or after spectral filtering the static fluorescent light of an excited location on the specimen 7 when the fluorescent light has continued to radiate for a determined period of time without being excited simultaneously and the excitation beam has moved beyond the excited location of the specimen 7 by distance x1 within a time t1 due to the constant scanning speed shown in fig2 a the fluorescent light which still radiates from the excited location on the specimen 7 and which is imaged in the detector plane in a known manner by the scanning system no longer strikes the confocal detector 8 but rather strikes a detector 10 which is displaced by distance x1 39 relative to the confocal detector b the distance x1 39 required for the measurement process is given by the measured delayed scanning of the fluorescence decay time and the scanning speed when the excitation beam 2 has moved beyond the excited location of the specimen 7 by distance x2 during time t2 the fluorescent light which is still emitted from the excited location of the specimen 7 at time t2 strikes a detector 11 which is arranged at a distance x2 39 from the confocal detector 8 in this case the fluorescent light must pass through the scanning system in the opposite direction to that of the excitation beam as a result of the arrangement according to the invention there is a transformation or conversion from the temporal region to the spatial region the scanning time ti is given by the distance xi of the i th detector from the confocal detector.