SENSITIVITY ASSESSMENT OF THE METHOD OF INTROSCOPY USING FAST MONOENERGETIC ELECTRONS

V. I. BOIKO, V. V. EVSTIGNEEV, V. M. ZYKOV

(Submitted by the Scientific Seminar of the Research Institute of Electron Introscopy)

For monitoring inhomogeneities and internal defects in relatively thin \((<5\ \mathrm{g}/\mathrm{cm}^2)\) materials opaque to light, sources of monoenergetic electrons may be used; their radiation penetrates through the samples and creates a shadow image of the internal structure of the latter. To transform an invisible electron image into a visible one, it is necessary to use some electron-optical converter. Promising in this respect is the scintillation method of electron-optical conversion, which gives a direct optical image. This image, after appropriate amplification by an electron-optical light amplifier, can be observed directly by the eye or transmitted to the photocathode of a television system and observed on a television screen.

A. M. Jakobson and F. N. Novitskii carried out an assessment of the sensitivity of a beta-introscope [1]. In doing so, they assumed that the beta image is produced mainly by the primary component of beta radiation, while the scattered radiation gives the overall background.

It is obvious that the thickness of the material being viewed must be small in comparison with the particle range.

The present work is devoted to assessing the possibilities of the scintillation method of electron introscopy using a monoenergetic beam of fast electrons, when the thickness of the material being inspected is almost equal to the extrapolated range of the electrons.

When an electron beam passes through matter, the beam intensity, the distribution of particles with respect to energy, and the direction of their motion change. The change in these characteristics is determined by the mass thickness of the sample traversed by the electron beam and depends only weakly on the atomic number of the material. This makes it possible to use an electron beam for monitoring inhomogeneities and internal defects of layered products and materials [2]. In measurements with a scintillation detector, its readings will be proportional to the area under the curve of the distribution of absorbed energy in the scintillator behind the sample. The sensitivity of the scintillation method for homogeneous samples can be estimated from the distributions of absorbed energy \((D(x))\), assuming that the material of the scintillator located directly behind the sample does not significantly distort the distribution \(D(x)\). The absorbed-energy curve for all substances has a maximum and fol-

followed by a rapid, nearly linear decline. The rapid decrease of ionization with the depth of the material provides the necessary accuracy in measuring the thickness of the entire specimen or in detecting the location of a defect. The change in absorbed energy \(D(x)\), close to a linear dependence, occurs in the interval \((0.5 \div 0.9)R_{\mathrm{e}}\), where \(R_{\mathrm{e}}\) is the extrapolated range. We write the sensitivity of the method in the form of the ratio

\[ \frac{\delta D}{\delta x}, \]

where

\[ \delta D=\frac{\Delta D}{D} \]

is the relative increment of absorbed energy,

\[ \delta x=\frac{\Delta x}{x} \]

is the relative change in thickness.

For the derivative \(D'(x)\) within the limits of the linear section, the relation holds:

\[ D(x)=\frac{\Delta D}{\Delta x}=-\frac{D(x)}{R_{\mathrm{e}}-x}. \tag{1} \]

Then

\[ \frac{\delta D}{\delta x}= \frac{D'(x)\cdot x}{1-\dfrac{R_{\mathrm{e}}}{x}}. \tag{2} \]

From expression (2) it is clear that the relative change in intensity is larger the larger \(x\) is, i.e., as the thickness for a given energy increases, detectability improves. However, the interval \(x=(0.7 \div 0.9)\cdot R_{\mathrm{e}}\) should be regarded as the working region, since at \(x<0.7\cdot R_{\mathrm{e}}\), \(\Delta D/D\) is small, while at \(x>0.9\cdot R_{\mathrm{e}}\) the intensity is small and signal fluctuations are large.

