| Summary: | The phase retrieval problem occurs in a number of areas in physics and is the subject of continuing investigation. The one-dimensional case, e.g., the reconstruction of the temporal profile of a charged particle bunch, is particularly challenging and important for particle accelerators. Accurate knowledge of the longitudinal (time) profile of the bunch is important in the context of linear colliders, wakefield accelerators and for the next generation of light sources, including x-ray SASE FELs. Frequently applied methods, e.g., minimal phase retrieval or other iterative algorithms, are reliable if the Blaschke phase contribution is negligible. This, however, is neither known a priori nor can it be assumed to apply to an arbitrary bunch profile. We present a novel approach which gives reproducible, most-probable and stable reconstructions for bunch profiles (both artificial and experimental) that would otherwise remain unresolved by the existing techniques.
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