Method for making electron gun

A method for manufacturing an electron gun, comprising:

• obtaining a first beam spot coefficient from an electrostatic lens magnification and a spherical aberration coefficient of a selected resistance distribution;
• executing a first process loop to find a resistance distribution that provides an approximate minimum value of a first beam spot coefficient;
• determining whether the first beam spot coefficient is an approximate minimum value;
• repeatedly executing the first process loop until the first beam spot coefficient is determined to be equal to the approximate minimum value;
• executing a second process loop to find another resistance distribution that provides an approximate minimum value of a second beam spot coefficient by determining whether the second beam spot coefficient is substantially equal to a minimum value, where the second beam spot coefficient is obtained by modifying the approximate minimum value of the first beam spot coefficient and an aberration-independent function that is dependent upon an electrostatic lens magnification and is not dependent upon the spherical aberration coefficient;
• and
• returning to the first process loop using the another resistance distribution as the selected resistance distribution when the second beam spot coefficient is not substantially equal to the minimum value.