On the Question of Evaluating the Efficiency of Converting a Gamma Image into a Potential Relief by an X-ray Vidicon Target
Abstract Generated abstract
This paper examines how efficiently an X-ray vidicon target converts a gamma-ray image into an absorbed-energy distribution and, subsequently, a potential relief relevant to television radiation introscopy. It formulates the conversion stage in terms of the mean absorbed energy per incident quantum, its variance, and the spatial distribution of absorbed energy, relating these quantities to signal-to-noise losses and frequency-contrast losses. Approximate expressions are given for selenium targets under practical conditions, accounting for target thickness, glass faceplate absorption, photoelectric absorption, and Compton scattering. Calculations for typical target thicknesses indicate how radiation energy and target parameters affect absorbed energy, variance, spectral sensitivity, and the limiting signal-to-noise ratio attainable in an X-ray vidicon introscope.
Full Text
ON THE ESTIMATION OF THE EFFICIENCY OF CONVERTING A GAMMA IMAGE INTO A POTENTIAL RELIEF BY THE TARGET OF AN X-RAY VIDICON
A. P. Shpagin
(Presented by the Joint Seminar of the Sectors for Monitoring Forest Materials and RSD, Research Institute of EI)
X-ray vidicons—transmitting television tubes sensitive to X-rays and gamma rays—have found wide application in industry for the flaw detection of small products. Nevertheless, X-ray vidicons have been studied very little. No formulas have been obtained that relate the sensitivity of X-ray vidicons to the energy of the radiation used and to the parameters of the semiconductor layer; therefore it is difficult to judge how far the sensitivity achieved at present is from the limiting possible value, i.e., what the prospects are for further increasing the sensitivity. For the development of optimal introscopes with X-ray vidicons and for the further improvement of the X-ray vidicons themselves, it is necessary to have a mathematical model of an X-ray-vidicon introscope.
To obtain a mathematical model of an introscope, it is necessary to divide the information-transmission channel in the introscope into successive independent stages and to carry out a separate analysis of each stage. In an introscope with an X-ray vidicon, the following stages may be distinguished:
a) conversion of the modulated flux of gamma radiation into the distribution of energy absorbed in the target;
b) conversion of the distribution of absorbed energy into a potential relief on the inner surface of the target;
c) readout of the potential relief;
d) amplification of the video signal;
e) processing of the video signal in order to increase the sensitivity of the introscope to defects of a certain type;
f) reproduction of the image.
At each stage of information conversion, in the general case, two types of losses are possible.
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Gradational losses, which are due to a decrease in the signal-to-noise ratio.
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Frequency-contrast losses, manifested in a decrease in image sharpness and a decrease in the contrast of small defects. They are due to a decrease in the transfer coefficient for the upper spatial frequencies.
To estimate information losses at the stage of converting the modulated radiation flux into the distribution of energy absorbed in the target, it is sufficient to determine the following three characteristics of the X-ray vidicon, which are functions of the energy of the incident quanta:
a) the mean energy \(\Pi(E)\) absorbed in the semiconductor layer of the target, for normal incidence on the target surface of one quantum with energy \(E\);
b) the variance of this energy \(\Pi_\Delta(E)\);
c) the averaged distribution of the absorbed energy in the target, normalized to one radiation quantum.
The first two characteristics make it possible to determine the signal-to-noise ratio after the first stage, while the third makes it possible to calculate the frequency-contrast characteristic after the first stage.
The physical meaning and significance of the functions \(\Pi(E)\) and \(\Pi_\Delta(E)\) can be explained by the following concrete example. Suppose an object is irradiated by a monoenergetic beam of gamma quanta with energy \(E\), and that, on average during one frame time, \(N_\phi\) quanta fall on some section of the faceplate of the X-ray vidicon equal in area to a resolution element and located opposite an intact (defect-free) section of the object, while \(N_\phi+N_s\) quanta fall on an equal section located opposite a defective section. To simplify the discussion, let us assume that there is no scattered radiation (for example, an object of small thickness made of a material with a high photoelectric cross section is being irradiated). Then the signal energy and the variance of the background energy at the output of an idealized introscope, for which the signal-to-noise ratio is completely determined by the statistical noise of the absorbed quanta and the transfer coefficient of all subsequent stages of signal conversion in the introscope is equal to unity, are determined by the formulas:
\[ W_s=N_s\Pi(E), \tag{1} \]
\[ \Delta^2 W_\phi=N_\phi\Pi_\Delta(E), \tag{2} \]
and the signal-to-noise ratio at the output of the introscope is
\[ \Psi_{\mathrm{out}}= \frac{N_s\Pi(E)}{\sqrt{N_\phi\Pi_\Delta(E)}}= \frac{\Psi_{\mathrm{in}}\Pi(E)}{\sqrt{\Pi_\Delta(E)}}, \tag{3} \]
where \(\Psi_{\mathrm{in}}\) is the signal-to-noise ratio at the input of the introscope.
