When a very intense beam is used for illuminating an object in coherent x-ray diffraction imaging, the intensities at the center of the diffraction pattern for the object are cut off by a beam stop that is utilized to block the intense beam. Until now, only iterative phase-retrieval methods have been applied to object reconstruction from a single diffraction pattern with a deficiency of central data due to a beam stop. As an alternative method, I present a noniterative solution in which an interpolation method based on the sampling theorem for the missing data is used for object reconstruction with our previously proposed phase-retrieval method using an aperture-array filter. Computer simulations demonstrate the reconstruction of a complex-amplitude object from a single diffraction pattern with a missing data area, which is generally difficult to treat with the iterative methods because a nonnegativity constraint cannot be used for such an object.
© 2010 Optical Society of America
Original Manuscript: April 28, 2010
Revised Manuscript: June 24, 2010
Manuscript Accepted: June 24, 2010
Published: July 19, 2010
Nobuharu Nakajima, "Noniterative approach to the missing data problem in coherent diffraction imaging by phase retrieval," Appl. Opt. 49, 4100-4107 (2010)