Positron-sensitive detection was used to measure the spatial decay in intensity of twelve transitions in Fe XIII to Fe XVI. A two-meter grazing incidence spectrometer was equipped with a 25 mm microchannel plate coupled to a resistive anode encoder and was positioned to simultaneously record all EUV radiation in the wavelength range from 24.5 to 31 nm. Data for foil-excited Fe ions at 35 MeV was accumulated at each of 37 foil positions until a fixed amount of beam charge had been collected in a Faraday cup. The considerable advantages of this improved beam-foil time-of-flight technique are discussed.