Quantitative aspects of coherent hard X-ray imaging: Talbot images and holographic reconstruction

Free space propagation or Fresnel diffraction is an effective method to sense the phase modulation of hard X-ray beams. We use the variation with propagation distance ri of the diffraction pattern both to study periodic objects and to handle the inverse problem, ire. to extract information on the phase and amplitude of the transmitted wave from the intensity distribution in the defocused images. The 'Talbot effect', a special manifestation of Fresnel diffraction, implies that the intensity distribution of coherent light transmitted through a periodic object is periodic both in the direction of the object periodicity (period a) and in the propagation direction (period 2a(2)/lambda, lambda being the wavelength). We have performed a first investigation of the Talbot effect fits hard X-rays (lambda=0.7 Angstrom) on two phase, gratings. Apart from a lateral shift of a/2, identical intensity distributions are ideally expected in two recording planes a distance a(2)/lambda apart. Actually, a decrease of contrast occurs as a result of the partial coherence of the incident beam, providing a measure of the degree of coherence. Focus variation, as applied in transmission electron microscopy, consists in recording at different cl a series of images which are combined through a suitable algorithm to reconstruct the wave function. The algorithm is briefly presented and is used to reconstruct the phase modulation introduced by a polymer fiber from the experimental data.