A radiation receiving system for an inspection apparatus, used to perform measurements on target structures on lithographic substrates as part of a lithographic process, comprises a spectrometer with a number of inputs. The radiation receiving system comprises: a plurality of inputs, each input being arranged to provide radiation from a target structure; a first optical element operable to receive radiation from each of the plurality of inputs; a second optical element operable to receive radiation from the first optical element and to scatter the radiation; and a third optical element operable to direct the scattered radiation onto a detector. The second optical element may for example be a reflective diffraction grating that diffracts incoming radiation into an output radiation spectrum.