Section 4.2.5.2. Mirrors and capillaries

In the laboratory, mirrors are used in conjunction with conventional sealed tubes and rotating-anode sources, the emission from which consists of Bremsstrahlung upon which is superimposed the characteristic spectrum of the anode material (Subsection 2.3.5.2 ). The shape of the Bremsstrahlung spectrum can be significantly modified by mirrors, and the intensity emitted at harmonics of the characteristic wavelength can be significantly reduced. More importantly, the mirrors can be fashioned into shapes that enable the emitted radiation to be brought to a focus. Ellipsoidal, logarithmic spiral, and toroidal mirrors have been manufactured commercially for use with laboratory X-ray sources. Since the X-rays are emitted isotropically from the anode surface, it is important to devise a mirror system that has a maximum angle of acceptance and a relatively long focal length.

At synchrotron-radiation sources, the high intensities that are generated over a very broad spectral range give rise to significant heat loading of subsequent monochromators and therefore degrade the performance of these elements. In many systems, mirrors are used as the first optical element in the monochromator, to reduce the heat load on the primary monochromator and to make it easier for the subsequent monochromators to reject harmonics of the chosen radiation. Shaped mirror geometries are often used to focus the beam in the horizontal plane (Subsection 2.2.7.3 ). A schematic diagram of the optical elements of a typical synchrotron-radiation beamline is shown in Fig. 4.2.5.2 . In this, the primary mirror acts as a thermal shunt for the subsequent monochromator, minimizes the high-energy component that may give rise to possible harmonic content in the final beam, and acts as a vertical collimator. The radii of curvature of mirrors can be changed using a mechanical four-point bending system (Oshima, Harada & Sakabe, 1986). More recent advances in mirror technology enable the shape of the mirror to be changed through use of the piezoelectric effect (Sussini & Labergerie, 1995).

Figure 4.2.5.2| top | pdf | The use of mirrors in a typical synchrotron-radiation beamline. The X-rays are emitted tangentially to the orbit of the stored positron beam. They pass through a beam-defining slit onto a mirror that serves three purposes, viz energy discrimination, heat absorption, and focusing, by means of a mechanical four-point bending system. The beam then passes into a double-crystal monochromator, which selects the desired photon energy. The second element of this monochromator is capable of being bent sagittally using a mechanical four-point bending system to focus the beam in the horizontal plane. The beam is then refocused and redirected by a second mirror.

Capillaries, and bundles of capillaries, are finding increasing use in situations where a focused beam is required. The radiation is guided along the capillary by total external reflection, and the shape of the capillary determines the overall flux gain and the uniformity of the focused spot. Gains in flux of 100 and better have been reported. There is, however, a degradation in the angular divergence of the outgoing beam. For single capillaries, applications are laboratory-based protein crystallography, microtomography, X-ray microscopy, and micro-X-ray fluorescence spectroscopy. The design and construction of capillaries for use in the laboratory and at synchrotron-radiation sources has been discussed by Bilderback, Thiel, Pahl & Brister (1994), Balaic & Nugent (1995), Balaic, Nugent, Barnea, Garrett & Wilkins (1995), Balaic et al. (1996), and Engström, Rindby & Vincze (1996). They are usually used after other monochromators in these applications and their role as a low-pass energy filter is not of much significance.

Bundles of capillaries are currently being produced commercially to produce focused beams (ellipsoidally shaped bundles) and half-ellipsoidal bundles are used to form beams of large cross section from conventional laboratory sources (Peele et al., 1996; Kumakhov & Komarov, 1990).

For one interface, the reflectivity (R) and the transmissivity (T) of the surface are determined by the Fresnel equations, viz: and where and are the angles between the incident ray and the surface plane and the reflected ray and the surface plane, respectively.

If a succession of interfaces exists, the possibility of interference between successively reflected rays exists. Param­eters that define the position of the interference maxima, the line breadths of those maxima, and the line intensity depend inter alia on the regularity in layer thickness, the interface surface roughness, and the existence of surface tilts between successive interfaces. Algorithms for solving this type of problem are incorporated in software currently available from a number of commercial sources (Bede Scientific, Siemens, and Philips). The reflectivity profile of a system having a periodic layer structure is shown in Fig. 4.2.5.3 . This is the reflectivity profile for a multiple-quantum-well structure of alternating aluminium gallium arsenide and indium gallium arsenide layers (Holt, Brown, Creagh & Leon, 1997). Note the interference maxima that are superimposed on the Fresnel reflectivity curve. From the full width at half-maximum of these interference lines, it can be inferred that the energy discrimination of the system, ΔE/E, is 2%. The energy range that can be reflected by such a multilayer system depends on the interlayer thickness: the higher the photon energy, the thinner the layer thickness.

Figure 4.2.5.3| top | pdf | The reflectivity of a multiple-quantum-well device is shown. This consists of 40 alternating layers of AlGaAs and InGaAs. Shown also, but shifted downwards on the vertical scale for the purpose of clarity, is the theoretical prediction based on standard electromagnetic theory.

Commercially available multilayer mirrors exist, and hitherto they have been used as monochromators in the soft X-ray region in X-ray fluorescence spectrometers. These monochromators are typically made of alternating layers of tungsten and carbon, to maximize the difference in scattering-length density at the interfaces. Whilst the energy resolution of such systems is not especially good, these monochromators have a good angle of acceptance for the incident beam, and reasonably high photon fluxes can be achieved using conventional laboratory sources.

A recent development of this, the Goebel mirror system, is supplied as an accessory to a commercially available diffractometer (Siemens, 1996a,b,c; OSMIC, 1996). This system combines the focusing capacity of a curved mirror with the energy selectivity of the multilayer system. The spacing between layers in this class of mirror multilayers can be laterally graded to enhance the incident acceptance angle. These multilayers can be fixed to mirrors of any figure to a precision of 0.3′ and can therefore can be used to form parallel beams (parabolic optical elements) as well as focused beams (elliptical optical elements) of high quality.