A spectrometer has a multi-input aperture for admitting an input wavefront and an array of multiple waveguide structures terminating at the multi-input aperture. The input wavefront is incident on each of the waveguide structures, which provide a dispersive function for the input wavefront. Interferometers are formed by elements of the waveguide structures. The interferometers have different optical path length differences (OPDs). The interferometers provide a wavelength responsive output for spatially extended light sources. The output of the interferometers is detected with a detector array. The spectrometer has an improved etendue, and in some embodiments very high resolution.