Patent Number: 050162675
Section: description

DETAILED DESCRIPTION OF THE INVENTION By way of example of the first aspect of the invention, the simple case of a parabolically curved micro-channel plate with parallel faces will now be considered, with reference to FIG. 1A. The example is confined to the case of x-rays. For mathematical convenience, certain simplifying assumptions shall be applied to this example, viz that: (i) the reflectivity of the channel walls is perfect (that is 100%) for x-rays incident on the walls at grazing angles up to the critical angle .gamma..sub.c for total external reflection; PA1 (ii) the thickness of the walls is negligible relative to the diameter of the channels; PA1 (iii) the focusing properties can be considered in one dimension at a time; PA1 (iii) the x-rays emanate isotropically from a point source, at least over the small solid angular ranges relevant to the effective angular apertures of the device; PA1 (v) the micro-channel plate consists of substantially parallel straight-walled channels perpendicular to the two parallel end faces of the plate; and PA1 (vi) at most single reflection occurs in the channels. PA1 1. They are more compact (e.g. 1 or 2 mm thick) than, say, single-bore glass x-ray guide tubes (e.g. 20 cm long) and can focus with much shorter focal lengths so that they may be incorporated with minimal modification of existing instruments and the air path can be shorter leading to lower absorption losses in the air; PA1 2. They are rigid with no moving parts in the device itself and are stable in an x-ray beam; PA1 3. They are quite efficient; PA1 4. They may be readily produced economically by mechanically bending of conventional micro-channel or micro-filament plates or can be moulded thermally to a wide variety of shapes in order to produce desired focusing properties in two or three dimensions; PA1 5. They also act as short wavelength filter, hence reducing harmonic contamination when used in conjunction with x-ray monochromators. PA1 6. Can produce focusing and collimation in 2-dimensions with a large effective angular aperture. PA1 7. Capable of producing very short focal lengths. For example, conventional plate glass mirrors have a minimum focal length of the order of 1 m, whereas the device of the invention can achieve a focal length of the order of 1 cm. PA1 8. Can allow for fine tuning of device in situ to optimize focusing properties. PA1 9. Can automatically provide collimation out of the focusing plane due to their action of fine Soller slits. PA1 10. Can be used to produce quasi-parallel beams from extended sources. Assuming ray optics, the x-ray focusing properties of a flat (i.e. uncurved) two-dimensional, lens device according to the first aspect of the invention are illustrated in FIG. 1A. It will be better appreciated from what follows that this and the other diagrams are not to scale and exaggerate the size of the channels for purposes of illustration. Micro-capillary plate 10 has multiple tubular channels 12 which are elongate and open-ended. A divergent beam 14 from source S is focused as convergent beam 16 by plate 10. The reflection efficiency E at a point y above the origin O is here defined as: ##EQU1## where .DELTA..phi..sup.ter and .DELTA..phi..sup.channel are respectively the angular apertures for total external reflection and for intercepting the cross-section of the channel at height y above the optic axis. Integrated reflectivity refers to the integral of expression (1) over the full effective angular aperture of the focusing collimator and is an angle in radian measure. For illustrative purposes, and as noted in part at assumption (vi) above, the effective angular aperture of the device may be considered to be limited by the minimum of the angle at which double reflection in the channel begins to become possible and the angle at which total external reflection at the channel wall no longer becomes possible. In practice the aperture will usually be limited by the value of .gamma..sub.c rather than by the single reflection condition. For a given value of .gamma..sub.c (i.e. choice of channel-wall material), the optimum efficiency of the focusing device within the single reflection condition is given by choosing ##EQU2## Calculations have been made for parameter values typical of the sorts of values which may be achieved for the devices in practice and which would be suitable (but not necessarily optimum) for achieving focusing. For example, the selected .gamma..sub.c value refers to quartz glass while the d/t value is typical of