V. G. Kohn

On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation

Coherent properties of the x-ray beam delivered at the ESRF allow the observation of very weak perturbations of the wave front, resulting in the phase contrast. A straightforward experimental setup for phase contrast imaging is proposed and used to record holographic images from organic samples of 10-100 pm at energy lo-50 keV with the contrast up to 50%-100%. The theory of phase contrast imaging is considered and some theoretical estimations are made to reveal the performance of the proposed technique in terms of resolution, sensitivity, geometrical requirements, and ehergy range applicability. It is found that for carbon-based fibers a detectable size with 2% contrast is 0.1 ,um for 10 keV and - 1 pm for 100 keV, It is demonstrated that the fine interference structure of the image is very sensitive to the shape, density variation, and internal structure of the sample. Some prospects for the practical use and future development of the new coherent techniques such as phase contrast microscopy, microtomography, holography, and interferometry at high energies are also discussed. 0 I995 American Institute of Physics.

Diffraction theory of imaging with X-ray compound refractive lens

Specific features of X-ray compound refractive lens (XCRL) with parabolic profile of concave surfaces for hard Xray focusing and micro-imaging are analyzed theoretically. Large longitudinal size L of the XCRL requires a verification of the thin lens approximation widely used in the literature. We show that the parabolic XCRL can be treated as a thin lens placed in the middle of the XCRL with the focal length Fl ¼ F þ L=6, where F is the XCRL focal distance in the thin lens approximation. The relatively small aperture of XCRL due to the absorption of X-rays leads to finite resolution and phase effects (or artifacts) of the images. This feature reveals itself as a visibility of transparent objects. It is shown that XCRL allows one to visualize the local phase gradient of the radiation wave field produced by the object. This opens quite a new technique of micro-imaging for purely phase objects which is different from the traditional phase contrast micro-imaging techniques. Optical properties of XCRL as a Fourier transformer are considered as well. 2002 Elsevier Science B.V. All rights reserved.

On the requirements to the instrumentation for the new generation of the synchrotron radiation sources. Beryllium windows

Abstract It was shown that the high spatial and time coherency of the X-ray beam delivered at the ESRF allows one to observe very weak perturbation of the wave front, resulting in the phase contrast and undesirable speckle structure of the beam, that impose special requirements to all elements to be installed in the optical path such as beryllium windowns, filters and mirrors. The contrast from existing beryllium windows at the ESRF beamlines and specially polished Be foils was experimentally studied at an energy range from 10 to 20 keV. It was revealed that the uneven surface of the beryllium windows leads to a beam structure with intensity changes up to 50–100%. The theory of the phase contrast imaging by a transparent object was presented and some theoretical estimations were made to formulate the requirements imposed on the roughness of the Be window surface to avoid the unwanted deterioration of the beam spatial coherence.

Focusing femtosecond X-ray free-electron laser pulses by refractive lenses

The possibility of using a parabolic refractive lens with initial X-ray free-electron laser (XFEL) pulses, i.e. without a monochromator, is analysed. It is assumed that the measurement time is longer than 0.3 fs, which is the time duration of a coherent pulse (spike). In this case one has to calculate the propagation of a monochromatic wave and then perform an integration of the intensity over the radiation spectrum. Here a general algorithm for calculating the propagation of time-dependent radiation in free space and through various objects is presented. Analytical formulae are derived describing the properties of the monochromatic beam focused by a system of one and two lenses. Computer simulations show that the European XFEL pulses can be focused with maximal efficiency, i.e. as for a monochromatic wave. This occurs even for nanofocusing lenses.

Interferometric characterization of spatial coherence of high energy synchrotron X-rays

A simple and direct interferometric technique for characterization of the source size and the transverse coherence length of synchrotron hard X-rays is discussed. A high level of spatial coherence of the X-ray beam allows us to detect the diffraction images (phase contrast patterns) of both the boron fiber of about 100 μm diameter and the slit of different widths. We characterize the level of coherence by comparison of the measured visibility of the interference fringes with the theoretical values by means of simple analytical formulas derived in this work. The analytical theory of both the fiber and the slit diffraction images is discussed in details. The results obtained analytically are confirmed by computer simulations. The proposed technique is well suited for third-generation synchrotron sources and was applied at the European Synchrotron Radiation Facility.

