Experimental compressive phase space tomography

Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
Optics Express (Impact Factor: 3.49). 04/2012; 20(8):8296-308. DOI: 10.1364/OE.20.008296
Source: PubMed


Phase space tomography estimates correlation functions entirely from snapshots in the evolution of the wave function along a time or space variable. In contrast, traditional interferometric methods require measurement of multiple two-point correlations. However, as in every tomographic formulation, undersampling poses a severe limitation. Here we present the first, to our knowledge, experimental demonstration of compressive reconstruction of the classical optical correlation function, i.e. the mutual intensity function. Our compressive algorithm makes explicit use of the physically justifiable assumption of a low-entropy source (or state.) Since the source was directly accessible in our classical experiment, we were able to compare the compressive estimate of the mutual intensity to an independent ground-truth estimate from the van Cittert-Zernike theorem and verify substantial quantitative improvements in the reconstruction.

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    • "However, tomography becomes challenging when the dimensionality of the correlation matrix becomes large. Recently, it was proposed experimentally in [9] to recover an approximately low-rank correlation matrix, which often holds in physics, by only taking a small number of measurements in the form of (1). • Phase Retrieval: Due to the physical constraints, one can only measure amplitudes of the Fourier coefficients of an optical object. "
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