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Representation of Focal Properties of the Equal-Diameter Two-Tube Electrostatic Lens for Computer Calculations



A Galejs, C Kuyatt


Previous calculations have given accurate first-order focal properties for the two-tube electrostatic lens at discrete voltage ratios. For computer optimization, calculations involving systems of two-tube lenses, one must be able to calculate the focal properties continuously over some arbitrary range of voltage ratios. Hence the data must be displayed in a continuous manner, and a method of interpolation is needed which yields functions having a high degree of smoothness. Special care must be taken to describe the lens behavior correctly near zero strength or for the voltage ratio approaching unity. A satisfactory solution to this problem has been achieved using cubic splines. The resulting functions of the focal properties are continuous and have continuous first and second derivatives. The total beam behavior, and hence the system design, is determined by the transfer matrix which is obtained from the focal properties. To achieve sufficient accuracy in the lens calculations over the entire range of required focal properties, the region near zero lens strength had to be treated separately.
Journal of Vacuum Science and Technology


Galejs, A. and Kuyatt, C. (1973), Representation of Focal Properties of the Equal-Diameter Two-Tube Electrostatic Lens for Computer Calculations, Journal of Vacuum Science and Technology, [online], (Accessed July 24, 2024)


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Created October 31, 1973, Updated October 12, 2021