Overview of polycapillary X-ray optics
X-ray optics, polycapillary, X-ray analysis, electron-excited spectroscopy, X-ray diffraction, X-ray fluorescence, XRD, XRF
Polycapillary optics are utilized in a wide variety of applications and are integral components in many state of the art instruments. Polycapillary optics operate by collecting X-rays and efficiently propagating them by total external reflection to form focused and parallel beams. We discuss the general parameters for designing these optics and provide specific examples on balancing the interrelations of beam flux, source size, focal spot-size, and beam divergence. The development of compact X-ray sources with characteristics tailored to match the requirements of polycapillary optics allows substantial reduction in size, weight, and power of complete X-ray systems. These compact systems have enabled the development of portable, remote, and in-line sensors for applications in industry, science and medicine. We present examples of the utility and potential of these optics for enhancing a wide variety of X-ray analyses.
Polycapillary optics are widely used for all types of X-ray analysis as a result of over a decade of research and development by a few groups around the world (Kumakhov and Komarov, 1990; Yan and Ding, 1993; Gibson and Mac-Donald, 1994; Gibson and Gibson, 2001). These optics can dramatically enhance the performance of conventional X-ray instruments and are becoming integral components of state-of-the-art instruments rather than an optional part.
Experimentalists and developers of these optics are using their ingenuity and innovation to expand the capabilities of X-ray optics for all types of X-ray instruments to approach the physical limitations intrinsic to each application. This paper reviews the physics of polycapillary optics for X-rays, and the important parameters for optimizing their performance. Several applications of X-ray analysis enabled by polycapillaries are provided to illustrate the breadth of their utility.
2. POLYCAPILLARY OPTICS FOR X-RAY ANALYSIS
Polycapillary optics are comprised of 10 000 and to several million hollow glass channels bundled together (Figure 1). X-ray photons propagate in the hollow space of the capillary channels by the process of total reflection at the glass surface. The phenomenon and physics of total reflection was discovered and investigated by Compton(1923) and Hagenow in the early 1920s, and the feasibility of utilizing total reflection to guide X-rays was demonstrated by Jentzch and Naring (1931). Reflection of photons occurs at the boundary between media with different refractive indices.
In the case of glass capillaries and X-ray photons, the gas atmosphere inside the capillary channel has a refractive index > the refractive index of glass. Therefore, the phase speed of an X-ray traveling in glass is higher than in a gas. The X-ray beam refracts by decreasing the angle to the glass surface to accommodate the increase in wavelength while maintaining a constant frequency and energy. Total external reflection of X-rays from a glass surface occurs when the incident beam strikes the glass surface at an angle ≤ the critical angle (θe). The behavior of X-ray photons contrasts the behavior of photons in the visible energy range where the refractive index of a gas is < the refractive index of glass. Total internal reflection of light photons occurs when the incident beam strikes the glass-gas interface at an angle ≤the critical angle(θc).
The production of multifiber monocapillary optics was reported by Arkd’ev et al. in 1989 and then by Kumakhov and Komarov in 1990. These first-generation optics were comprised of an array of single, thin-walled glass capillaries supported and aligned by several metal screens along the length of the optic. Significant improvement was accomplished by using an array of fibers (a multifiber) containing many capillary channels in each fiber (polycapillary fibers), instead of the array of single capillaries (Figure 1).
Multifiber, polycapillary optics allowed significant reduction in the size of the optic and also increased the range of X-ray energies that could be used. A major advancement in capillary-optic technology was the development of monolithic, polycapillary optics (Figures 2 and 3).
B. Physics of monolithic polycapillary optics
Figure 4 shows the trajectories of two X-ray photons in a capillary.
As the angle of the X-ray beam incident on the glass surface decreases from relatively high angles, the refracted beam in the glass will approach the critical angle（θc）and have an increased probability of propagating along the channel by multiple reflections. Photons>θe will not be propagated by reflection. For a borosilicate glass, θc is ～determined by the X-ray photon energy:
Table 1 provides examples of θc for the range of photon energies which polycapillary optics are typically used. Polycapillary optics can be used in focusing and collimating modes (Figure 5) by gently bending the capillaries to an appropriate curvature.
The radius of curvature(R) of the bend is limited by the total reflection condition (Figure 6):
Figure 6. X-rays entering a curved capillary tube. Photon “A”strikes the glass surface at an angle ≤0 and continues to propagate along the interior of the tube. Photon “B”enters just below”A” and strikes the surface at an angle >ea and is not propagated. The tube diameter(d) is typically 2-25 μm.
