Abstract
As the brightness obtained in the measurement is always the mean brightness averaged over a certain aperture angle and a certain area, it is not equal to the Langmuir's theoretical value except for a special operating condition of the electron gun and in general becomes lower than the theoretical value. The amount of decrease of the measured brightness depends on the sizes of the apertures used in the measurement and the electron optical characteristics of the electron gun. When the bias voltage is much reduced, the electron gun may be considered approximately as the plane, spherical or cylindrical diode system. From this point of view, the expressions for the mean brightness in these diode systems are derived both for thermionic and field emissions. It is also shown that these results will be able to apply to the calculation of the mean brightness of the triode electron gun.
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