A radiation detector comprising a plurality of detector elements (1, 2, 3) each having an active region (14, 24, 34) provided for radiation reception and for signal generation, wherein - the detector elements are monolithically integrated into an epitaxially grown semiconductor body of the radiation detector and are arranged one above the over in the semiconductor body in a direction extending vertically to a lateral main direction of extent; - the semiconductor body has a radiation entry side; - a signal generated in a first detector element can be tapped off separately from a signal generated in a second detector element; - the first detector element is partly transmissive to visible radiation; and - visible radiation that passes through the first detector element generates a signal in the second detector element; - a filter layer structure, which is monolithically integrated in the semiconductor body, with at least one filter layer is arranged downstream of at least one detector element (1, 2, 3) in the direction of the radiation entry side of the semiconductor body, wherein a wavelength region of absorption of the filter layer is determined by a band gap of the filter layer; - in each case a contact layer (11, 123) and a counter-contact layer (212, 23), between which the detector element is arranged, is assigned to the detector element, wherein via the contact layer and the counter- contact layer a signal generated in the active region of the detector element can be received and wherein the contact layer or the counter-contact layer are arranged between the detector element and a detector element adjacent thereto, and - the contact layer or the counter-contact layer (11, 123, 212) of at least one detector element (1, 2, 3) is simultaneously configured as the filter layer of the filter layer structure assigned to this detector element. - the detector elements are monolithically integrated into an epitaxially grown semiconductor body of the radiation detector and are arranged one above the over in the semiconductor body in a direction extending vertically to a lateral main direction of extent; - the semiconductor body has a radiation entry side; - a signal generated in a first detector element can be tapped off separately from a signal generated in a second detector element; - the first detector element is partly transmissive to visible radiation; and - visible radiation that passes through the first detector element generates a signal in the second detector element; - a filter layer structure, which is monolithically integrated in the semiconductor body, with at least one filter layer is arranged downstream of at least one detector element (1, 2, 3) in the direction of the radiation entry side of the semiconductor body, wherein a wavelength region of absorption of the filter layer is determined by a band gap of the filter layer; - in each case a contact layer (11, 123) and a counter-contact layer (212, 23), between which the detector element is arranged, is assigned to the detector element, wherein via the contact layer and the counter- contact layer a signal generated in the active region of the detector element can be received and wherein the contact layer or the counter-contact layer are arranged between the detector element and a detector element adjacent thereto, and - the contact layer or the counter-contact layer (11, 123, 212) of at least one detector element (1, 2, 3) is simultaneously configured as the filter layer of the filter layer structure assigned to this detector element.