Compressive sensing—the foundations of which are associated with names such as Candès, Romberg, Tao and Donoho—is sweeping through many areas at the forefront of optics research. The basic idea is that with an appropriate choice of error metric one can perform reconstructions using less data than would “traditionally” be required under the Nyquist-sampling criterion. The key assumption needed is that one must know a priori that the system of equations to be solved (assumed linear) is sparse in the sense that most of the required unknowns are zero.

The paper upon which we shine today’s Spotlight applies the ideas of compressive sensing to experimentally reconstruct two-point correlation functions of partially coherent light using phase-space tomography. In this context, compressive sensing’s assumption of sparseness amounts to the assumption of a low-entropy optical source. In the language of partial coherence theory, this is equivalent to the partially coherent source being well described by a small number of coherent modes, in Wolf’s coherent-mode expansion. As the authors point out, this is a good assumption for a variety of optical sources, including optical lasers, light-emitting diodes (LEDs), X-ray synchrotrons and certain forms of visible-light microscopy.

The authors’ experimental proof of concept using LEDs, which is prefaced by a convincing set of computer simulations, therefore has applicability to a wide variety of areas of optical physics. Applications to quantum optics are also anticipated by the authors. Note too that the close relationship between the two-point coherence functions of classical-optics theory for partially coherent fields, and the two-point density matrices of quantum-mechanical mixed-state wavefunctions, implies that the present work has important ramifications beyond optical physics.

One more thing: If you don’t know about the key features of compressive sensing, consider absorbing them from this paper, as they may be applicable to your areas of research interest!

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