Noise-robust coherent diffractive imaging with a single diffraction pattern

The resolution of single-shot coherent diffractive imaging at X-ray free-electron laser facilities is limited by the low signal-to-noise level of diffraction data at high scattering angles. The iterative reconstruction methods, which phase a continuous diffraction pattern to produce an image, must be able to extract information from these weak signals to obtain the best quality images. Here we show how to modify iterative reconstruction methods to improve tolerance to noise. The method is demonstrated with the hybrid input-output method on both simulated data and single-shot diffraction patterns taken at the Linac Coherent Light Source.

[1]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[2]  J. Miao,et al.  Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Veit Elser.  Phase retrieval by iterated projections. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  V. Elser.  Random projections and the optimization of an algorithm for phase retrieval , 2002, math/0207172.

[5]  I. Robinson,et al.  Three-dimensional imaging of microstructure in Au nanocrystals. , 2003, Physical review letters.

[6]  J. Rodenburg,et al.  Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. , 2004, Physical review letters.

[7]  J. Kirz,et al.  Biological imaging by soft x-ray diffraction microscopy , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[8]  W. H. Benner,et al.  Femtosecond diffractive imaging with a soft-X-ray free-electron laser , 2006, physics/0610044.

[9]  S. Marchesini,et al.  High-resolution ab initio three-dimensional x-ray diffraction microscopy. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[10]  S. Marchesini,et al.  Invited article: a [corrected] unified evaluation of iterative projection algorithms for phase retrieval. , 2006, The Review of scientific instruments.

[11]  Ian Robinson,et al.  Effectiveness of iterative algorithms in recovering phase in the presence of noise. , 2007, Acta crystallographica. Section A, Foundations of crystallography.

[12]  Curved beam coherent diffractive imaging , 2007 .

[13]  S Marchesini,et al.  Invited article: a [corrected] unified evaluation of iterative projection algorithms for phase retrieval. , 2006, The Review of scientific instruments.

[14]  Jian-Min Zuo,et al.  Coordination-dependent surface atomic contraction in nanocrystals revealed by coherent diffraction. , 2008, Nature materials.

[15]  O. Bunk,et al.  High-Resolution Scanning X-ray Diffraction Microscopy , 2008, Science.

[16]  D. R. Luke.  Relaxed averaged alternating reflections for diffraction imaging , 2004, math/0405208.

[17]  Keith A. Nugent,et al.  Coherent diffractive imaging: a new statistically regularized amplitude constraint , 2010 .

[18]  Veit Elser,et al.  Recovering magnetization distributions from their noisy diffraction data. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  A. H. Walenta,et al.  Large-format, high-speed, X-ray pnCCDs combined with electron and ion imaging spectrometers in a multipurpose chamber for experiments at 4th generation light sources , 2010 .

[20]  Georg Weidenspointner,et al.  Single particle imaging with soft x-rays at the Linac Coherent Light Source , 2011, Optics + Optoelectronics.

[21]  Garth J. Williams,et al.  Single mimivirus particles intercepted and imaged with an X-ray laser , 2011, Nature.

[22]  W. H. Benner,et al.  Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight , 2012, Nature.