COMPARISON OF THE SENSITIVITY OF IDEALIZED INTROSCOPE SYSTEMS USING X-RAY VIDICONS WITH SELENIUM AND LEAD OXIDE TARGETS

A. P. Shpagin, V. S. Derkach

(Presented by the scientific seminar of the Research Institute of Electron Introscopy)

The results are presented of calculations of the dependences of signal-to-noise ratios for idealized introscope systems using X-ray vidicons with selenium and lead oxide targets for two target thicknesses in the energy range of monoenergetic radiation 20–200 keV.

The sensitivity of an introscope is determined by the combined influence of all its links, the parameters of these links, and the processes occurring in them. In particular, for an introscope with an X-ray vidicon, the sensitivity is determined by the change in the fraction of radiation energy absorbed in the target, the electrophysical properties of the target, its geometry, the method of reading out the potential relief, amplifier noise, and the parameters of the reproducing apparatus. The sensitivity of an introscope may be characterized by the signal-to-noise ratio provided by the given introscope when irradiating a reference flaw detector—for example, a groove-type flaw detector with a specified ratio of groove depth to flaw-detector thickness.

For analysis of an introscope and determination of the influence of its individual parameters on sensitivity, it is expedient to divide the information-transmission channel in the introscope into successive independent stages and to analyze each stage. In an introscope with an X-ray vidicon, the first stage may be taken as the conversion of the modulated flux of gamma radiation into a distribution of the energy absorbed in the target. The second stage is the conversion of the distribution of absorbed energy into a potential relief on the inner surface of the target, and the third stage is the conversion of the potential relief into a video signal and the processing of the video signal.

At each stage of information conversion, additional noise arises, which is equivalent to a decrease in the signal-to-noise ratio and, consequently, in the sensitivity of introscopes.

The purpose of the present work is to estimate the influence of the target material on the first stage of information conversion in an X-ray vidicon introscope. This estimate can be made by comparing the signal-to-noise ratio of idealized introscopes characterized by the fact that all conversion stages except the first introduce no additional noise; i.e., the signal-to-noise ratio at the output of the introscope is equal to the signal-to-noise ratio after the first conversion stage. In this case it is convenient to take the signal-to-noise ratio at the input of the introscope as equal to unity. Then the signal-to-noise ratio at the output of the idealized

...of an introscope for the case of monoenergetic radiation can be determined by the formula [1]

\[ \psi(E)=\frac{\Pi(E)}{\sqrt{\Pi_{\Delta}(E)}}, \tag{1} \]

where

\(\Pi(E)\) is the mean energy absorbed in the target under normal incidence on it of one quantum with energy \(E\);

\(\Pi_{\Delta}(E)\) is the variance of the absorbed energy.

For a selenium target in the energy range from 20 to 200 keV, the functions \(\Pi(E)\) and \(\Pi_{\Delta}(E)\) can be calculated with accuracy sufficient for practical use by formulas obtained taking into account only the first collision and under the assumption that all the energy transferred to the electrons is expended on ionization directly at the collision point:

\[ \Pi(E)=\frac{1}{\mu}\left(1-e^{-\mu h}\right)\left(\tau E+\sigma \bar{E}_{\sigma}\right)e^{-\mu_c h_c}, \tag{2} \]

\[ \Pi_{\Delta}(E)=\frac{1}{\mu}\left(1-e^{-\mu h}\right)\left(\tau E^2+\sigma f_e\right)e^{-\mu_c h_c}, \tag{3} \]

where

\(\tau\) and \(\sigma\) are the linear coefficients of the photoeffect and Compton scattering for the target material;

\(h\) and \(h_c\) are the thicknesses of the semiconductor layer of the target and of the glass faceplate of the X-ray vidicon, respectively;

\(\mu\) and \(\mu_c\) are the linear absorption coefficients of the semiconductor layer of the target and of the glass faceplate of the X-ray vidicon;

\(E_{\sigma}\) and \(f_e\) are the energy transferred to the recoil electron on average per one Compton-scattering event and the variance of this energy. Formulas determining \(E_{\sigma}\) and \(f_e\) are given in the literature [1, 2].

For a target material made of lead oxide, in the energy region up to 200 keV, when calculating the functions \(\Pi(E)\) and \(\Pi_{\Delta}(E)\) it is necessary to take into account the energy carried away by characteristic quanta arising during the photoeffect on the \(K\)-shell of lead atoms. In this case it is convenient to represent the function \(\Pi(E)\) in the form of two functions

\[ \Pi(E)=\Pi_1(E)+\Pi_x(E)e^{-\mu_c h_c}, \tag{4} \]

where

\(\Pi_1(E)\) takes into account the energy absorbed in the target under the condition that all characteristic quanta leave the target. At energies of the incident quanta below 200 keV and for small thicknesses of the semiconductor layer, the function \(\Pi_1(E)\) can be calculated with accuracy sufficient for practical use by a formula obtained taking into account only the first collision,

\[ \Pi_1(E)=\frac{1}{\mu}\left(1-e^{-\mu h}\right)\left(\tau E-\tau_k E_k+\sigma \bar{E}_{\sigma}\right)e^{-\mu_c h_c}, \tag{5} \]

where

\(\tau\) is the coefficient of photoabsorption only due to the photoeffect on the \(K\)-shell of lead atoms.

