EFFECT OF THE THICKNESS OF THE CONVERTING SCREEN ON THE OPTICAL DENSITY AND IMAGE BLUR IN THE PHOTOGRAPHIC METHOD OF NEUTRON DETECTION

V. I. GORBUNOV, G. Sh. PEKARSKII

(Submitted by the scientific seminar of the Research Institute of Nuclear Physics)

The paper proposes a method for calculating the optimal thickness of a converting screen and carries out the calculation for a cadmium screen.

The purpose of the present work is to study the influence of the thickness of the converting screen on the optical density and image blur in the photographic method of neutron detection.

Cadmium, which has a large cross section for interaction with thermal neutrons, was chosen as the material for the converting screen:

\[ \mathrm{Cd}^{113}(n,\gamma)\mathrm{Cd}^{114}. \]

With point collimation of the neutron flux \(N_0\), the point at which it falls on the surface of the screen corresponds to an emitting filament, the activity of which decreases exponentially with depth. Under the action of secondary \(\gamma\)-radiation, an image is formed on the film, the optical density of which decreases away from the geometric center and is related to the thickness of the converting screen.

As in X-ray radiography [1], we took as a point image the region of radius \(R_0 = 0.03\) mm.

For calculations, the converting screen was divided through its thickness into \(n\) sections, and then the contribution made by each section \(l/n\) to the optical density and the amount of image blur was estimated (Fig. 1). The formula for calculating the optical density of a point region was obtained from the following considerations: the probability that one quantum from the section \(\left(l/n\right)_k\) will enter the region of radius \(R_0\) can be written

\[ \omega_\kappa=\frac{1}{2}\cdot\left(1-\cos\operatorname{arc\,tg}\frac{R_0}{l-\kappa}\right), \]

and the number of quanta in the segment \(\left(\dfrac{l}{n}\right)_\kappa\) can be determined as

\[ N_\kappa=N_0\int_\kappa^{\kappa+\frac{l}{n}} e^{-\mu x}\,dx; \tag{1a} \]

\[ \kappa=0,\ \frac{l}{n},\ \frac{l}{n}\cdot 2,\ldots,\frac{l}{n}\cdot(n-1). \]

Summation over all segments determines the number of quanta falling into the region of radius \(R_0\)

\[ A_0=\frac{N_0}{2}\cdot\sum_{0}^{\frac{l}{n}\cdot(n-1)} \left(1-\cos\operatorname{arc\,tg}\frac{R_0}{l-\kappa}\right)\cdot \int_\kappa^{\kappa+\frac{l}{n}} e^{-\mu x}\,dx, \tag{1} \]

where

\(N_0\) is the number of incident neutrons,
\(\mu\) is the linear coefficient of neutron absorption by cadmium,
\(R_0=0.03\) mm.

The basic assumptions in this method of calculation are that the angular distribution of \(\gamma\)-quanta is taken to be isotropic (in accordance with the theory of nuclear reactions through a compound nucleus) and that the absorption of this radiation in the screen material is negligibly small (for \(l=0.4\) mm the losses amount to \(0.3\%\)). By this method we performed calculations of the blackening density for four possible ways of using converting screens. The results of these calculations are presented in Fig. 2. In it, the frontal arrangement of the screen corres—

Fig. 2.

Fig. 3.

corresponds to curve 1; the frontal arrangement of the film is represented by curve 2; curve 3 corresponds to a “sandwich” of two screens and a film, with the thickness of the front screen being varied, while the thickness of the rear one was chosen to be optimal (according to curve 2); and, finally, curve 4 corresponds to a “sandwich” of two films and one screen. In order to characterize the magnitude of image blur, we introduced the concept of “relative blackening,” by which we mean the ratio of the blackening density of the region bounded by the radii \(R_1\) and \(R_0\) to the blackening density of the point region. Figure 3 presents the dependence of relative blackening on screen thickness for all four cases listed above.

