The duality between the axial irradiance distribution originated by any circularly symmetric diffracting aperture under monochromatic illumination and its diffracted spectral intensity at a fixed on-axis point under broadband illumination is highlighted and experimentally investigated. Two applications are derived from this basic result. On the one hand, we suggest the use of a broadband source and a spectrometer for a single-shot measurement of the axial response of pupil filters. Second, we implement a spectral filter having a transmission spectrum with a fractal structure of frequencies. Experimental results and potential applications in synthetic spectra designs are provided
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