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Multiscale Phase Retrieval

While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize the field. The need for a reference severely restricts the utility of holography. Phase retrieval, in contrast, is theoretically consistent with sensors that directly measure coherent or partially coherent fields with no prior assumptions. Unfortunately, phase retrieval has not yet been successfully implemented for large-scale fields. Here we show that both holography and phase retrieval are capable of quantum-limited coherent signal estimation and we describe phase retrieval strategies that approach the quantum limit for >1 megapixel fields. These strategies rely on group testing using networks of interferometers, such as might be constructed using emerging integrated photonic, plasmonic and/or metamaterial devices. Phase-sensitive sensor planes using such devices could eliminate the need both for lenses and reference signals, creating a path to large aperture diffraction limited laser imaging.

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