Broadband light source systems, devices, and methods with a tunable spectrum are described by multiplexing a plurality of light sources, such as LEDs, with thin-film filters or diffraction gratings. A plurality of light sources with different or same wavelengths are multiplexed together to construct a combined broadband light source. A diffraction grating diffracts light beams from the plurality of light sources to a slit-shaped aperture, depending on selected light sources, the relative positions of the light sources to the slit-shaped aperture, and the type of grating to produce a tunable spectrum.