Lighting system for the spatially evenly distributed emission of light from light sources (12a-12c) which emit light in different spectral ranges, comprising a) light sources of a first type, which emit light in a first spectral range b) light sources of a second type, which emit light in a second spectral range c) light sources of a third type, which emit light in a third spectral range d) a carrier layer, on which the light sources (12a-12c) are arranged in groups which are regularly spaced apart from each other, wherein each group comprises three light sources (12a-12c) and in each group each light source (12a-12c) belongs to a different one of the three types than the other light sources (12a-12c) in the group, e) a luminescent-material layer arranged in the beam direction of the light sources (12a-12c), comprising i. a first luminescent material in a first luminescent-material film, which is caused to luminesce by the light sources of the first type, ii. a second luminescent material in a second luminescent-material film arranged on the first luminescent-material film in the beam direction of the light sources (12a-12c), which is caused to luminesce by the light sources of the second type, iii. a third luminescent material in a third luminescent-material film arranged on the second luminescent-material film in the beam direction of the light sources (12a-12c), which is caused to luminesce by the light sources of the third type. a) light sources of a first type, which emit light in a first spectral range b) light sources of a second type, which emit light in a second spectral range c) light sources of a third type, which emit light in a third spectral range d) a carrier layer, on which the light sources (12a-12c) are arranged in groups which are regularly spaced apart from each other, wherein each group comprises three light sources (12a-12c) and in each group each light source (12a-12c) belongs to a different one of the three types than the other light sources (12a-12c) in the group, e) a luminescent-material layer arranged in the beam direction of the light sources (12a-12c), comprising i. a first luminescent material in a first luminescent-material film, which is caused to luminesce by the light sources of the first type, ii. a second luminescent material in a second luminescent-material film arranged on the first luminescent-material film in the beam direction of the light sources (12a-12c), which is caused to luminesce by the light sources of the second type, iii. a third luminescent material in a third luminescent-material film arranged on the second luminescent-material film in the beam direction of the light sources (12a-12c), which is caused to luminesce by the light sources of the third type. i. a first luminescent material in a first luminescent-material film, which is caused to luminesce by the light sources of the first type, ii. a second luminescent material in a second luminescent-material film arranged on the first luminescent-material film in the beam direction of the light sources (12a-12c), which is caused to luminesce by the light sources of the second type, iii. a third luminescent material in a third luminescent-material film arranged on the second luminescent-material film in the beam direction of the light sources (12a-12c), which is caused to luminesce by the light sources of the third type.