We introduce a noniterative image-reconstruction technique for coherent diffractive imaging. Through the application of differential and integral operators, an extended reference can be used to recover the complex-valued transmissivity of an object, in closed form, from a measurement of its far-field (Fraunhofer) diffraction intensity. We demonstrate the feasibility of this approach, using a reference of a pair of crossed wires and slits, through numerical simulations and a soft x-ray coherent diffractive imaging experiment.
© 2010 Optical Society of America
Original Manuscript: December 15, 2009
Revised Manuscript: January 27, 2010
Manuscript Accepted: January 29, 2010
Published: March 19, 2010
Vol. 5, Iss. 8 Virtual Journal for Biomedical Optics
Manuel Guizar-Sicairos, Diling Zhu, James R. Fienup, Benny Wu, Andreas Scherz, and Joachim Stöhr, "Holographic x-ray image reconstruction through the application of differential and integral operators," Opt. Lett. 35, 928-930 (2010)