BLOCK DIAGRAM FOR THE GENERAL ANALYSIS OF RADIATION FLAW DETECTORS

V. A. VOROB'EV, G. P. TARASOV

(Presented by the scientific seminar of the Faculty of Physics and Technology)

The main task of nondestructive testing is that of obtaining information on the quality of the material being tested. Thus, in terms of the kind of tasks assigned to nondestructive-testing means, the latter are information systems, which are becoming ever more complex and are taking the form of complex automated systems. A convenient means for solving problems of the general analysis and synthesis of systems is provided by the interrelated methods of statistical decision theory and information theory. A general analysis of nondestructive-testing means (we shall hereafter call them NDT systems) is necessary because, on the one hand, information on the quality of the material being tested in an NDT system is carried by carriers having different physical natures (electromagnetic radiation, electric current, the number of developed grains of photographic film, etc.), and the criteria for evaluating the operating quality of individual links often prove to be incommensurable; on the other hand, it may turn out that, in designing an NDT system, individual links are of unnecessarily high quality, i.e., the characteristics of the links are not matched.

Fig. 1. Block diagram:
1 — source of information, 2 — signal-transformation operation, 3 — source of the information carrier, 4 — source of interference, 5 — operation of the action of interference on the signal, 6 — receiver-converter, 7 — recipient of information

In a general analysis one may consider the block diagram of an NDT system shown in Fig. 1, emphasizing the informational aspects of the question under consideration. More specifically, we shall speak of radiation...

flaw detection; in this case the diagram describes the following processes, using the terminology of information theory [5, 6].

1. The source of information, naturally, is the volume of the body under investigation, since the purpose of the NDT instruments under consideration is the detection of discontinuities. Detection of a defect in a known volume of material \(V\) is equivalent to specifying the density of the material \(\rho(\vec r)\) at each point of the volume \(\vec r_{(x,y,z)}\). In a defect-free material the density of the substance is constant at every point (the material is homogeneous), i.e.

\[ \rho(\vec r)=\mathrm{const}, \]

\[ \vec r \in V. \]

The presence of a defect changes the form of the function \(\rho(\vec r)\). Thus, to each \(\rho(\vec r)\) there can be assigned a definite set of defects. Because the set of functions \(\rho(\vec r)\) in \(V\) is infinite, the set of events that can occur during inspection of a material of volume \(V\) will also be infinite; i.e., in order to detect an arbitrarily small defect it is necessary to obtain an arbitrarily large amount of information. In practice the task is not posed of detecting any defect, however small it may be, so that a defect of volume \(\Delta V_{\mathrm{d}} < \varepsilon\) may be regarded as insignificant. Such a consideration transfers the question to another plane.

The larger the volume \(V\) of the body under investigation and the smaller the magnitude of the minimum detectable defect \(\varepsilon\), the more information must be obtained for its detection:

\[ Q_k=\log \frac{V}{\varepsilon}, \]

\(Q_k\) is the quantity of “inspection” information.

The logarithmic measure is introduced on the same grounds as in the definition of measurement information [1, 7], signal information [3, 6], and information on the accuracy of image reproduction [2]. The minimum detectable defect determines the accuracy of defect measurement.

1. The source of the information carrier is a generator of electromagnetic radiation (betatron, x-ray tube, isotope), producing a flux of penetrating radiation that carries information about the body under investigation to the receiver.

2. Signal formation (modulation). By means of radiographic irradiation with a flux of penetrating radiation, a spatial defect is mapped into a plane image representing the intensity distribution of the transmitted radiation \(I_{\mathrm{out}}(y,z)\). In the general case this operation can be written in the form of a functional expression:

\[ I_{\mathrm{out}}(y,z)=V[\rho(\vec r); I_0]. \]

The operation of \(V\)-formation of the signal is based on the process of radiation transfer through matter, described by the well-known transport equation [4].

1. The receiver-transducer is a set of devices for recording the transmitted radiation, for extracting the information carried by the received flux of radiation about the state of the substance under investigation, and for transforming this information into a form convenient for the recipient.

In general it is a system for panoramic recording of the \(\gamma\)-image; in practice it is implemented in the form of various devices: x-ray film, ionization chamber, scintillation count-

a counter, a fluorescent screen, an X-ray television installation, and so forth.

If \(I\) is the received signal distorted by noise \(\xi\), then at the receiver output the information is represented as

\[ Y = W(I). \]

1. The recipient of the information (an operator—a human being, or an automatic device), for whom the information about the state of the object under examination is intended.

2. The source of noise—an equivalent generator of noise acting at the receiver input. For the scheme under consideration, the presence of two kinds of noise is characteristic:

a) noise associated with the signal, caused by the statistical nature of the generation of the information carrier, the statistical nature of the process of signal formation, and the statistical nature of the conversion of \(\gamma\)-radiation into other kinds of information carriers;

b) noise not associated with the signal: the background of the room and the noise of electronic circuits. In addition, if the recipient of the information is subjective (a human operator), it is necessary to take into account psychophysiological aspects (for example, the contrast sensitivity of the eye).

The signal \(I\), distorted by noise \(\xi\), can be represented as

\[ I = v \left[J_{\text{out}}(y,z)\,\xi\right]. \]

It is obvious that information about a defect is multidimensional in character [1]. First, it is information about detection, i.e., the establishment of the very fact that a defect of a certain size is present in a given volume of material. This component characterizes the known characteristics of flaw detectors: detectability and productivity. Therefore

\[ Q = Q_k , \]

a quantity, i.e., the amount of information obtained at the output of the system, may be called informational detectability.

The quantity inverse to the minimum energy of the \(\gamma\)-flux expended per unit amount of obtained information will be called informational sensitivity [2]:

\[ G = \frac{1}{W_{\text{in}}/Q_k} = \frac{Q_k}{W_{\text{in}}}. \]

Further, there is a component of the information concerning the location of the defect and the nature of the defect.

The information capacities of the links of the information chain must be matched for each component, since the total information capacity is determined by the smallest values of the components of the information capacity of the links of the chain [2].

REFERENCES

1. S. B. Gurevich. Efficiency and Sensitivity of Television Systems. “Energiya,” 1964.
2. A. Brillouin. Science and Information Theory. FM, 1960.
3. F. P. Tarasenko. Introduction to the Course of Information Theory. Tomsk: Tomsk State University Publishing House, 1963.
4. U. Fano, L. Spencer, M. Berger. Transport of Gamma Radiation. Atomizdat, 1963.
5. A. A. Kharkevich. The Struggle Against Noise. “Nauka,” 1965.
6. K. Shannon. Works on Information Theory. IL, 1963.
7. A. M. Yaglom, I. M. Yaglom. Probability and Information. FM, 1960.