Xmpl2d56, 56th 'example' data file for CPO2D

2-aperture lens with curved electrodes.


Prepared for paper 68 in the publications list,  Optimization of the shapes of electrodes of electrostatic lenses, by F H Read, Microscopy and Microanalysis 21 Suppl S4, 276-279 (2015)

See the paper for more detailed information.

The use of the curved surface gives a large improvement in the spherical aberration, compared with traditional designs with flat apertures.


See also xmpl2d57, for 3D tube lenses. 

The data lines that define the first curved surface are:

users equns n

r 0.5 2.1 name of variable number 1 and its limits

a 1 name of parameter number 1 and its fixed value

s 3.06 name of parameter number 2 and its fixed value

R 2.1 name of parameter number 3 and its fixed value

0 name of parameter number 4 and its fixed value



1 1 numbers of 2 applied voltages (can be same, for equipotential electrode)

200 102 number of subdivisions, type of subdivision


In fact this equation is that of an elliptical curve, but with a = 1 it becomes circular.

So the ‘users equation’ could have been written more simply as:

z = R – sqrt(R^2 – r^2) – s (but elliptical shapes were being explored).

Rewriting again,

(z – (R – s))^2 + r^2 = R^2,

which is a circle of radius R centred at z = R - s.

We have s = 3.06, R = 2.1, r = 0.5 to 2.1 in 200 steps, so z goes from -3.00 to 0.96.


One further point: the ‘type of subdivision’ is 102 to give concentration of segments

at both ends.

See xmpl2d57, for quantitative data on the 2 types of lenses.