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 samplingcoherenceLimits 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 LIMITATIONS AND PERSPECTIVES Dose and flux limitations Femtosecond CXD

Why coherent X ray diffraction (CXD)? The rapid growth of nanoscience (“the next industrial revolution”) has produced an urgent need for techniques capable of controlling, in three dimensions, the assembly of inorganic, organic, biologic nanostructures Scanning probe methods: limited to surface structures Electron microscope: provide atomic resolution images of projections of crystalline materials in thicknesses up to about 50nm, or tomography of macromolecular assemblies and inorganics at lower resolution. INTRODUCTION

(a)the sample is illuminated by monochromatic coherent x-rays and a recording is made of a single diffraction pattern (for 2D) or a tilt series (for 3D) (b)phasing diffuse scattering (c)the unknown object is recovered by phasing techniques. THE CXD TECHNIQUE

In a coherent scattering experiment, 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. Why coherence?

Limits on the sample size arising from samplingsampling coherencecoherence

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 oversmpling ratio as Sampling:

where d pix is the pixel size. The Shannon frequency becomes The sample-detector distance (L) is given by

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. The required spatial and temporal coherence of the incident x rays are related to the oversampling degree by where Res is a desired resolution, and Δθ the divergence angle of the incident x rays.

Phasing of diffuse scattering: image reconstruction Successful phase retrivial methods for non-periodic objects: (a)Gerchberg-Saxton-Fienup HiO algorithm (Fienup, 1982, 1987); (b)techniques based on analyticity and complex zeros (Liao et al., 1997); (c) the study of projections onto convex sets (Bautschke et al., 2002); (d)the transport of intensity equations (Paganin & Nugent, 1998); (e) direct methods, for real and positive objects (Spence et al., 2003, Carrozzini et al., 2004)

Breve descrizione del metodo

APPLICATIONS Recovered charge density using the modified SIR2002 program. Experimental soft X-ray transmission diffraction pattern SEM image of a random set of gold balls of 50 nm diameter at 550 eV. B. Carrozzini et al., Acta Cryst. A60, 331, (2004) Reconstruction of non-periodic array of gold balls of 50 nm diameter Parametri sperimentali

(a) SEM image of a double-layered sample made of Ni (~2.7 x 2.5 x 1µm 3 ) (b) Coherent diffraction pattern from (a) ( d) Iso-surface rendering of the reconstructed 3D structure (c) Reconstructed image from (b) Miao et al., Phys. Rev. Lett. 89, (2002) 3-D Imaging of non-crystalline structure at 50-nm resolution

The dense regions inside the bacteria are likely the distribution of proteins labeled with KMnO4. The semitransparent regions are devoid of yellow fluorescent proteins. Miao et al., Proc. Natl. Acad. Sci. USA 100, 110 (2003) Imaging whole Escherichia coli bacteria (A) diffraction pattern from E. coli bacteria displayed in a logarithmic scale. (B) An image reconstructed from (A) Parametri sperimentali

…..what can we do with CXD & FEL-SPARX? At the micrometric scale (support dimension) the SPARX source provides a beam already temporarily and spatially coherent, which can be used for CXD experiments. If we move at a nanometric scale? Our plans, new experiments

At a nanometric scale: we propose to use array of 2D Waveguides to reduce the area coherently illuminated preserving the coherence degree. C. Ollinger et al. Physica B 357 (2005) 53–56  Collimazione angolare (~N)  Intensity (~N 2 )  Controllo dei massimi secondari mediante il controllo dei parametri a WG e d WG : d WG random d WG ~a WG

Oversampling condition It fixes the CCD pixel size Far-field condition It defines the minumum value for WG to sample distance L1; the number of waveguides (2N) is given by Overlapping condition EXPERIMENTAL CONDITIONS Given Oa, ::>> the minimum value for sample to CCD distance L2 is defined

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

LIMITATIONS AND PERSPECTIVES Dose and flux limitations: fluence (total photons per unit area) and dose (absorbed energy per unit mass) required to make a 3D CXD image at given resolution

Femtosecond CXD: beyond the radiation-damage limit: A way of overcoming the radiation damage limit in x ray imaging is to use pulses of x-rays that are shorter in duration than the damage process itself.