commonly available micro-channel plates. It has been found that integrated reflectivities of the order of 1 mrad in one-dimension are in principle possible with these parameter values (and 5 mrad if t/d were optimized in the manner described in (2) above). Integrated reflectivities of this order correspond to a flux increase of order 13 for Gelll Bragg reflection and CuK.alpha. radiation, if collimation is achieved to better than 15 seconds of arc. If a focusing distance l.sub.F is desired for a source distance on the other side of the plate of l.sub.S, then the channel at height y above the x axis, that is the central optical axis of the diverging x-ray beam emanating from source S, should be tilted by the angle w(y) given by: ##EQU3## where .rho. is the radius of curvature of the plate 10 required to produce w(y). The general flat plate, parallel channel case is geometrically explained in FIG. 1A and 1B. The general focusing condition is shown in FIG. 2: here, the inclination of the channel side walls progressively change from channel to channel with increasing distance from the optical axis. The result is an enhanced focusing effect. A special case of equation (3) occurs when l.sub.f equals infinity and corresponds to the production of a quasi-parallel x-ray beam from a point source. The geometry for this case is illustrated in FIG. 3. In FIG. 3, the side walls of each channel are curved end-to-end by virtue of the bending of the micro-capillary plate about the z axis: this is demonstrated by the parallelism of the emerging beam segments reflected by each channel side wall from a divergent beam segment received from source S. By way of example, with reference to FIG. 3, where l.sub.S is 100 mm, the channel width and length are respectively 0.025 mm and 1.0 mm, and the critical angle .gamma..sub.c is 5 mrad, the bending displacement at y=10 mm from the axis of the x-ray beam passing through the plate is 0.25 mm. A bending of a micro-channel plate to this extent clearly involves no severe mechanical problems in practice. Alternatively, the curving of the micro-capillary plate may be carried out by slump forming on heating the plate above the appropriate glass softening temperature. The channels may be tapered, shaped or may be of non-circular cross-section, e.g. hexagonal, to produce special or improved focusing effects, and to reduce off-axis aberrations. The aforedescribed exemplification assumed that the thickness of the walls in the micro-capillary plate matrix is negligible relative to the diameter of the channels. In reality, a capillary to matrix cross-section ratio of about 50% is typical and this simply results in a reduced transmission intensity. However, by careful design of the micro-capillary plate, a capillary to matrix cross-section ratio as high as 90% is presently possible. As mentioned, the principle of increasing inclination of the side walls of the channels, as shown in two dimensions in FIG. 3, may be readily extended to three dimensions by curving a micro-filament plate so that its outer and inner surfaces in which the channels open are of part paraboloidal formation. By varying the curve in the two dimensions, different effects can be produced in the respective dimensions, e.g. collimation in one plane and focusing to substantially a spot in the other. It will be understood that even in two dimension, a physical embodiment of the first aspect of the invention is possible in the form of a stack of thin x-ray mirror plates, and would have practical applications. FIG. 4 shows such an embodiment of lens device 10 ''' according to the first aspect of the invention. Multiple metal sheets 11 are fixed by suitable spacers (not shown) at uniform intervals in a stack. The sheets 11 are highly polished and reflective to x-rays, and the device is effective to focus a divergent x-ray beam from a source S substantially to a focus F. The sheets may be of variable increasing inclination and be curved under tension, as with the previously described embodiment. It will be seen that the cavities between the stack form multiple open-ended channels 12''' arranged across the optical path. In a particular embodiment, an aperture may be formed in the lens device (in any of the above forms) to allow unimpeded propagation of a direct portion of the incident beam consistent with the collimation requirements of the instrument. This aperture may then be bordered by an x-ray lens device in accordance with the invention to gather additional x-ray flux outside the aperture. In general, the front and back faces of eg, plate 