Phase retrieval from coherent soft X-ray optics

We have recently probed the coherence of soft X-ray flux from a third generation synchrotron source [D. Paterson, B.E. Allman, PT McMahon, J. Lin, N. Moldovan, K.A. Nugent, I. McNulty, C.T. Chantler, C.C. Retsch, T.H.K. Irving, D.C. Mancini, Opt. Commun. 195 (2001) 79; C.Q. Tran, A.G. Peele, D. Paterson, A. Roberts, I. McNulty, K.A. Nugent, Opt. Lett. 30 (2005) 204.]. The 1-2keV radiation exhibits transverse coherence lengths of 60 mu m, which means that coherent optical effects may be observed in reasonably sized objects. We present experimental results demonstrating the creation of a phase singularity in a synchrotron beam by passing the beam through a phase mask at similarly low X-ray energies. This complements our earlier work at higher energies and demonstrates that we can now produce phase singularities across a range of energies where we have tested certain intensity-based phase recovery methods. These methods fail when the field contains phase singularities. We describe the X-ray optical vortex and outline its use as a pathological test object for phase retrieval methods. We also present recent progress towards overcoming the problem of phase retrieval in singular optics. (c) 2005 Elsevier B.V. All rights reserved.