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Coherent X-ray Diffraction (CXD) X-ray imaging of non periodic objects

Coherent X-ray Diffraction (CXD) X-ray imaging of non periodic objects Campi G ., De Caro L., Giannini C., Guagliardi A., Margonelli A., Pifferi A. INTRODUCTION Why coherent X ray diffraction (CXD )? THE CXD TECHNIQUE Limits on the experimental setup arising from sampling and coherence

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Coherent X-ray Diffraction (CXD) X-ray imaging of non periodic objects

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  1. Coherent X-ray Diffraction (CXD) X-ray imaging of non periodic objects Campi G., De Caro L., Giannini C., Guagliardi A., Margonelli A., Pifferi A.

  2. INTRODUCTION • Why coherent X ray diffraction (CXD)? • THE CXD TECHNIQUE • Limits on the experimental setup arising from sampling and coherence • Phasing of diffuse scattering: image reconstruction • APPLICATIONS • Examples of image reconstruction from CXD • Our plans, new experiments • LIMITATIONSAND PERSPECTIVES • Dose and flux limitations • Femtosecond CXD

  3. INTRODUCTION why coherent X ray diffraction (CXD)? Crystallography… without crystals nano-materials: assembly of inorganic, organic, biological nanostructures …with coherent and intense x-rays flux we can image non periodic objects with larger thickness in comparison with Scanning probe methods and Electron microscopy

  4. THE CXD TECHNIQUE • Coherence: the sample is illuminated by monochromatic coherent x-rays; • Sampling: recording is made of an oversampled diffraction pattern • Beam coherence: the oversampling degree is correlated with spatial and temporal beam coherence; • Image reconstruction: phasing diffuse scattering:

  5. Coherence The main role of the crystal in diffraction is that in the Bragg directions it acts as an extremely powerful amplifier of the coherent scattering signal. Can the beam coherence and intensity produce the same amplification effect (also without a periodic object arrangement) ? Yes in CXD,the collected pattern is the result of an interference process of the beams diffracted from each single object. The typical `speckle‘ pattern contains the spatial information about the single scattering object.

  6. Sampling The Shannon interval for frequency-space sampling of the intensity is This corresponds to surrounding the electron density of the sample with a non-density region; generally, we can define the oversampling ratio as

  7. The Shannon frequency becomes The sample-detector distance (L) is given by where dpixis the pixel size. A physical limit on L comes from the condition to have a constant phase. dpix = 24 µm

  8. Beam coherence The oversampling method is strongly correlated with the coherence of the incident x rays.The higher the oversampling degree, the finer the correspondingly features of the diffraction pattern have to be recorded faithfully, and hence the larger the coherence length of the incident beam needs to be. Spatial (transverse) coherence: Degree to which wave front has a well defined phase where Δθ is the divergence angle of the incident x rays Temporal (longitudinal) coherence: Degree to which waves have a well defined phase where Res is a desired resolution, given by Res=λ/2sinθmax where sinθmax = Npixdpix/2L

  9. Image reconstruction: phasing of diffuse scattering Fienup HiO algorithm (Fienup, 1982, 1987) Modified direct methods (Spence et al., 2003; Carrozzini et al.,2004) • We search for a more general phasing procedure, based on • no use of any support, such as masks based on the autocorrelation function or SEM images. • no prior knowledge of the scattering factor of particles or of their number. The algorithm iterated back and forth between real and reciprocal space with a random phase set as the initial input. In real space, B, a finite support has to be defined to separate the electron density and the no-density regions.

  10. APPLICATIONS State of the art by …3 significant experiments……

  11. The first demonstration experiment Recording diffraction patterns from noncrystalline specimens: Au dots (100nm in diameter, 80nm in thick) on a silicon nitride membrane (a) SEM image of a layered sample (b) Coherent diffraction pattern from (a) (c) Reconstructed image from (b) l = 1.7 nm Npix = 512 dpix = 24 μm L = 250 mm To make a small clean beam: a 20-µm pinhole placed at 25 mm upstream of the sample. Oa ~10 µm Res = 75 nm Miao et al., Nature 400, 342 (1999)

  12. Our reconstruction method: the modified SIR2002 program non-periodic array of gold balls of 50 nm diameter SEM image Soft X-ray transmission diffraction pattern Recovered charge density λ = 2.11 nm Npix = 1025 dpix = 25 μm L = 110 mm Oa ~ 9 μm Res ~ 50 nm B. Carrozzini et al., Acta Cryst. A60, 331, (2004)

  13. Imaging whole Escherichia coli bacteria (undulator beamline at SPring-8) . Beam divergence: 6 ∙10-6 rad by setting a 150-mm pinhole at a distance of 27 m upstream of the experimental instrument CCD-sample distance:743 mm x-rays wavelength: 2Å Res:30 nm To make a small clean beam: a 20-mm pinhole and a corner slit placed at 25.4 and 12.7 mm upstream of the sample. (A) diffraction pattern from E. coli bacteria displayed in a logarithmic scale. The dense regions inside the bacteria are likely the distribution of proteins labeled with KMnO4. The semi transparent regions are devoid of proteins. (B) An image reconstructed from (A) Miao et al., Proc. Natl. Acad. Sci. USA 100, 110 (2003)

  14. OUR PLANS, NEW EXPERIMENTS: …..what can we do with CXD & FEL-SPARX? Limits of the 3 experiments: Oa > 1 µm Pin holes and slits: coherence degree… …not so good

  15. The SPARX source provides a beam already temporarily and spatially coherent at the micrometric scale (support dimension) but… if we move at a nanometric scale? We need coherentx-ray nano-beams!

  16. And so... we propose to use array of 2D Waveguides at SPARX Arrays of 2D waveguide nanostructures have been fabricated by e-beam lithography. • the area coherently illuminated is reduced • the coherence degree is preserved with respect to pinholes or slits Ollinger et al., Physica B 357, 53 (2005)

  17. Angular divergence (~N) • Intensity (~N2) • We can control the interference peaks by aWG,dWG: • dWG~aWG

  18. Experimental conditions Oversampling condition Far-field condition Given Oa,  ::>> the minimum value for sample to CCD distanceL2 is defined Overlapping condition It defines the minumum value for WG to sample distanceL1; the number of waveguides (2N) is given by It fixes the CCD pixel size

  19. …for example… dpix = 80 μm Support: Npix = 1024 N~7 λ = 1 nm Wavelength: Wavelength: L2 ≥ 16 mm L2 ≥ 80 mm L1 ≥ 1.35 mm L1 ≥ 6.76mm Δθ ≤ 2.5 mrad Δθ ≤ 0.5 mrad Res ≥ 1.1 nm Res ≥ 2.7 nm

  20. LIMITATIONS AND PERSPECTIVES Dose and flux limitations: Radiation damage Femtosecond CXD: beyond the radiation-damage limit: S. Solemn et al., Science 218, 229-235 (1982). With picosecond pulse duration X-rays, biological specimens remain morphological unchanged to an accuracy of a few nm. N. Neutze et al., Nature 400, 752-757 (2000). With an X-FEL of pulse leng. < 50 fs and 3 x 1012 photons focused down to a spot of ~ 0.1 m, a 2D diffraction pattern could be recorded from a biomolecule before the radiation damage manifests itself.

  21. Iin summary… • CXDprovides a new imaging methodology by combiningcoherent X-rays with the oversampling method. • CNXDis possible with FEL-SPARX source and arrays of waveguides

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