10 may be shaped to optimise performance according to desired parameters. In an instrumental application, an x-ray lens device according to the first aspect of the invention may be provided in conjunction with an x-ray source tube, for example in place of the existing pin hole or rectangular slit aperture which is the effective source of x-rays from the tube. A collimating and focusing device according to the first aspect of the invention provides a very practical and cost effective means for increasing the x-ray intensity and flux in a wide variety of x-ray scattering instruments such as x-ray powder diffractometers, four circle diffractometers, small-angle scattering systems and protein crystallography stations. It should also be of value in the construction of x-ray microprobes, microscopes and telescopes. This will be especially so where conventional systems use very primitive x-ray optics, such as narrow slits or pin hole collimation. Micro-channel and micro-filament plates are very well suited to mechanical and plastic deformation as a means to achieving the desired focusing or collimating properties, in contrast to the case of single crystal diffraction systems which are much more difficult to bend with a high risk of damage. A closely similar application of such device also pertains to the case of collimating and focusing of neutrons. The advantages of x-ray lens devices according to the first aspect of the invention include: Table 1 is a summary of properties of some exemplary devices according to the first aspect of the invention, including an indication of a practical set of values for hypothetical but highly practical case. __________________________________________________________________________ SUMMARY OF PROPERTIES OF FOCUSING COLLIMATORS FOR A POINT SOURCE AND PARALLEL CHANNELS WITH WALLS OF NEGLIGIBLE THICKNESS FOCUSING TO A FOCUSING TO A POINT QUASI-PARALLEL BEAM __________________________________________________________________________ 1. maximum value of .phi. such that .gamma..sub.c (5 .times. 10.sup.-3) 2.gamma..sub.c (10 .times. 10.sup.-3) total external reflection can still occur in channel (.phi..sup.ter) 2. maximum value of .phi. such that at most only one reflection ##STR1## (0.025) ##STR2## (0.05) can occur in channel (.phi..sup.apert) 3. effective anngular semi- aperture of collimator (.phi..sup.apert) ##STR3## (5 .times. 10.sup.-3) ##STR4## (10 .times. 10.sup.-3) 4. semi-aperture of collimator on y-scale (y.sup.apert) ##STR5## (0.5 mm) ##STR6## (1.0 mm) 5. Reflection efficiency at y when aperture is .gamma..sub.c ##STR7## (0.4 y) ##STR8## (0.2 y) 6. mean efficiency averaged in 1-dimension out to effective ##STR9## (0.1) ##STR10## (0.1) aperture limit of system for .gamma..sub.c limited case. 7. intergrated reflectivity of focusing collimator when ##STR11## (1 .times. 10.sup.-3) ##STR12## (2 .times. 10.sup.-3) system is .gamma..sub.c limited (note factor of 2 to cover .+-. y contributions). 8. bending locus for MCP in order to achieve focusing x = 0 ##STR13## (-0.0025 y.sup.2) 9. bending requirements for z = 0 z = 0 sagittal focusing with 1.sub.F.sup.sag = 1.sub.s 10. integrated reflectivity if t/d value is optimized to ##STR14## (5 .times. 10.sup.-3) 2 .times. .gamma..sub.c (10 .times. 10.sup.-3) match .gamma..sub.c (i.e. d/t = .gamma..sub.c) distance to focus from 0 1.sub.s (100 mm) .omega. (.infin.) error in focusing along x - axis: (i) spatial spread 2t (2 mm) . . . (ii) angular divergence ##STR15## (10 .times. 10.sup.-3) ##STR16## (0.05 .times. 10.sup.-3) __________________________________________________________________________ N.B. Values in parenthesis relate to values of relevant quantities when the following representative values of the key quantities are chosen: ##STR17## - Turning now to the second aspect of the invention, the condensing-collimating channel-cut monochromator illustrated in FIG. 5 and 6 is a single perfect or nearly perfect-crystal of silicon, germanium or other suitable material. The crystal has been cut to form the converging channel 22 with opposed perpendicular lateral faces 24, 26. These faces are cut at respective angles, known as asymmetry angles (see FIG. 15), of .alpha..sub.l =0, .alpha..sub.2 =10.degree. to the Bragg lll planes 17 of the crystal. In operation, the at least partially collimated incident x-ray beam 28 is multiply reflected and emerges as a relatively spatially condensed and angularly collimated pencil 30. Monochromator 20 is usually formed in silicon or germanium because of their ready availability in near perfect-crystal form and