The calculation was carried out by the formula

\[ \hat{\delta} = \frac{ \displaystyle \sum_{0}^{\frac{l}{n}\cdot(n-1)} \left( \cos \operatorname{arctg}\frac{R_1}{l-k} - \cos \operatorname{arctg}\frac{R_0}{l-k} \right) \cdot \int_{k}^{k+\frac{l}{n}} e^{-\mu x}\,dx }{ \displaystyle \sum_{0}^{\frac{l}{n}\cdot(n-1)} \left( 1-\cos \operatorname{arctg}\frac{R_0}{l-k} \right) \cdot \int_{k}^{k+\frac{l}{n}} e^{-\mu x}\,dx } \times \frac{R_0^2}{R_1^2-R_0^2}, \tag{2} \]

where \(\hat{\delta}\) is the relative blackening;

the term

\[ A_1=\frac{N_0}{2}\cdot \sum_{0}^{\frac{l}{n}\cdot(n-1)} \left( \cos \operatorname{arctg}\frac{R_1}{l-k} - \cos \operatorname{arctg}\frac{R_0}{l-k} \right) \cdot \int_{k}^{k+\frac{l}{n}} e^{-\mu x}\,dx \]

gives the number of \(\gamma\)-quanta from the segment \(\left(\frac{l}{n}\right)_k\) into the ring bounded by circumferences \(R_1\) and \(R_0\), where \(R_1>R_0\), and the term

\[ \frac{R_0^2}{R_1^2-R_0^2} \]

is the ratio of the areas of the regions being compared. In the calculations

\[ R_0=0.03\ \text{mm}, \]

\[ R_1=0.04\ \text{mm}. \]

The calculated results obtained (the calculation was carried out for thicknesses \(0.01;\ 0.02;\ 0.03;\ 0.04;\ 0.06;\ 0.08;\ 0.1;\ 0.2;\ 0.3;\ 0.4\ \text{mm}\)) make it possible to draw a number of conclusions concerning the practical use of converting screens.

When a converting screen is used, there exists a quite definite optimal thickness, which is a compromise with respect to the opposing phenomena—the blackening density and image blur (which in various specific cases can be specified by means of \(R_0\) and \(\sigma\)). It should be noted that, in the absence of stringent requirements on the magnitude of image blur, the optimal thickness for obtaining the maximum blackening density of the film shifts toward greater thicknesses.

As \(R_0\to\infty\) (when recording a neutron flux), the curve has a saturating character. However, beginning with a certain thickness, a decline is observed in the course of the curve, caused by the increase in the self-absorption effect of \(\gamma\)-radiation.

Fig. 4 illustrates this transformation of the curve (the numbers at the curves indicate the value of the adopted point region \(R_0\)).

In comparison with the frontal arrangement, the rear screen is more preferable both from the standpoint of the magnitude of the blackening density (it increases by a factor of 1.4) and from the standpoint of the amount of blurring (16% less); however, in this case the curve has a saturating character. The use of a “sandwich” of two screens and a film makes it possible to increase the blackening density still further (by a factor of 1.9) and to reduce the amount of blurring (by 23%). A “sandwich” of two films and one screen gives a blackening density 2.4 times greater, while the relative blackening remains the same.

Fig. 4.

In work [2] experimental data are presented which only qualitatively confirm our conclusions regarding the effect of screen thickness on blackening density and image blurring, but do not make it possible to give a quantitative estimate of this effect.

The question of using a “sandwich” of two films and one screen in neutronography has not, up to the present time, been covered in the literature. However, precisely this method, as our calculations show, is the most effective in the photographic method of neutron detection.

The calculation method presented makes it possible to choose the optimal screen thickness depending on the specific working conditions and the principal requirements imposed on image quality.

LITERATURE

1. Industrial Radiography, edited by U. J. Wiltshire.
2. H. Berger, J. Appl. Phys. 33, No. 1, 48–55, 1962.