An method for generating illuminating radiation in an illumination apparatus for use in an inspection apparatus for use in lithographic processes is described. A driving radiation beam is provided that comprises a plurality of radiation pulses. The beam is split into first and second pluralities of driving radiation pulses. Each plurality of driving radiation pulses has a controllable characteristic. The first and second pluralities may be used to generate an illuminating radiation beam with an output wavelength spectrum. The first and second controllable characteristics are controlled so as to control first and second portions respectively of the output wavelength spectrum of the illuminating radiation beam.