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Frontiers in Optics

Compressive Direct Measurement of the Transverse Photonic Wavefunction

Mohammad Mirhosseini, Omar S. Magaña‐Loaiza, Seyed Mohammad Hashemi Rafsanjani, Robert W. Boyd

Published Jan 1, 2014• 1 citation
Publisher

Abstract

We generalize the method of direct measurement and combine it with compressive sensing.Using our method, we measure a 19200-dimensional state using only 20% of the total required measurements.
DOI
10.1364/fio.2014.fm4e.5

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The direct measurement of a complex wave function has been recently realized by using weak values. In this Letter, we introduce a method that exploits sparsity for the compressive measurement of the transverse spatial wave function of photons. The procedure involves weak measurements of random projection operators in the spatial domain followed by postselection in the momentum basis. Using this method, we experimentally measure a 192-dimensional state with a fidelity of 90% using only 25 percent of the total required measurements. Furthermore, we demonstrate the measurement of a 19,200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.
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