The minimum defect size in thickness in the static mode is determined from expression (2):

\[ \delta x=\frac{\delta D\cdot D(x)}{D'(x)\cdot x} =\delta D\left(1-\frac{R_{\mathrm{e}}}{x}\right). \tag{3} \]

In the last expression we replace \(\delta D\) by the contrast-sensitivity threshold of the detecting device \(K\), take into account that the operating point is at \(x=0.8\cdot R_{\mathrm{e}}\), and introduce the reliability coefficient \(\xi=30\); then

\[ |\delta x|_{\min}=\xi\cdot K\left(1-\frac{R_{\mathrm{e}}}{x}\right). \tag{4} \]

We take \(K\) equal to 2%, since the sensitivity of existing electro-optical converters is \((2 \div 4)\)%.

Thus, the limiting value of the sensitivity of the electron-introscopy method is

\[ |\delta x|_{\min}\geq 1.5\%. \]

The greatest effect should be expected in the case of layered articles, when a thin, light material (film, coating) is deposited on a heavy material of thickness \((0.6 \div 0.8)R_{\mathrm{e}}\), and it is the latter that must be inspected. The total thickness must not exceed \(0.9R_{\mathrm{e}}\). In this case, inspection will be carried out in the region of thicknesses equal to \((0.7 \div 0.9)R_{\mathrm{e}}\), and the electron beam will be incident on the specimen from the side of the heavy material. The electrons, after passing through the entire specimen, enter the defective region in the light material and then, almost without scattering, strike the scintillator. This will make it possible to obtain good contrast-

... thickness. Images of defects lying in the thickness range \((0 \div 0.5)R_{\mathrm{e}}\), however, will be blurred as a result of the multiple scattering undergone by the electron in the specimen.

Above we considered the magnitude of the minimum inhomogeneity \(\Delta x\) that can be detected by an electron introscope. It was assumed that the transverse size of the defect \(q\) can be arbitrary. In reality, the number of electrons \(N\) absorbed by a scintillator element of area \(q^2\) during a time \(t\) will experience fluctuations whose mean square is equal to \(N\). The number of electrons is determined as follows:

\[ N=\eta(x)\cdot N_0\cdot q^2\cdot t, \tag{5} \]

where

\(\eta(x)\) is the electron absorption coefficient,

\(N_0\) is the number of electrons incident on unit area of the specimen per unit time.

As a result of fluctuation variations in the number \(N\), the brightness \(B\) of an element \(q^2\) will be perceived by the eye or by a detector with accumulation time \(t\) as a quantity varying randomly with a mean relative amplitude of oscillations

\[ \left|\frac{\Delta B}{B}\right|_{\mathrm{fl}} \approx \frac{\Delta N}{N} \approx \frac{1}{\sqrt{N}} . \tag{6} \]

It is assumed here that each electron absorbed in the scintillator produces a sufficiently large number of light quanta. For normal viewing of a defect it is necessary that the relative amplitude of the fluctuation variations be several times smaller than the minimum image contrast, i.e.,

\[ \xi\left|\frac{\Delta B}{B}\right|\leqslant K, \tag{7} \]

where

\(\xi\) is the coefficient by which the signal exceeds the noise — \((2 \div 4)\).

From formula (7), on the basis of formulas (5, 6), we obtain

\[ q^2 \geqslant \frac{\xi^2}{N_0\cdot \eta(x)\cdot t\cdot K^2}. \]

Taking the eye accumulation time \(t \approx 0.1\ \mathrm{s}\), \(K=0.02\), \(\xi=4\), \(N_0=10^{12}\) electrons/\(\mathrm{cm}^2\,\mathrm{s}\), and the electron absorption coefficient at a depth of about \((0.8 \div 0.9)R_{\mathrm{e}}\), \(\eta(x)=(0.1 \div 0.2)\), we determine the minimum linear size of a defect detectable by an introscope:

\[ q=(0.1 \div 0.2)\ \mathrm{mm}. \]

Thus, the calculations performed show that, using existing apparatus and sources of monoenergetic electrons, it is possible to create effective electron introscopes.

REFERENCES

1. A. M. Yakobson and F. N. Novitskii. “Zavodskaya laboratoriya,” No. 10, 1194, 1963.

2. B. A. Kononov, K. A. Dergobuzov, Yu. M. Stepanov. “Defectoscopy,” No. 4, 77, 1968.