The X-
ray irradiation apparatus (100) includes an X-
ray source device (110) for generating X-rays (2) having a polychromatic spectrum, and an X-
ray optical device (120) having a longitudinal beam axis (3), the X-ray optical device (120) including a polycrystalline reflector device (121) having a reflector geometry, a reflector mosaicity, and a reflector thickness, the reflector device (121) being configured to receive a portion of the X-rays (2) within an acceptance angle of the reflector device (121) and to direct the X-rays (2) along the beam axis (3) to a
focal position thereof. The X-
ray irradiation device (100) is arranged to generate a beam (4) by Bragg reflection, the beam having a spectral distribution determined by the polychromatic spectrum of the X-rays (2), the reflector geometry, the reflector mosaicity and the reflector thickness, the X-
ray irradiation device (100) comprising a reflector device (121) arranged downstream from the reflector device (121) for forming a filter gap (123) which transmits a first spectral portion (4A) of the spectral distribution of the X-ray beam (4) and blocks a second spectral portion (4B) and a third spectral portion (4C) of said spectral distribution. The reflector device (121) further comprises a spectral filter aperture device (122), the first spectral portion (4A) having a higher energy than the second spectral portion (4B) and a lower energy than the third spectral portion (4C), the reflector device (121) having an acceptance
solid angle of at least 100 microsteradians, and the reflector geometry, reflector mosaicity, reflector thickness, and acceptance angle of the reflector device (121) are such that the
radiation flux of the first spectral portion (4A) is reflected by a reflector having a peak reflectance of at least 1%. The first spectral portion (4A) has a spectral bandwidth of at most 15%, the second and third spectral portions (4B, 4C) have a flux that is reduced by at least three orders of magnitude compared to the flux of the first spectral portion (4A), and the X-ray beam (4) has a
focal spot size of less than 1.5 mm in the
transverse dimension relative to the longitudinal beam axis. Further, methods of using the X-ray
fluorescence imaging apparatus (200) and the X-
ray irradiation apparatus (100) are described.