X-ray multilens interferometer based on Si refractive lenses

We report a multilens X-ray interferometer consisting of six parallel arrays of planar compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. Overlapping such coherent beams produces an interference pattern demonstrating substantially strong longitudinal functional dependence. The interference fringe pattern produced by multilens interferometer was described by Talbot imaging formalism. Theoretical analysis of the interference pattern formation was carried out and corresponding computer simulations were performed. The proposed multilens interferometer was experimentally tested at ID06 ESRF beamline in the X-ray energy range from 10 to 30 keV. The experimentally recorded fractional Talbot images are in a good agreement with computer simulations.

Theory of Imaging a Perfect Crystal under the Conditions of X-Ray Spherical Wave Dynamical Diffraction

A theory of the formation of interference patterns due to X-ray spherical wave two-beam dynamical diffraction in a perfect crystal is presented. An asymmetrical Laue case is analyzed in detail, when a polychromatic focus is realized with different distances in front of and behind the crystal. Such a property is essential for high-energy X-rays produced by synchrotron radiation sources of the third generation because of the long distance between source and object. It is shown that a monochromatic X-ray spherical wave is focused due to dynamical diffraction when a definite relation between distances and crystal thickness is held. An X-ray beam of less than 10 μm width may be obtained. A two-dimensional intensity distribution (topograph) may be registered with a wedge-shaped crystal. It shows interference fringes of different kinds depending on crystal thickness and asymmetry rate. It is also discussed how a slit in front of the crystal influences the interference pattern. An example of an interference pattern is presented under the condition of highly asymmetrical diffraction which was obtained by a computer simulation technique. Fringes of a new kind are observed and their physical nature is discussed.

High energy X-ray nanofocusing by silicon planar lenses

Optimizing the lens design and improving the technological process, we manufactured X-ray planar compound refractive lenses with vertical sidewalls up to 70 microns deep. The lens surface roughness in the order of 20 nm was attained. The minimal thickness of the material between two individual lenses of 2 μm was realized. The optical tests of the new planar lenses were performed at the ESRF BM05 and ID15 beamlines. The technological breakthrough allows reaching the nanometer focusing. The resolution below 200 nm was measured in the energy region of 15–80 keV. The best resolution of 150 nm was demonstrated at 50 keV X-rays.

Far-field x-ray phase contrast imaging has no detailed information on the object

We show that x-ray phase contrast images of some objects with a small cross-section diameter d satisfy a condition for a far-field approximation d r1 where r1 = (λz)1/2, λ is the x-ray wavelength, z is the distance from the object to the detector. In this case the size of the image does not match the size of the object contrary to the edge detection technique. Moreover, the structure of the central fringes of the image is universal, i.e. it is independent of the object cross-section structure. Therefore, these images have no detailed information on the object.

On the Theory of X-Ray Diffraction and X-Ray Standing Waves in the Multilayered Crystal Systems

The theory for the Bragg dynamical X-ray diffraction and the yield of the secondary radiation scattered via incoherent channels under conditions of X-ray diffraction (X-ray standing wave technique) is developed for the crystal systems composed from many layers. The formulae are derived in a form suitable for a computer simulation of the experimental angular or energy spectra as well as for a determination of unknown parameters via fitting. The Bragg case (reflection) and the Laue case (transmission) are considered within the same approach. The universal computer program is created and its operation is demonstrated on two examples. It is shown that the model of the multilayered crystal system may be a useful tool for analyzing a lot of problems where the one-dimensional crystal-lattice distortions of different kinds influence the rocking curve and the curve of the secondary radiation yield. In the first example the In 0.5 Ga 0.5 P epitaxial film on the GaAs substrate is considered. The experimental angular spectra of the X-ray reflectivity and the yield of the In L α and P K α fluorescence in the Bragg case are described by fitting the parameters of the structure. In the second example the Laue case of X-ray diffraction in a sample having a monotonously increasing (decreasing) shift of the Bragg angle with increasing depth is analyzed. The phenomenon of the complete switching of the X-ray beam from the incident direction to the direction of reflection is calculated and discussed.