Abstract: To measure the brightness uniformity of an image intensifier, an area source electron gun is needed to emit uniform electrons. In order to design an electron gun, the electron quantity emitted by each point of filament, the electric filed distribution, the electron trail and the uniform electrons vertically striking the fluorescence screen were investigated theoretically and calculated. It is pointed out that the heat uniformity of the area source electron gun in a vacuum system is a prerequisite for equal electron quantity emitted from each point of the filament, and is also the first problem to be solved before designing the shape of the filament. In the vacuum system, the heat radiation is the main factor to affect the temperature of each point of the filament in area source electron gun. A theoretical analysis of the heat radiation uniformity from the filament of an electron gun in vacuum environment is made with reference to some relevant papers. Three filament structures are designed and their heat balances are calculated. In comparison with each other, the spiral filament is the best. This work sets the foundation for the next step of field analysis and electron trail analysis.