  We presents the results of study of focusing and imaging properties of
double-lens system for hard x-ray radiation consisting of two Fresnel zone
plates (ZP) made from silicon. We demonstrate for the first time the phenomenon
of focusing by two crystal ZP located at significant distance from each other.
We investigate by both theoretically and experimentally the peculiarities of
intensity distribution at the focal plane during a scan by second ZP normally
to the optical axis of the system. We investigate as well the intensity
distribution along the optical axis for our double-lens system from crystal ZP.
We realize experimentally a registration of the focused image of the object by
means of double-lens system based on ZP. Measurements are performed on the beam
line BM-5 of the European Synchrotron Radiation Facility (ESRF) at the x-ray
energy 9.4 keV. We elaborate a computer program for theoretical simulation of
the optical properties of x-ray double-lens system based on ZPs. A calculation
is made by convolution of transmission function and Kirchhoff propagator in
paraxial approximation by means of Fast Fourier Transformation.
