A cathode obtaining method includes producing a plurality of cathodes each including an electron emission member and a cover part, provided with a gap, which covers a side surface of the electron emission member, measuring an outer dimension of the upper surface of the electron emission member, for each of a plurality of cathodes, measuring an outer dimension of the gap at the same surface as the upper surface of the electron emission member, for each of a plurality of cathodes, calculating an area ratio by dividing the area of the gap, for each of a plurality of cathodes, obtaining an upper limit of the area ratio corresponding to a desired brightness by using a correlation between brightness and the area ratio, and selecting a cathode having the area ratio less than or equal to the upper limit from a plurality of cathodes that have been produced.