Assuming that the ratio between \(\tau\) and \(\tau_k\) will remain the same over the entire energy interval as in the jump region, for lead oxide one may write \(\tau_k=0.81\tau\).

\(E_k\) is the mean energy of the characteristic quanta; for lead \(E_k=75\) keV.

The function \(\Pi_x(E)\) in formula (4) takes into account the energy of characteristic radiation absorbed in the semiconductor layer of the target. Thus...

Since the absorption of characteristic quanta occurs mainly through the photoelectric effect, the function \(\Pi_x(E)\) can, with high accuracy, be determined by taking into account only a single collision. Assuming that the characteristic quanta have an isotropic distribution, and that the number of quanta produced is proportional to the probability of the photoelectric effect on the \(K\)-shell of lead atoms, one can obtain the following formula for \(\Pi_x(E)\):

\[ \Pi_x(E)=\tau_k E_k \left\{ \frac{1}{\mu}\left(1-e^{-\mu h}\right) +\frac{1}{2}\int_{0}^{1} \frac{\left(e^{-\frac{\mu_x h}{y}}-e^{-\mu h}\right)} {\frac{\mu_x}{y}-\mu}\,dy -\frac{1}{2}\int_{-1}^{0} \frac{\left[e^{h\left(\frac{\mu_x}{y}-\mu\right)}-1\right]} {\frac{\mu_x}{y}-\mu}\,dy \right\}, \tag{6} \]

where

\(\mu_x\) is the attenuation coefficient of the characteristic radiation in lead oxide; in the present case \(\mu_x=1.73\ \mathrm{cm^2/g}\), \(y=\cos\Theta\) is the cosine of the angle between the directions of the primary and characteristic quanta.

The relation for the variance of the energy \(\Pi_\Delta(E)\) absorbed in the target material can be obtained if it is assumed that all absorbed characteristic quanta are absorbed in a volume corresponding to one decomposition element. In this case the current pulse arising in the target due to absorption of a characteristic quantum will be added to the corresponding photoelectron pulse, since they occur simultaneously. Therefore, absorption of characteristic quanta will simply be equivalent to a decrease in \(\tau_k\) and, correspondingly, to an increase in the number of completely absorbed quanta. Then the function \(\Pi_\Delta(E)\) is expressed as

\[ \Pi_\Delta(E)= \left\{ \frac{1}{\mu}\left(1-e^{-\mu h}\right) \left[\tau E^2-E_k\tau_k(2E-E_k)+\sigma f_e\right] +\Pi_x(E)(2E-E_k) \right\}e^{-\mu_c h_c}. \tag{7} \]

Using formulas (1–7), calculations were carried out of the signal-to-noise ratio for idealized introscopes based on X-ray vidicons with selenium targets of thickness 0.1 and 0.5 mm and lead oxide targets of thickness 0.1 and 0.5 mm. In the calculations it was assumed that the density of selenium is \(4.8\ \mathrm{g/cm^3}\), and the density of lead oxide is \(8\ \mathrm{g/cm^3}\) [3]. The calculations were performed for X-ray vidicons with an input glass of thickness \(h_c=2\) mm, consisting of 34% silicon, 7.2% calcium, 10.8% sodium, and 48% oxygen. The effect of the signal plate was not taken into account in the calculation, because it was assumed that a thin layer of aluminum is used as the signal plate, and the attenuation coefficients of radiation in aluminum and glass are approximately the same. If, however, a layer of stannous chloride is used as the signal plate, it is necessary additionally to take into account the attenuation of radiation by the signal plate.

The dependences obtained as a result of the calculations are shown in Fig. 1, where curves 1 and 2 show the dependences of the signal-to-noise ratio of idealized introscopes based on X-ray vidicons with targets made of

lead oxide, with thicknesses of 0.5 mm and 0.1 mm, respectively, and 3, 4 are with selenium targets, with thicknesses of 0.5 mm and 0.1 mm.

From a comparison of curves 1–4 in Fig. 1 it is evident that idealized X-ray-vidicon introscopes with lead oxide targets have signal-to-noise ratio values greater than introscopes with selenium targets at equal target thicknesses and equal values of the radiation energies of a monoenergetic source, especially in the energy region from 90 to 120 keV.

Fig. 1. Signal-to-noise ratio for idealized introscopes based on X-ray vidicons with lead oxide and selenium targets, with thicknesses of 0.5 and 0.1 mm, respectively: curves 1, 2, 3, 4

Thus, if for equal thicknesses of selenium and lead oxide targets of 0.5 mm in the energy region from 50 to 90 keV the difference in the signal-to-noise ratio values is ≈25%, then in the energy region from 90 to 200 keV the signal-to-noise ratio values for selenium targets are smaller by a factor of 2.5–3. In the energy region from 90 to 200 keV, the signal-to-noise ratio values even for a lead oxide target 0.1 mm thick exceed the signal-to-noise ratio values for a selenium target 0.5 mm thick. The second maximum for the lead oxide target and the jump at an energy of 88 keV are caused by the photoelectric effect on the \(K\)-shell of lead atoms. The first maximum of the signal-to-noise ratio for both target materials in the energy region 30–50 keV corresponds to the maximum spectral sensitivity of X-ray vidicons with targets made of the above-mentioned materials. Consequently, introscopes based on X-ray vidicons with lead oxide targets are more promising than those currently produced with selenium targets.