the reflections typically chosen are the lll reflections because they have the largest structure factor and so the largest wave-length band-pass or angular acceptance and hence lead to the highest integrated (with respect to angle of divergence at exit face) reflectivity from the monochromator. However, other reflections may be chosen and these may confer advantages in special cases. The channel-cut crystal monochromator of FIGS. 5 and 6 has been made in accordance with certain specified tolerances, viz that for CuK.alpha..sub.l radiation (1.54051 Angstrom), the emergent x-ray beam will have a FWHM angular divergence less than 1 minute of arc, a wavelength band-pass of the order of 2.5 by 10.sup.-4, and a spatial condensation factor of about 6. By the latter is meant that, in the plane of diffraction, the ratio of the width of the incident beam to emergent beam is about 6. An example spatial condensation of the beam is shown in FIG. 7, in which image A shows the beam incident to the monochromator and image B (on the same scale as image A) shows the emergent beam. FIG. 8 is a contour plot of the spatial condensation factor, as just defined, for various values of the asymmetry angle, .alpha..sub.1, at the first lateral face of the channel, plotted against values of the asymmetry angle, .alpha..sub.2, at the second face. It will be seen that the spatial condensation factor increases with increasing .alpha..sub.1 and that, for a given .alpha..sub.1 value, increasing values of .alpha..sub.2 further enhance the condensing effect. However, these observations must be considered together with the effects of varying asymmetry angles on bandwidth, angular collimation and integrated reflectivity. For example, FIG. 9 is a contour plot of the full width of the reflectivity curve (that is the reflectivity versus the angle of divergence of the existing beam) taken as twice the standard deviation of the reflectivity distribution. FIG. 10 is a contour plot of integrated reflectivity (i.e. reflectivity integrated with respect to angle of divergence at the exit face of monochromator) versus the asymmetry angle .alpha..sub.2 for various values of .alpha..sub.1. It will be noted that for a given value of .alpha..sub.1, the integrated reflectivity tends to increase with increase in .alpha..sub.2. It seems from these curves that a good net result for silicon lll planes and CuK.alpha. radiation is obtained for .alpha..sub.1 =0 and .alpha..sub.2 =+10.degree.. A significant improvement in spatial condensation is obtained with this difference relative to no difference (FIG. 8) and integrated reflectivity is still quite high (FIG. 10), while angular collimation remains within acceptable limits and certainly below the aforementioned criterion of 1 minute of arc. For general choices of asymmetry angles for multiple reflections in a channel, the net reflectivity curve must be calculated as the product for each face treated according to the dynamical theory of x-ray diffraction. FIG. 11 shows the individual and integrated reflection curves for the ideal case (graph A), at which, as mentioned, .alpha..sub.l =0 and .alpha..sub.2 =10.degree., and for two less satisfactory arrangements (graph B: .alpha..sub.1 =9.degree., .alpha..sub.2 5.degree. and graph C: .alpha..sub.1 =3.degree.,.alpha..sub.2 =10.degree.). The former reduces the final intensity and the latter gives too sharp a peak in the net curve. The reflectivity peak for a single reflection from a perfect-crystal falls off quite slowly with angle (as can be seen in FIG. 11), with the result that long tails may occur in the primary beam coming off the monochromator and swamp the small-angle scattering intensity from the sample. Bonse and Hart showed that the undesirable tails in the beam coming rom a perfect-crystal could be reduced in intensity by man orders of magnitude, with negligible reduction in peak intensity, by using multiple reflections in a parallel-face channel-cut monochromator. For parallel faces in a channel, the reflectivity curve for a series of m identical pairs of reflections in a channel is just the m.sup.th power of the reflectivity curve for one pair. This relationship is not so for general choices of asymmetery angles for multiple reflections in a channel but the overall effect remains: the net reflectivity is the product of the individual reflectivities for the individual faces. The embodiment of FIGS. 5 and 6 uses a small number of such reflections-and the reduction of the tails can be seen in FIG. 11. The tails may be reduced even further by careful design involving