Investigation of a Television Introscope

A. P. Shpagin, V. A. Malyshev, G. A. Kucher

(Presented by the joint scientific seminar of the DSM and MRD sectors).

The creation of modern systems for continuous automatic control presupposes the development of the most promising radiation methods of nondestructive testing. One such method is the television radiation method, which has the greatest efficiency in recording radiation, high productivity, and convenience in operation.

The further development of this method requires investigation of the sensitivity as a function of the principal parameters of a television introscope. In works [1, 2], certain methods were developed for calculating the sensitivity of television introscopes.

Theoretical investigation of the introscope reduces to constructing a mathematical model reflecting the basic concepts of the physical processes in the introscope channel, and to optimizing it with respect to the totality of the principal parameters.

To characterize the sensitivity of the introscope, the contrast of the minimum defect \(K\) and the signal-to-noise ratio \(\psi\), characterizing the probability of detecting a defect [2], were selected.

\[ K=\frac{w_c}{w_{\phi}}; \tag{1} \]

\[ \psi=\frac{w_c}{\sqrt{\Delta^2 w_{\phi}}}; \tag{2} \]

\[ w_c=N_0 \cdot \Pi \, l \cdot \mu(E_0) \tag{3} \]

\[ w_{\phi}=N_0\left[\Pi+\operatorname{const}\int_{0}^{E_0} N \cdot \Pi \, dE\right] \tag{4} \]

\[ \Delta^2 w_{\phi}=N_0\left[\Pi_{\Delta}+\operatorname{const}\int_{0}^{E_0} N \cdot \Pi_{\Delta}\, dE\right] \tag{5} \]

\[ N_0=s\cdot t\cdot N_s\cdot e^{-x\cdot \mu(E_0)} \tag{6} \]

\[ N=N_1= \left[ \frac{E_0}{E}+\frac{E}{E_0}+\cos^2\Theta-1 \right] \frac{ 1-e^{\,x\cdot \mu(E_0)-\frac{x\mu(E)}{\cos\Theta}} }{ \mu(E)-\mu(E_0)\cos\Theta }, \tag{7} \]

where

\[ \cos\Theta=1+\frac{mc^2}{E_0}-\frac{mc^2}{E}, \qquad \operatorname{const}=\frac{0.069\mu c^2}{E_0^2} \]

These quantities are defined for the area \(s\) of an element of decomposition during the frame time \(t\). \(N_0\) and \(N\) are the spectra, by number of quanta, of unscattered and scattered radiation beyond the barrier, obtained from \(N_s\)-quanta incident per unit area normally to the surface of the barrier; \(\mu(E)\) is the coeffi-

coefficient of attenuation of radiation with energy \(E\) by the barrier material; \(x\) is the barrier thickness; \(l\) is the linear size of the defect; \(w_c\) is the mean signal energy at the converter; \(w_\phi\) and \(\Delta^2 w_\phi\) are the background energy (barrier without a defect) and its mean-square fluctuation. The quantities \(\Pi\) and \(\Pi_\perp\), which characterize the mean energy absorbed in the converter, are normalized to one quantum incident normally on the screen surface. The calculation of \(\Pi(E)\) and \(\Pi_\perp(E)\) is considered in [3].

The model contains a set of blocks (programs) corresponding to the links of the introscope, and an organizing program that reflects the block diagram of the introscope. All calculations were performed on the M-20 computer.

For working out the model, a simple introscope was chosen, consisting of a radiation source, a single-crystal screen, and an ideal television system. For simplicity, a monoenergetic radiation source was taken; in block \(N\) only the first collision is taken into account. For a set of thicknesses \(x\) of an iron barrier and a series of thicknesses \(x_0\) of a CsI(Tl) single-crystal screen, the dependences of the contrast and of the signal-to-noise ratio at the converter output were obtained in the energy range from the source energy \(E_0\) to 30 MeV.

In Fig. 1 the dependence \(K(E_0)\) is presented on a logarithmic scale for barrier thicknesses of 0.1, 1, and 10 cm and a screen of 0.5 cm. The dashed curves correspond to complete absorption of energy in the screen in the second collision. It follows from this that neglecting the third and subsequent collisions in the screen introduces into the image contrast an error of no more than three percent.

Fig. 1. Dependence of the contrast on a CsI(Tl) single-crystal screen 0.5 cm thick on the radiation energy

Fig. 2. Dependence of the signal-to-noise ratio at the converter output on the radiation energy

In Fig. 2 the dependence \(\psi(E_0)\) is given for barrier thicknesses of 0.5, 1, and 10 cm and screen thicknesses of 0.1 cm (dashed curves) and 2 cm. In the calculation, pri-

It was taken that \(1/x = 0.01\), \(N_s st = 10^6\). The characteristic maximum of sensitivity is attained with an optimal combination of the quantities \(x\) and \(E_0\), which is analogous to the relation \(\mu \cdot x = 2\) indicated in [4]. For a barrier thickness of \(10\ \mathrm{cm}\), there is no such optimum, since for iron \(\mu(E_0) > 0.2\).

A more complex task in the further development of the mathematical model is to determine the optimal relations among the principal parameters of the introscope in order to ensure the maximum value of \(\psi\).

REFERENCES

1. A. M. Yakobson. In the collection Proceedings of the A. A. Baikov Institute of Metallurgy, Academy of Sciences of the USSR, issue 8, p. 188.

2. A. P. Shpagin. Candidate dissertation, Tomsk, 1967.

3. A. P. Shpagin, G. A. Kucher, V. A. Maltsev. Evaluation of the efficiency of monocrystalline screens. Proceedings of the Second Interuniversity Conference on Nondestructive Testing Methods (in press).

4. A. M. Yakobson. Zavodskaya laboratoriya, 31, No. 3, 1965, p. 318.