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

The effective distance of a lens can be calculated

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the direct beam gives the same intensity as in the focal spot of a lens. The effective distance of a lens can be calculated according to the formula: D eff = D gain , (3.5) where D is a source–sample distance with a lens. The size of the spot on a sample can be estimated according to the expression (3.4), where d is now the diameter of an individual channel. The contribution of the second term is usually dominant for polycapillary lenses with channel diameters below ca. 10 µ m, so that the size of the focal spot is determined by the divergence of the beam from individual channels. Typical spot sizes obtained in the energy range 8–17 keV are of the order of ca. 20–100 µ m for the working distances F 2 of ca. 10–40 mm. Further reduction of the spot size can be achieved by manufacturing lenses with smaller working distances F 2 [65, 66]. As mentioned above, a polycapillary X-ray lens has a relatively wide pass- band with a maximum at some fixed energy. This optimal energy depends on the lens parameters, first of all, on channel diameters. One can achieve more homogeneous transmission in a wide energy range, combining channels with different diameters within the same lens. Such lenses with a complicated polycapillary structure containing different channel diameters are being man- ufactured now [67]. A spatially resolved X-ray fluorescence analysis can also be done by the use of a capillary optics on the detector side. For this a polycapillary conic collimator (Poly-CCC), proposed in [68], can be applied. In this approach focusing is not necessary for obtaining space resolution and a primary beam irradiates the whole of a sample, while a Poly-CCC is placed between a sample and a detector. Polycapillary “sees” only a small spot on a sample and collects fluorescence signal from it. Spatial resolutions between 150 and 20 µ m were experimentally obtained [68, 69]. On the other hand, the combination of a focusing optics and a Poly-CCC made it possible to realize 3-D micro-XRF with spatial resolution not only laterally on the sample surface, but also into the sample depth [70] (see also section “Micro-XRF”). While polycapillary optics concentrates X-ray radiation by means of mul- tiple reflections and does not possess true focusing properties, certain types of tapered monocapillaries can really focus X-ray radiation by means of single
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X-Ray Optics 99 reflections. Two main types of focusing capillary optics are elliptic and par- abolic monocapillaries [71–73]. An elliptic capillary has two foci and must be aligned relative to a source so that the position of a source coincides with the first focus. The radia- tion captured by the capillary is reflected towards the second focus, which lies on a sample. The angular aperture of elliptic capillaries is determined by the critical angle of the total external reflection as it is typical for op- tics with single reflection. Therefore, total intensity on a sample is usually smaller than that obtained with polycapillary optics due to a smaller solid angle of radiation capture. On the other hand, the size of a spot can also be much smaller due to pure focusing. Asymmetric cutting of an elliptic capil-
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