *r* – ray distance from the axis of rotation.

The inverse problem – the reconstruction of the spatial distribution of the OUT’s electromagnetic parameters – is mathematically described by the inverse Radon transform [9, 11]:

$$\begin{array}{}{g}_{\mathrm{R}}\left(x,y\right)={\displaystyle \underset{0}{\overset{\pi}{\int}}\underset{-\mathrm{\infty}}{\overset{\mathrm{\infty}}{\int}}R\phantom{\rule{thinmathspace}{0ex}}\left(\mathit{\Theta},r\right)\phantom{\rule{thinmathspace}{0ex}}\delta \phantom{\rule{thinmathspace}{0ex}}\left(\mathit{r}\mathit{-}\mathit{x}\mathrm{cos}\mathit{\Theta}\right.}\\ \phantom{\rule{2em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\left.-y\mathrm{sin}\mathit{\Theta}\right)drd\mathit{\Theta}\end{array}$$(2)

In this paper terahertz computed tomography system with pulsed excitation is shown. Moreover, the reconstruction algorithm based on standard inverse Radon transform (2) and artificial neural network is proposed and verified using tomographic inspections of phantoms made of foamed polystyrene.

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