increasing the numbers of faces. This may involve splitting up one or both faces of the channel. FIG. 12 diagrammatically depicts one such design viewed in plan with values for .alpha..sub.1 =0.degree., .alpha..sub.2 =10.degree., .alpha..sub.3 =-10.degree. and .alpha..sub.4 =10.degree. respectively for the four successive reflections in the monochromator. The reflectivity curves for the faces and for the device as a whole are depicted in FIG. 13. This embodiment has high reflectivity in the central range of Bragg reflection but in addition has the desirable property that the Bragg tails fall off as approximately the eights power of the angular devation from the Bragg condition. It should be noted that, the net spatial condensation factor for a monochromator with reflectance at m faces is the product of the spatial condensations at the individual faces. In the case where beams possessing a high-degree of plane polarization are required, this may be achieved by choosing reflections having 2.theta..sub.B (i.e. twice the Bragg angle) close to 90.degree. for the given wavelength. For example, for CuK.alpha., the 333 or 511 reflections of silicon or germanium are suitable. Although the discussion above of channel-cut monochromators in accordance with the second aspect of the invention has been in terms of parallel-beam optics, improvements in integrated reflectivity of such devices is clearly possible if the faces of the monochromator are suitably bent or if surface modification is carried out, for example, by ion implantation, liquid phase epitaxy or molecular-beam epitaxy. Since reflectivity of a perfect crystal depends on atomic number, one approach would be to grow an epitaxial layer or implant and anneal a heavier atom material at or near the surface of a perfect crystal of, e.g. silicon. Similarly, production of a lattice parameter gradient perpendicular to the diffracting planes, for example by the sort of means mentioned above, leads to an increase in the width of the reflectivity curves in a manner very similar to that of crystal bending. Variation of lattice parameters parallel to the diffracting planes can also lead to a one or two dimensional focusing effect similar to that achievable by bending. Improvements in transmitted power of the monochromator system of the second aspect of the invention may be achieved by use of a pre-collimator such as a bent crystal monochromator with lattice parameter gradient or x-ray mirror, or a lens means according to the first aspect of the invention. The ideal incident beam for the monochromator is collimated at least to some extent and the device of the first aspect of the invention is ideal for such pre-collimation. The monochromator of itself accepts a maximum angle or divergence in the incident beam of approximately 15"; the angular acceptance from the source can be increased from 15" to 11/2.degree. by use of the lens device of the first aspect of present invention between the source and the monochromator as shown in FIG. 16. In more advanced versions of the present types of monochromators, the degree of overlap of the two reflectivity curves, and hence the angular divergence of the beam coming from the monochromator, could be varied extrinsically by making a flexure cut in the monochromator and by using a piezo-electric or electro-magnetic transducer to vary the angle between the sets of Bragg planes corresponding to each face. An arrangement adaptable to this varability is shown in FIG. 14. Such an extension of the invention makes possible the development of compact multi-stage beam-condensing monochromators of ultimate beam condensing power, estimated to be of the order of 1 micron or less, and typically limited by the depth of penetration of the x-ray beam into the crystal face. The monochromator of the invention is of particular value in small-angle x-ray scattering and x-ray powder diffraction systems in that the incident beam on the sample is condensed to a width consistent with the detector pixels of position-sensitive detectors. The monochromator would also be valuable in x-ray microprobes for x-ray fluoresence analysis, scanning x-ray probes and for medical diagnostic and clinical purposes, in scanning x-ray lithography and as analyser crystals in powder diffractometers and fluorescence spectrometers. The described arrangement has been advanced merely by way of explanation and many modifications may be made thereto without departing from the spirit and scope of the invention which includes every novel feature and combination of novel features herein disclosed.