A STUDY OF THE INFLUENCE OF A LONGITUDINAL MAGNETIC FIELD ON THE RESOLVING POWER OF AN ELECTRONIC INTROSCOPE

V. I. GORBUNOV, D. I. SVIRYAKIN, K. B. UMBLIA

The electron-optical display, on the luminescent screen of an electronic introscope [1], of the pattern of the spatial distribution of the energy of an electron flux absorbed in the object under inspection may be regarded as the transmission of messages. Therefore the principles of information theory are applicable here. The electron flux that has passed through the object under study possesses informational redundancy, since it contains a low-information background and information about inhomogeneities caused by the technological and structural features of the object. However, the analog transformations of information adopted in the electronic introscope have the advantage that they do not destroy the structure of the image, preserving the possibility of its direct perception. The configuration of the field of the electron-optical refractive index in electrostatic and electromagnetic lenses can be substantially changed by redistributing the voltages between the electrodes and the currents in the winding sections. This makes it possible to simplify and make readily controllable the process of transformation. At the same time, however, the possibilities of purely electron-optical (simultaneous) transformations are limited. Therefore, for obtaining high-quality reproduction, only stigmatic imaging is of practical interest—when each point of the object plane is likewise imaged as a point on the reproduction plane. Stigmatic images permit only affine transformations. This means that images may be shifted, rotated, rescaled, stretched, or compressed in two mutually perpendicular directions, but no more. Projective transformations, which are so necessary, for example, for correcting perspective distortions, cannot be carried out without violating the point correspondence between the object and the image. Still less accessible are other nonlinear geometric transformations without substantial deterioration of image quality.

The possibilities of geometric transformations are nevertheless expanded if one abandons the requirements of image continuity and simultaneity of transformation. In electron-beam systems with sequential scanning, aberrations can be corrected separately and geometric transformations can be performed. But the principal drawback of transformations of this kind is that they are performed only after the video signal has already been formed, and consequently the noise of the switching and formation circuits is mixed into the image being transformed. In view of all the above, in the development of electronic introscopes, pre-

preference was given to electron-optical conversion, which makes it possible by simple means to distinguish features of visual images that are essential for recognition in visual analysis of images [2]. In any system for transmitting visual information, one of the most important parameters is the resolving power, or the spatial-frequency characteristic, which is expressed as the product of the characteristics of its individual links. By analyzing each of the links independently, one can determine its contribution to the overall characteristic and, in particular, identify the “weakest” links and correct their characteristics. In an electron introscope, the link requiring correction of the spatial-frequency characteristic is the interval between the object under study and the luminescent converting screen. After passing through the object, the electrons of the beam undergo angular scattering; therefore, as the distance from the rear wall of the object to the screen increases, the image formed by the electron flux on the screen becomes increasingly blurred. As a result, a contradiction arises between the requirements of obtaining maximum image contrast and obtaining the highest resolving power. To improve the contrast it is necessary to cut off the low-energy component of the electron flux [2], which is achieved by installing electrostatic lenses formed by grids to which the corresponding potentials are applied; that is, in order to place the grids it is necessary to increase the distance between the rear wall of the object under study and the screen, while to increase the resolving power of the introscope it is necessary to reduce this distance. It follows from this that an element must be introduced into the system which, in the presence of an electron energy selector, would make it possible to preserve the resolving power of the introscope. Such an element may be a solenoid that creates a homogeneous longitudinal constant magnetic field intersecting the object under study, the selector grids, and the converting screen (Fig. 1).

Fig. Diagram of the motion of an electron that has passed through the illuminated object in the magnetic field of the solenoid.

The magnetic field interacts only with a moving electron whose velocity vector is not parallel to the lines of force of the magnetic field. The force acting on the electron is determined by the expression

\[ \mathbf{F} = m \frac{d\mathbf{V}}{dt} = - e [\mathbf{V} \times \mathbf{B}], \]

where \(\mathbf{B}\) is the vector of magnetic-field induction;
\(\mathbf{V}\) is the vector of the electron velocity;

\(m\) — mass of the electron;
\(e\) — charge of the electron.

