[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

Asymmetric cutting of an elliptic capil lary so that

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much smaller due to pure focusing. Asymmetric cutting of an elliptic capil- lary so that a source–capillary distance is much larger than a capillary–sample distance can additionally reduce the size of a focal spot on a sample, because in this case an elliptic capillary images a source onto a sample with some reduc- tion factor in accordance with optics laws. In this way it is possible to obtain focal spots on a sample smaller than the size of a source. Elliptic capillaries are especially suitable for focusing soft X-ray radiation with energies below ca. 3 keV due to the large value of the critical angle θ cr , which determines the value of the aperture. Polycapillary optics has in the soft X-ray range some limitations connected with the increasing absorption, which becomes especially significant at multiple reflections. Besides, the size of the spot for an X-ray lens is dominated by the large exit divergence (the second term in (3.4)) and can be as large as several hundreds of µ m in the soft energy range. Parabolic capillaries have one focus and are suitable for focusing quasi- parallel beams, especially on synchrotron beam lines. Spots below 1 µ m are reported to have been realized with an intensity gain of several tens. The required working distances F 2 are well below 1 mm. The main advantage of elliptic and parabolic capillaries for focusing radia- tion is the existence of a focus, which lies at some distance from the capillary exit so that reasonable capillary–sample working distances can be realized. Other types of tapered capillaries (e.g., conical capillaries) are less suitable for obtaining microspots because they have no focal point at all, so that ra- diation, confined in a capillary, spreads very quickly after leaving it. Designing Capillary Optics Designing capillary optics involves a number of steps. The choice of the opti- mal type of an optical element is dictated first of all by the concrete applica- tion under consideration: energy range, source size, source–sample distance, desired size of a focal spot on a sample, etc. Large intensity gains are achievable when the capture angle of an optical element is large. As a rule of thumb, in this respect polycapillary optics has potential advantages over monocapillary optics because its angular aperture can considerably exceed the value of the
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100 V. Arkadiev and A. Bjeoumikhov critical angle of the total external reflection, which determines the angular aperture of a monocapillary. The angular aperture of a polycapillary lens can be increased either by increasing its entrance diameter or by reducing its focal distance to a source. The first way meets certain technological problems connected with manufac- turing polycapillary optics with a large diameter. At present the second way of reducing the focal distance is preferred. However, small focal distances put several restrictions on a source size. First of all, each channel of an X-ray lens can capture radiation only from a spot with the dimensions of ca. d + 2 θ cr F 1 on a source. For the efficient use of the total source its size
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