Method has laser scanner for pixel-precise imaging of fluorescent samples having fluorescent dyes. The scanner has sample table, laser and first optical system providing laser beam for exciting the samples, scanner head with deflecting element for scanning sample, first lens, second optical system for forwarding emission beams triggered by the laser beam and deflected by first lens and deflecting element to a detector, position encoder emitting position signals indicating location of the scanner head, electronic element for filtering the detector signals with a time constant and an A/D converter for digitizing the filtered detector signals. The filtered detector signals and the position encoder signals are acquired independently, in parallel and continuously by a computer and are related to a common time base, the A/D conversion being carried out often so that each pixel of an image is always assigned more than one data point.