The invention relates to processes and devices for detecting an analyte in a sample by fluorescence measurement of a fluorophore, wherein the detection medium which contains a fluorophore or a precursor of the fluorophore is admixed with an absorber whose absorbance spectrum superimposes the fluorescence excitation range of the fluorophore. The system consisting of the fluorophore and the absorber, which is produced in the detection medium, has an altered effective fluorescence excitation range with an altered fluorescence excitation maximum. Illumination with fluorescence excitation light can take place within the range of this altered excitation maximum. The measured signal obtained from determining fluorescence emission exhibits only low dependence on the wavelength of the excitation light.