The magnetic field inside the coil, in a region sufficiently far from its edges, may be regarded as homogeneous, i.e., the field induction has a single component \(B_z\). Let us choose on the inner surface of the specimen a point \(a\) and assume that it is a source of electrons. Let an electron enter the field in the plane of the drawing, having velocity \(V = V_z + V_y\).

The velocity component \(V_z\) is parallel to the direction of the field lines. Consequently, it will not cause interaction of the electron with the field, and the electron will move uniformly along the \(Z\) axis. The velocity component \(V_y\), however, is perpendicular to the direction of \(B\) and will determine the force acting on the electron at the initial instant, obviously perpendicular to the plane of the drawing in the direction toward the observer. Numerically, the magnitude of this force may be expressed as

\[ F_m = e \cdot V_y \cdot B. \]

This force will curve the trajectory of the electron and, consequently, will be the centripetal force \(F_{\mathrm{c}}\), which, as is known from mechanics, is determined by the formula

\[ F_{\mathrm{c}} = \frac{m V_y^2}{R}, \]

where \(R\) is the radius of curvature of the trajectory at the given point. Consequently,

\[ e V_y B = \frac{m V_y^2}{R}. \]

From this we obtain the expression for the radius of curvature of the electron trajectory in the form

\[ R = \frac{m V_y}{eB}. \]

The expression obtained does not depend on the coordinates of the electron; hence \(R = \mathrm{const}\), and the electron moves in a plane perpendicular to the axis of the coil along a circle. At the same time, however, owing to the presence of \(V_z\), it is displaced with constant velocity along the \(z\) axis, i.e., in the end it moves along a helical line. In this case, after a certain time \(T\), during which the electron completes a full revolution around the circle, it will again intersect the original field line \(aa'\). This time is equal to

\[ T = \frac{2\pi R}{V_y} = \frac{2\pi m}{eB} \]

and does not depend on the magnitude of the initial velocity of the electron.

Therefore, if several electrons emerge simultaneously from the point \(a\) chosen by us, then after one and the same time, independently of the magnitudes and directions of their velocities, they will all intersect the original field line \(aa'\). In this case, because of the different axial components of the velocities of the electrons, they will all intersect this field line at different points.

Let us now imagine that the beam of electrons entering the field at point \(a\) is monochromatic. This means that the velocities of all electrons are identical and paraxial, which gives us the right to take the magnitude of the total velocity as equal to its component \(V_z\). Then such an electron beam, emerging from point \(a\), after time \(T\), will again converge at point \(a'\) at a distance \(V_z T\) from point \(a\). Consequently, point \(a'\) may be regarded as the electron image of point \(a\).

Such images of the initial point will, obviously, be obtained at equal intervals along the field line, as long as the field remainsանոթ

homogeneous. Everything said is valid for any point located in a plane perpendicular to the axis and passing through the point. Therefore, if an object emitting electrons is located in this plane, then at distances \(V_z T\) from this plane each point of the object will likewise be imaged as a point. One may say that such a long magnetic lens transfers the image parallel to itself.

Magnetic focusing, as indicated above, should be used in combination with a device for selecting electrons by velocities \(V_z\). The higher the cutoff level, the smaller the spread of electron velocities and, consequently, the higher the resolving power of the electron-optical system. In addition, it should be noted that a sufficiently strong magnetic field significantly reduces the scattering of the electron beam as it passes through the nonmagnetic specimen and the luminescent layer of the screen, and the broader, therefore, is the spatial-frequency characteristic of the introscope.

REFERENCES

1. V. I. Boiko, V. I. Gorbunov, V. V. Evstigneev, D. I. Sviryakin. Betatron electron introscope. Defektoskopiya, 1973, No. 6.

2. V. I. Gorbunov, D. I. Sviryakin, K. B. Umbliya, V. V. Evstigneev. On increasing the contrast of an electron image by cutting off slow electrons. This collection.