A field emission cathode electron gun with two stages of acceleration has been built in order to measure the electron beam brightness that can be produced in practice from a tungsten field emission cathode. The gun is similar to that reported by A. Crewe except that the accelerating electrodes are plane, rather than shaped, apertures, and the cathode is located by a gimbal mechanism which allows the cathode to be tilted over an arc of 70° in any direction and positioned laterally. The gun electrodes have been precisely machined with the apertures round within 0.25 micron and aligned with respect to each other to better than 10 micron. The second accelerating electrode is followed by scan plates, a test grid, and an electron detector which together allow the probe size to be measured in the usual scanning electron microscope mode.