This paper introduces a new, to the best of our knowledge, simple, fast, and affordable spectroscopy technique, in which Fresnel diffraction caused by a phase gradient step is used to determine the spectral profile of light sources by Fourier transformation of the interferogram data. To realize the phase gradient step, a Fresnel biprism or double mirror can be used. In principle, a single interferogram is sufficient to obtain the line profile. To demonstrate the technique, four light-emitting diode (LED) sources have been investigated using a Fresnel biprism with 0.52 degrees apex angle and a Fresnel double mirror with an adjustable angle. The obtained results are confirmed by a commercial spectrometer showing relative uncertainties on the order of 10(-2) for the linewidth. (C) 2019 Optical Society of America
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