Statistical error analysis of electrode construction for electrostatic spline lenses

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)3539-3542
Number of pages4
JournalJournal of Applied Physics
Volume62
Issue number9
DOIs
StatePublished - 1987

Fingerprint

error analysis
splines
lenses
electrostatics
electrodes
aberration
lens design
coefficients
optical properties

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Statistical error analysis of electrode construction for electrostatic spline lenses. / Szép, J.; Szilagyi, Miklos N.

In: Journal of Applied Physics, Vol. 62, No. 9, 1987, p. 3539-3542.

Research output: Contribution to journalArticle

@article{88fedb735ba44ed898ec2d59f0b101a1,
title = "Statistical error analysis of electrode construction for electrostatic spline lenses",
abstract = "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.",
author = "J. Sz{\'e}p and Szilagyi, {Miklos N}",
year = "1987",
doi = "10.1063/1.339277",
language = "English (US)",
volume = "62",
pages = "3539--3542",
journal = "Journal of Applied Physics",
issn = "0021-8979",
publisher = "American Institute of Physics Publising LLC",
number = "9",

}

TY - JOUR

T1 - Statistical error analysis of electrode construction for electrostatic spline lenses

AU - Szép, J.

AU - Szilagyi, Miklos N

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4143127455&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4143127455&partnerID=8YFLogxK

U2 - 10.1063/1.339277

DO - 10.1063/1.339277

M3 - Article

AN - SCOPUS:4143127455

VL - 62

SP - 3539

EP - 3542

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 9

ER -