Compressive Coherence Sensing

The coherence function [1] of a stationary, ergodic electromagnetic field is the complete description of its second-order statistics [2, 3]. In a twodimensional aperture, this function comprises the correlations between all pairs of points, so that the coherence is a four-dimensional function. While coherence is a rich source of sensing data, it is almost always impractical to measure the entire four-dimensional function. Compressive sensing [4, 5, 6] is a means by which one may accurately reconstruct an image sampling only a small fraction of the coherence samples. This is accomplished by imposing a sparsity constraint on the possible reconstructed images. If the data is such that the reconstructed image satisfies the sparsity constraint, the object can be reconstructed with an exceedingly small probability of error given a sufficient amount of data is sampled. This approach may enable new coherence instruments that infer object properties without exhaustive coherence data sampling. In this paper the framework of compressed coherence sensing is presented, and an experimental demonstration of compressed coherence sensing of a simple object through turbulence is presented. 1. COHERENCE SENSING Partial coherence is a seldom exploited property of the electromagnetic field for remote sensing and image formation. Most instruments are imaging instruments and treat the formed image as incoherent and do not attempt to infer coherence properties of the source from the image. However, coherence is a potentially rich source of information that could be used for imaging, for example imaging through turbulence. The coherence function is the complete description of the second-order statistics of the electromagnetic field. In a two-dimensional aperture, the coherence is a four-dimensional function comprising the correlations between every pair of points in the aperture. Unfortunately, the size of the coherence function is often an impediment to its use in image formation, as in general a large portion of this function must be measured to produce an