Friday, March 30, 2012

Experimental compressive phase space tomography

Lei Tian just sent me the following:

Dear Igor,

I'm Lei, a graduate student working in Dr. Barbastathis' lab ( at MIT.  Your blog is becoming my must-read everyday since I started working on projects related to compressive imaging. I appreciate a lot of your efforts to manage such a good platform for this vibrant community.
We have just published a work in optics express titled "Experimental compressive phase space tomography" (, which I thought might interest you.
In this work, we showed that using the tomographic formalism (i.e. phase space tomography) commonly used in statistical optics community, a partially spatially coherent source can be reconstructed from a heavily under-sampled measurement. The reconstruction method was based on the matrix completion theory. This method can be used given the fact that the partially coherent source can be represented with high accuracy using a small number of independent coherence modes (analogous to the Karhunen-Loève theorem). This enables to formulate the recovery problem to a low-rank matrix recovery problem.

Thanks Lei !

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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