An inspection system may be configured to inspect objects, such as semiconductor wafers, using narrow-pulse broadband illumination. The illumination may be obtained in some embodiments using a laser configured to emit light into a material having a spectral broadening effect. The inspection system can include various filters which may be selectively placed in the illumination and/or imaging path in order to tune the spectrum of light impinging on the wafer and the light that is detected. The filters may include selectable filters, fixed filters, and filters whose characteristics can be adjusted in-place. In some embodiments, filters may be used to match the illumination/detection spectra of different tools. Additionally, the broadband illumination may be tuned between inspections and/or during inspections for best results. The system may support Fourier filtering whereby light, related to repetitive features of the object and in one or more wavelength sub-bands of the illumination, may be filtered.