1 Time resolved x-ray microscopy D. Pelliccia 1,2 , A. Cedola 1 , I. Bukreeva 1 , F. Scarinci 1 and S. Lagomarsino 1 1) Istituto Fotonica e Nanotecnologie - CNR - Roma 2) Dip. Fisica Univ. "La Sapienza" and INFN - Sezione Roma1 SCIENTIFIC MOTIVATION In the frame of R&D activity on future SPARX X-FEL source, the development of x-ray optics to successfully manipulate FEL radiation cannot be neglected. The unique characteristics of pulsed radiation produced by FEL have to be preserved both in beam transport and in conditioning optics for experimental purposes. This work gets into the larger field of x-ray optics development and testing in which the X-ray physics group of the Institute of Photonics and Nanotechnologies (IFN) headed by S. Lagomarsino, is involved for many years. The main new issue in working with FEL radiation (produced in a seeded scheme) with respect to ordinary synchrotron radiation is coherence and pulse duration in the femtosecond scale. Thus the first requirement for optics is the preservation of time structure of pulses and temporal (i.e. longitudinal) coherence of radiation. In other words, dispersion properties of different optics used should be understood in detail. Another important characteristic of FEL radiation is the high degree of spatial coherence which allows, in principle, coherent microimaging and diffraction, but which in turn requires optical elements which preserve the coherence properties. In view of time resolved x-ray microscopy with nanometer spatial resolution and femtosecond time resolution, an interesting optical element is the x-ray waveguide (WG) [1,2]. In fact, it has been demonstrated that WG is a suitable optics for x-ray microscopy because it can produce beams of nanometer size, fully coherent in transverse direction [3, 4]. Guiding optics, such as WGs and optical fibers are widely used for many types of radiation from microwave to visible optics and, in the last ten years, in hard x-ray range, too. The dispersion features of WGs and fibers were extensively studied in the past to fabricate suitable devices for optical communication. The utilization of WGs could be extended from XUV to hard x-ray spectral regions, however paying attention to their dispersion properties that, in principle, could affect dramatically the propagation of short pulses. A WG is an optical resonator in which incoming radiation can propagate only as discrete set of modes. The condition on refraction index n guid of guiding layer with respect of refraction index n cl of cladding layers for resonance to take place is