Daniel L. Marks (Duke University), Ashwin Wagadarikar (Duke University), David J. Brady (Duke University)
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Abstract:
The cross spectral density function provides a general model for optical field measurements. Wavefront characterization strategies, including phase diversity, Shack-Hartman sensors and wavefront coding, may be analyzed as projections of the cross spectral density. We have previously demonstrated exhaustive measurement of the cross spectral density using an “astigmatic coherence sensor” (ACS). We also demonstrated the use of an ACS to image through phase distortion. While conventional imaging methods exploit the aberrations of a distorted point spread function, a coherence measurement system applies coherence mode decomposition to distinguish and separate the fields of disparate incoherently emitting radiators. This decomposition is a powerful tool that can infer both the power of each source and the wavefront produced by each source.
The cross spectral density is four-dimensional and is greatly undersampled by most optical sensors. A new technique, compressive sensing, enables the inference of a sparse object even if the data is greatly undersampled. Sparsity, which requires the reconstruction to have only a few nonzero components in a specified basis, greatly constrains the number of possible objects and requires orders of magnitude fewer measurements to obtain an accurate reconstruction. By designing an instrument that samples a well-chosen small subset of projections of the partially coherent field, a sparse coherence function can be estimated with sufficient accuracy to enable coherence-mode analysis methods to be used. We introduce the idea of a sparse cross spectral density and present a new formalism to analyze the behavior and performance of compressive coherence sensors. This includes defining projections of the coherence function, how to enforce sparsity on coherence functions, what conditions are required of the measurements to enable sparse reconstruction of the coherence function, and the quality of the coherence mode decomposition that can be obtained from sparsely sampled projections. Simulations of this approach demonstrate the advantages and disadvantages when sensing phase distorted objects such as encountered when imaging through turbulence. A coherence sensing approach yields improvements over other well-established techniques such as inferring wavefronts using transport-of-intensity methods and blind deconvolution, and may offer a means of improving these established techniques.
Date of Conference: September 1-4. 2009
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