Advances in Electronics and Electron Physics, Vol. 76 by Peter W. Hawkes (Ed.)

By Peter W. Hawkes (Ed.)

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It should be kept in mind that since in the general case the trajectory equations for the planes xOz and yOz are different, x(z) and y(z) are also different. It is known from the theory of linear homogeneous second-order differential equations that their linearly independent solutions are related by the expressions (relativistic case) , j ” ~ ~ ( x , x - xuxh) ; = const, (43) & F m Y , Y h - Yay;) = const. At small velocities The expressions in brackets in Eqs. 5. Formation of electron optical image.

The aberration value is defined as the difference between the exactly calculated nonparaxial trajectory and the trajectory derived from the paraxial equation. However, this involves errors resulting from the subtraction of nearly equal quantities. Besides, numerous preliminary designs must often be calculated and compared before the electron optical system can 44 L. A. BARANOVA A N D S. YA. YAVOR be optimized, so it is more convenient to use the values of the aberration coefficients themselves rather than the values Ax and Ay.

A similar analysis may be made of the y-projections and of a parallel beam incident into the lens from the right; in this way we can find the positions of all the focal planes. If each projection is extended asymptotically to the lens field (solid lines in Fig. 6), the coordinates z ( H o ) and z ( H i ) of the interception points of the incident and outgoing asymptotes will determine the position of the principal planes H , and H,. The points where the principal planes intercept with the lens axis are called the principal points.

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