Until the ESRF went into operation, it seemed preposterous to envisage imaging phase objects with X-rays except with the very demanding technique of X-ray interferometry. Phase objects affect the phase (r) of the amplitude transmitted through a sample, with E = E_oe^i(r) right after the specimen if it is E_o just before, leaving the intensity I = |E|² unchanged. Several groups discovered that, thanks to the spatial coherence of the beams from third-generation synchrotron radiation sources, phase objects do produce intensity contrast, provided the beam is allowed to propagate over a distance after the sample. Fresnel diffraction, i.e. interference between non-affected and diffracted components of the beam, then produces fringes at phase jumps (discontinuities in the optical path-length) or an in-line hologram depending on the specimen-detector distance D. Because the phase jumps could, in a first approximation, be handled by the usual algorithm for absorption tomography, qualitative tomography could be performed using phase images recorded at small D for many orientations of the specimen with respect to the beam. This is useful to detect density discontinuities, such as reinforcing particles in a metal-matrix composite [1]. However, the spatial resolution is then limited by the Fresnel fringe distribution and artefacts occur due to the ill-suited algorithm.

Holotomography is a new approach which has been implemented to extract the quantitative distribution of the phase (and attenuation) in two-dimensional projection images, and then to turn it into 3-D reconstructions [2]. It is based on images obtained at several values of D for each angular position of the sample, in analogy with a technique developed for electron microscopy. In holotomography, the resolution is much improved because the Fresnel fringes are unravelled, and limited by the detector to about 1 µm. Reconstructed slices essentially show the mass density because, when dispersion can be neglected, the refractive index decrement is proportional to the electron or mass density. The need for many images means long acquisition times. Because high monochromaticity is not needed in this approach, it is feasible to use multilayers instead of perfect-crystal monochromators. The total acquisition time is then reduced below 1 hour on the wiggler beamline ID19.

This technique was used to study the connectivity of an aluminium-silicon alloy in the semi-solid state: the sample was partially remelted at 585°C during 5 minutes and then rapidly quenched in water. Figure 121a is a tomographic slice recorded at D = 7 mm, sensitive only to variations in absorption. It is impossible to distinguish the two phases. Some bright spots appear corresponding to iron-rich inclusions. Figure 121b is a tomographic slice obtained for a single distance D = 0.6 m, revealing density jumps as dark/light fringes. Binarisation of such an image is extremely tedious. Figure 121c is a reconstructed map of the refractive index decrement, clearly showing the slightly different densities of two (metallurgical) phases ( ~ 0.05 g/cm³). The grey phase was the liquid in the semi-solid state and is aluminium-silicon eutectic. The dark phase was the solid in the semi-solid phase and it is essentially pure aluminium with substitutional silicon. The data set consisted of 4 times 800 images recorded at distances of 7, 200, 600 and 900 mm from the sample, using the FRELON camera. The beam was monochromatised to 18 keV by a Ru/B₄C multilayer.

This research demonstrates the holotomographic approach, which makes it possible to fully exploit the sensitivity of phase contrast imaging. It also shows that ID19 is now operational for holotomographic studies.

References
[1] J-Y. Buffière, E. Maire, P. Cloetens, G. Lormand, R. Fougères, Acta Mater., 47, 1613-1625 (1999).
[2] P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.P. Guigay, M. Schlenker, Appl. Phys. Lett., 75, 2912-2914 (1999).

Authors
P. Cloetens (a), J.P. Guigay (a,b), W. Ludwig (a), L. Salvo (c), M. Schlenker (b), M. Suéry (c), S. Verrier (c).

(a) ESRF
(b) Lab. Louis Néel, CNRS, Grenoble (France)
(c) GPM2, ENSPG, Grenoble (France)