In the hard x-ray range, optics based only on refraction, as in the case of visible optics, require extremely small (a few microns) bending radii of the crystal monochromators, since the deviation of the refraction index (δ = 1-n) from unity is of the order of 10<sup>-6</sup>. Based on the principle of a series of N refractive lenses, compound refractive lenses provide an appreciable focus at a reasonable distance, but the photon flux is limited by absorption because of the generally high value of N required. As the effect of refraction is very weak, x-rays deviate considerably when diffraction occurs in a crystal in Bragg geometry: this is the base of many crystal optics devices. Focusing with crystal optics is generally achieved bending the crystals to modify the orientation of the lattices planes or modulating the entrance surface of a flat or curved crystal, the so-called Bragg-Fresnel lens. Sagittal focusing can be also obtained using asymmetrically cut crystals. From a general point of view the focusing by means of bent crystals in Laue geometry is interesting when high energies are used, because the absorption due to the transmission in the crystals is very limited. The use of bent crystals has two big advantages: it allows to accept a great divergence of the incoming radiation, thus increasing the flux of the focused radiation and allowing at the same time to select its frequencies, owing to the Darwin width of the considered reflection. Indeed, the crystal bending enables the diffracting planes to be crossed at the Bragg angle corresponding to each ray of the incident beam and, at the same time, the diffraction process produces a monochromatic beam. Actually, a small Bragg angle implies a rather long beam path in the crystal in the case of Bragg geometry, whereas in Laue geometry the incidence is almost normal: the absorption is therefore minimized upon using a suitably thin crystal. We suggest here a method allowing to improve the quality of high energy polychromatic focusing by bent crystals in Laue geometry.
One of the factors influencing the focus size in diffractive-refractive optics is the quality of diffracting surface. If the surface is uneven, then the diffraction at each point of the surface is a combination of an asymmetric and inclined diffraction (general asymmetric diffraction). This somewhat deviates and spreads the diffracted beam. The integration over the surface hit by an incident beam gives the angular spread of the diffracted beam. It is shown that in some cases (highly asymmetric, highly inclined cut) the etched surface may create the spread of the diffracted beam, such that it causes a significant broadening of the focus. In this case a mechanical-chemical polishing is necessary.
The high resolution, high asymmetric diffractive-refractive x-ray lens was tested at BM5 beamline in ESRF. The lens consists of two Si (111) channel-cut crystals in dispersive arrangement with the angle of asymmetry of 12.7°. The channels have a circular profile with the diameter of 22 mm. The test was performed for the energy of 7.8 - 8.1 keV and the focusing distance of 19 - 20 m. At the place of the focus the beam was squeezed horizontally from 8.8 mm (unfocused beam) to 0.4 mm, i.e. more than 20 times. To get a good reflectivity in such a highly asymmetric diffraction, the cylindrical surface had to be mechanically-chemically polished.
The sagittal focusing of x-ray beam diffracted on symmetrically cut crystals with a longitudinal parabolic groove on their diffraction surfaces has been proved experimentally and the results have been already published. This kind of focusing is based on the refraction phenomena occurring during Bragg x-ray diffraction. In this paper our new developments in this field are reported. First, it was shown experimentally that in some cases a channel-cut crystal monochromator with longitudinal parabolic grooves can be replaced by a single crystal with a round hole drilled parallel to diffracting planes. This substantially simplifies the manufacturing of such a focusing monochromator. Second, it has been experimentally proved that the refraction effect, on which the focusing is based, may be substantially enhanced by cutting the longitudinal parabolic groove into the surface of an asymmetrically cut crystal (or drilling a hole whose axis is tilted with respect to the diffracting planes). A very simple formula describing the focusing properties for this case is derived. Finally, the results of the first experiment on the meridional focusing of x-ray beam diffracted on a crystal with a transversal groove on its surface are reported. Some experimental results are compared with the results of ray- tracing simulations, which were developed for this purpose.
Proc. SPIE. 4356, 12th Czech-Slovak-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics
KEYWORDS: Digital signal processing, Digital photography, Visualization, Photography, Computing systems, Image registration, Signal processing, Image transmission, Transmittance, Mechanical engineering
The realized equipment for measurement of the granularity of black-and-white and color photographic materials is based on low-speed rotation of the optically transmitting granularity sample and microphotometrical scanning of its image. The obtained electrical analogous signal is amplified and converted to the digital form by an analog-to-digital converter and the processed by a special computer system. It is a modern digital-microphotometrical rotational granulometer with originally designed mechanical sample stage and electronical processing system which is useful for the laboratory practice. Its outputs consist of random optical transmittance data of the granularity sample under measurement their mean value and dispersion.
Conference Committee Involvement (1)
Crystals, Multilayers, and Other Synchrotron Optics
5 August 2003 | San Diego, California, United States