## Experimental compressive phase space tomography |

Optics Express, Vol. 20, Issue 8, pp. 8296-8308 (2012)

http://dx.doi.org/10.1364/OE.20.008296

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### Abstract

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.

© 2012 OSA

**OCIS Codes**

(030.0030) Coherence and statistical optics : Coherence and statistical optics

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(100.6950) Image processing : Tomographic image processing

(050.5082) Diffraction and gratings : Phase space in wave options

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: January 13, 2012

Revised Manuscript: February 24, 2012

Manuscript Accepted: March 20, 2012

Published: March 26, 2012

**Virtual Issues**

April 9, 2012 *Spotlight on Optics*

**Citation**

Lei Tian, Justin Lee, Se Baek Oh, and George Barbastathis, "Experimental compressive phase space tomography," Opt. Express **20**, 8296-8308 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8296

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