Errors in calculating the signal-to-noise ratio by formula (1) are mainly systematic and are determined by the errors admitted in calculating the functions \(\Pi(E)\) and \(\Pi_a(E)\). The first of these arises because part of the energy transferred to electrons near the target boundary is carried by them beyond the target, while, on the other hand, some fraction not accounted for in the calculation of the energy is brought into the target by electrons emitted from the end faceplate of the X-ray vidicon. However, in the case of a glass or aluminum faceplate, the energy brought from the faceplate is much less than the energy carried out of the target, and it may be neglected. At the energies considered above, the main contribution to the error is made by photoelectrons, since Compton recoil electrons have low energy and a short range. In calculating the error it was assumed that the energy is carried away only by photoelectrons, and that all photoelectrons fly perpendicular to the plane of the target and lose their kinetic energy over a path equal to the maximum penetration depth. Obviously, all these assumptions lead to an overestimation of the error; consequently, the calculated error will be greater than the true one. Taking the indicated assumptions into account, the relative error in calculating the function \(\Pi(E)\) for a selenium target is determined by the formula

where

\[ \delta = \frac{\tau l E_e \cdot 100\%}{2\Pi(E)} e^{-\mu h_c}, \tag{8} \]

where

\(l\) is the maximum penetration depth of an electron with energy \(E_e\) in the target material, \(E_e=E-E_{\mathrm{b}}\), where \(E_{\mathrm{b}}\) is the electron binding energy. In the calculation it was assumed that all photoelectrons are ejected from the \(K\)-shell; then \(E_{\mathrm{b}}=13\ \mathrm{keV}\).

The relative error \(\sqrt{\Pi_{\Delta}(E)}\) has the same sign and, probably, the same order as the error made in calculating the function \(\Pi(E)\), and consequently the relative error made in calculating the signal-to-noise ratio is smaller than the error in \(\Pi(E)\).

To determine the relative error made in calculating \(\Pi(E)\) for a lead oxide target, the following formula can be obtained:

\[ \delta = \frac{ \left[ \tau_k l_1 \left(E-E_k^1\right) + l_2\left(\tau-\tau_k\right)\left(E-E_L\right) + \tau_k l_3 \left(E_k^1-E_L\right) \right]100\% }{ 2\Pi(E) } e^{-\mu_c h_c}, \tag{9} \]

where

\(E_k^1\) and \(E_L\) are the binding energies of electrons in the \(K\)- and \(L\)-shells of lead atoms, equal respectively to \(88\ \mathrm{keV}\) and \(15\ \mathrm{keV}\).

\(l_1, l_2, l_3\) are the extrapolated electron ranges, taken at energies respectively \(E-E_k^1\), \(E-E_L\), \(E_k^1-E_L\), from the literature [4].

Calculation by formulas (8) and (9) gave the following values of the relative error of the function \(\Pi(E)\) for a lead oxide target \(0.1\ \mathrm{mm}\) thick: \(6\%\), \(6\%\), \(11\%\), respectively for energies of \(100\ \mathrm{keV}\), \(150\ \mathrm{keV}\), \(200\ \mathrm{keV}\), and for a selenium target \(0.1\ \mathrm{mm}\) thick: \(9\%\), \(16\%\), \(20\%\) for the same energy values. As the target thickness increases, the relative error decreases inversely proportionally to the absorbed energy (since the absolute error does not change with a change in target thickness).

Conclusions

The calculations presented show that introscopes based on X-ray vidicons with lead oxide targets should have greater sensitivity than introscopes based on X-ray vidicons with selenium targets at equal target thicknesses, especially in the energy range \(90\div 200\ \mathrm{keV}\), which is due to the high effective atomic number of the target material. The presence of a second maximum in the dependence \(\psi(E)\) for introscopes based on X-ray vidicons with lead oxide targets in the energy region \(100\div 200\ \mathrm{keV}\) makes it possible to suppose that the indicated introscopes with industrial X-ray units at \(120\div 200\ \mathrm{keV}\) can be used for radiographic inspection of products of medium thickness—from aluminum of about \(100\ \mathrm{mm}\), and from steel—\(30\ \mathrm{mm}\).

REFERENCES

1. A. P. Shpagin. Candidate’s dissertation. Tomsk, 1967.
2. S. V. Starodubtsev, A. M. Romanov. Interaction of Gamma Radiation with Matter. Part I, Nauka Publishing House, Uzbek SSR, Tashkent, 1964.
3. Chemist’s Handbook, Vol. I, 1963.
4. L. V. Spenser. Energy Dissipation by Fast Electrons. Nat. Bur. St(US), 1959.