Multiple-element electrostatic lenses: I. The five-element lens

Abstract

The authors have used matrix methods to calculate the electrode potentials required to maintain a given conjugate focus condition for two five-element electrostatic cylinder lenses of slightly different proportions. They show that there is a simple parametrisation which allows one to calculate the focusing potentials given the overall voltage ratio and the magnification required. By using an extension of a straightforward method for calculating the potential within two closely spaced coaxial cylinders they have determined the matrix elements for a two-cylinder lens for voltage ratios from 0.01 to 100 in 200 equal logarithmic steps. These small steps simplify accurate interpolation especially for ratios close to unity.

Multi-element cylindrical electrostatic lens systems for focusing and controlling charged particles

“…It is practical importance that the cases with V 2 /V 1 >1 and V 4 /V 1 >1 have smaller aberration coefficients. Then other cases have higher spherical and chromatic aberrations [47,48]. The dependences of the ratio V 2 /V 4 on the magnification for two type of lens system are shown in figure 13.…”

“…The dependences of voltage ratios on magnification and aberration coefficients are presented graphically for two modes of five-element lens systems, true and afocal zoom lens modes. [47] and Trager-Cowan et al [48] For the true zoom lenses, to form a focal point of electrons with the same starting angle, an optimized relationship between the voltages V 2 /V 1 and V 4 /V 1 has to be calculated for a given voltage ratio V 5 /V 1 of final to initial electron energy. The zoom lens condition for five-element lenses having the potentials of these middle electrodes may be achieved with each of the potentials at a high and low value.…”

“…It is practical importance that the cases with V 2 /V 1 >1 and V 4 /V 1 >1 have smaller aberration coefficients. Then other cases have higher spherical and chromatic aberrations [47,48]. Some example of calculated values of V 2 /V 1 and V 4 /V 1 are shown with the spherical and chromatic aberration coefficients, C s /D and C c /D, in figure 13 for V 5 /V 1 =0.1, 1 and 10 with V 3 /V 1 = (V 5 /V 1 ) 1/2 , for two types of lens system A/D=0.5 and 1.…”

“…In the literature, there have been mainly two previous studies on the five element lens systems. An experimental study of a five element lens was made by Heddle and Papadovassilakis [47] for afocal lens which described by Heddle [45] and for true-zoom lens, and Trager-Cowan et al [48] described the behaviour of two five-element lens systems by using standard matrix methods and calculated focal properties and spherical aberration coefficients of these lenses. They have concentrated on a five-element lens system having A/D=1.5, and calculated focusing properties of the lens system.…”