The existing methods for measuring the orbital-angular-momentum (OAM)spectrum suffer from issues such as poor efficiency, strict interferometricstability requirements, and too much loss. Furthermore, most techniquesinevitably discard part of the field and measure only a post-selected portionof the true spectrum. Here, we propose and demonstrate an interferometrictechnique for measuring the true OAM spectrum of optical fields in asingle-shot manner. Our technique directly encodes the OAM-spectrum informationin the azimuthal intensity profile of the output interferogram. In the absenceof noise, the spectrum can be fully decoded using a single acquisition of theoutput interferogram, and, in the presence of noise, acquisition of twosuitable interferograms is sufficient for the purpose. As an importantapplication of our technique, we demonstrate measurements of the angularSchmidt spectrum of the entangled photons produced by parametricdown-conversion and report a broad spectrum with the angular Schmidt number82.1.
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