If the conditions
\[ \mu x<1, \tag{4} \]
\[ r_0<x, \tag{5} \]
are satisfied, where \(x\) is the thickness of the semiconductor layer (target), \(\mu\) is the linear attenuation coefficient of the radiation in the target material, and \(r_0\) is the extrapolated range of electrons in the target material (penetration depth), then the functions \(\Pi(E)\) and \(\Pi_\Delta(E)\) can be calculated with accuracy sufficient for practical application from formulas obtained by taking into account only the first collision and under the assumption that all the energy transferred to the electrons is spent by them on ionization directly at the collision point [1].
\[ \Pi(E)=\frac{1}{\mu}\left(1-e^{-\mu x}\right)(\tau E+\sigma E_s)e^{-\mu_c h}, \tag{7} \]
\[ \Pi_\Delta(E)=\frac{1}{\mu}\left(1-e^{-\mu x}\right)(\tau E^2+\sigma f_e)e^{-\mu_c h}, \tag{8} \]
where \(h\) and \(\mu_c\) are the thickness and the linear absorption coefficient of the glass faceplate of the X-ray vidicon (the exponential factor after the second parenthesis in formulas (6) and (7) takes into account the attenuation of the radiation intensity by the glass faceplate), and \(\tau\) and \(\sigma\) are the linear coefficients
photoeffect and Compton scattering for the target material, \(E\sigma\) and \(f_e\) are the energy transferred to the recoil electron on average in one Compton-scattering event and the variance of this energy, respectively [1] (\(\tau\), \(\sigma\), \(E\sigma\), \(f_e\), \(\mu\), and \(\mu_c\) are functions of energy; this functional dependence is not shown in the formulas given above for simplicity of notation).
In actual X-ray vidicons the targets are most often made of selenium, and the target thickness varies from \(0.1\) mm to \(0.5\) mm. For such a target thickness, condition (4) is satisfied at quantum energies greater than \(50 \div 70\) keV; however, since at energies below 70 keV the coefficient of interaction of the radiation with the target material is determined entirely by the photoeffect, calculation by formulas (6) and (7) gives an accurate result in this energy range even for \(\mu x > 1\), i.e., condition (4) does not restrict the range of applicability of formulas (6) and (7). Condition (5) restricts the range of applicability of formulas (6) and (7) from above. Using the data available in the literature [2, 3] on the dependence between electron energy and their extrapolated range, one can establish that condition (2) is satisfied for a selenium layer thickness of \((0.2—0.5)\) mm for electron energies below \(200 \div 300\) keV.
Fig. 1. Dependences of the mean energy absorbed in the target, normalized to one incident quantum, on the quantum energy
Fig. 2. Dependences of the variance of the energy absorbed in the target, normalized to one incident quantum, on the quantum energy
Figures 1 and 2 show the functions \(\Pi(E)\) and \(\Pi_\Delta(E)\), calculated by formulas (6) and (7), for an X-ray vidicon with an entrance glass of thickness \(h = 2\) mm, consisting of 34% silicon, 7.2% calcium, 10.8% sodium, and 48% oxygen, the target of which consists of selenium with density \(4.8\ \text{g/cm}^3\) and has a thickness of 0.1 and 0.5 mm. The influence 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 stannic chloride is used as the signal plate, then it is necessary additionally to take into account the attenuation of radiation by the signal plate. Figure 3 gives the dependences, on energy, of the ratio \(\Pi(E)/\sqrt{\Pi_\Delta(E)}\) for two target thicknesses. They make it possible to judge the degree of change in the signal-to-noise ratio due to the fact that,
that only some fraction of all the radiation incident on the faceplate of the X-ray vidicon is absorbed in the target.
The functions \(\Pi(E)\) and \(\Pi_{\Delta}(E)\), which mainly characterize only the first stage of information conversion in the X-ray vidicon, make it possible to judge certain characteristics of the entire X-ray vidicon and even of an introscope with an X-ray vidicon. In particular, they make it possible to calculate the limiting value of the signal-to-noise ratio in the introscope which, for a given radiation-source intensity, can be achieved by increasing the efficiency of accumulation and readout of the potential relief and by improving the method of amplifying the video signal. The method of calculation for the case of a continuous spectrum is considered in [1]. The function \(\Pi(E)\), moreover, determines the spectral sensitivity of the X-ray vidicon. Indeed, since the processes of accumulation of the potential relief and its readout proceed identically for all radiation energies, the cause of the nonuniformity of the spectral sensitivity of X-ray vidicons may be either a nonlinear dependence of the quantum yield of the target on the quantum energy, or nonuniformity of the absorbing power of the target over the energy range. Experiments carried out for germanium, silicon, and certain other semiconductors show that the quantum yield in these semiconductors varies linearly with the change in energy [4]. If a linear dependence of the quantum yield on energy is also observed for selenium, then the spectral-sensitivity function of the X-ray vidicon is determined by the ratio of the radiation energy absorbed in the target to the energy incident on the faceplate. Since the function \(\Pi(E)\) is normalized to one incident quantum, the spectral-sensitivity function will be similar to the ratio \(\Pi(E)/E\).
Fig. 3. Change in the signal-to-noise ratio due to the fact that only part of the radiation incident on the faceplate is absorbed in the target.
REFERENCES
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A. P. Shpagin. Development and study of a television radiation introscope. Candidate dissertation, Tomsk, 1967.
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A. A. Vorob’ev, B. A. Kononov. Passage of electrons through matter, Tomsk, Tomsk State University Press, 1966.
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L. V. Spenser. Energy Dissipation Bu Fast Electrons. Nat. Bur. St. (US), 1959.
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V. S. Vavilov. The Action of Radiation on Semiconductors. Moscow, Fizmatgiz, 1963.