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 samplingsampling and coherencecoherence•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 dpix 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.

sampleDafor

sampleDaforO

3

23

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-layeredsample made of Ni (~2.7 x 2.5 x 1µm3)

(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, 088303 (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 (~N2)

Controllo dei massimi secondari mediante il controllo dei parametri aWG e dWG:

•dWG random•dWG~aWG

Oversampling condition

2 pixL d Oa It fixes the CCD pixel size

2

2Oa

L

Far-field

condition

2 3 2NWG WGN d a Na Oa

It defines the minumum value for WG to sample distance L1; the number of waveguides (2N) is given by

2 22 11

N dL

Overlapping

condition

EXPERIMENTAL CONDITIONS

Given Oa, ::>> the minimum value for sample to CCD distance L2 is defined

1Oa mSupport:

200WGa d nm

Wavelength: 5nm

4WGOaa

…for example…

L2 ≥ 16 mm

Δθ ≤ 2.5 mrad

Res ≥ 2.7 nm

L1 ≥ 1.35 mm

Wavelength: λ = 1 nm

L1 ≥ 6.76mmL2 ≥ 80 mm

Δθ ≤ 0.5 mradRes ≥ 1.1 nm

dpix = 80μmNpix = 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.