Statistical error analysis of electrode construction for electrostatic spline lenses

It is easy to calculate approximately the electrode shapes for a given axial potential distribution by neglecting its high-order derivatives. The lens with the electrodes determined this way has different optical properties than that with the original axial potential distribution. These differences were calculated for a large number of randomly generated samples with axial potential distributions in the form of cubic splines. The differences were found to be about ±5%–10% for the focal lengths and the chromatic aberration coefficients. The spherical aberration coefficients for the constructed electrode systems usually have smaller values than those of the original lens models, but the differences are larger. The conclusion is that this simple electrode construction method is usually accurate enough for practical lens design.