The capillary channel diameter （d） is typically 2-25 μm and is much smaller than R(～500 mm) in order to maximize the number of X-rays with incident angles <θe. Monolithic polycapillary optics are designed to have d vary along the length of the optic to optimize their transmission efficiency by preserving the conditions for total external reflection. Continued improvements in the manufacturing of monolithic optics have decreased the roughness of the internal glass surface to a few angstroms. The main benefit of polycapillary optics is to greatly reduce the inverse-square dependence of X-ray intensity on the distance from the source by capturing X-rays from a source and redirecting them into either a parallel beam or a focused beam. The large increase of intensity delivered to a 50 μm spot by a focusing polycapillary optic compared to a pinhole aperture is shown in Figure 7.
The alternatives to increasing the intensity via optics are relatively large, expensive, and complex sources, for example, rotating anode, laser plasma, free-electron laser, and synchrotron.
C. Focusing polycapillary optics
(1) Output focal distance
The output focal distance (OFD) is mainly determined by the required output spot size (S) of the full beam and can be estimated by
where dout is the channel diameter of the capillary at the output end of the optic, which is usually very small compared to S and can be neglected. θe is the critical angle of the capillary for the energy of interest. Combining Equations of θc(mrad) and above Equation S and neglecting dout, gives
For example，if a beam spot of 50 μm is required at Mo Ka radiation (17.5 keV), according to Eq. (4), the OFD is ～14.6mm.
TABLE 1. Critical angles calculated using Eq. (1) for several photon energies.
|wdt_ID||Energy (keV)||θc (mrad)||θc (°)|
|2||8.0 (Cu Ka )||3.8||0.22|
|3||17.5 (Mo Ka )||1.7||0.10|
According to Equation above (S(µm))，a focal spot ～10 μm can be achieved at 17.5 keV with a very short OFD of ~3mm. In practice, however, this will be limited by ability to work with the sample at less than 3 mm and by the “halo effect,” which is the penetration of high-energy X-rays through the glass. For example, photon “B” in Figures 4 and 6 could be transmitted through the glass walls of the capillary instead of being absorbed by the glass walls. The halo effect contributes intensity and breadth to the output beam.
The halo effect can be conveniently thought of as a combination of a “penetration halo” originating from high-energy X-rays penetrating through the whole optic, and an “escape halo”generated by X-rays penetrating through the glass near the end of the optic when the incident angle is greater than the critical angle. The penetration halo becomes important for X-rays >~40 keV and can be controlled by operating the X-ray tube at <40 kV, by increasing the length of the optic, and by tailoring the composition of the glass. The “escape effect,” however, can be generated by lower energy X-rays because it occurs near the output end of the optic where the number of thin glass walls possibly traversed by X-rays is relatively small. The off-track X-rays in both types of halos can smear the relatively sharp focal spot originating from the totally reflected X-rays. The “escape effect” becomes larger as the focal distance decreases, because X-rays are subject to more loss from transmission with shorter OFD. If critical to the application, the halo effect can be limited by shielding and by judicial choice of capillary materials, with a modest decrease in beam intensity.
(2) Input focal distance
The IFD is mainly determined by the X-ray source size and the access distance. In general, matching the size of the “input focal spot” of the optic with the X-ray source size will optimize the efficiency of the optic. The input focal spot is the region where divergent X-rays are collected by the optic. The relationship between the input focal spot size and the IFD is also governed by Equation above (S(µm). For instance, if the X-ray source is a Mo-anode tube with a spot size diameter of 200 μm， the IFD of the optic can be set around 60 mm for the Mo Kα radiation (17.5 keV).
(3) Optic length
The last parameter to determine is the optic length, which determines the optic performance at a given energy.
Figure 8 shows the simulation result of the output beam in-tensity as a function of the optic length for a sample optic with an IFD of 60 mm and an OFD of 10 mm with a fixed maximum channel diameter for Cu Ka and Mo Kα energies.
Other factors such as geometric constraints on both the X-ray source side and the sample side must be taken into consideration in the optic design. For example, if a Mo X-ray source has a spot size of 20 μm， the optimal IFD for Mo K a radiation, according to the discussion in Sec. IIC 2, is 5.8 mm. Most commercial X-ray sources, however, are not de-signed for such a short access distance. Also constraining the optic design is a reasonable working space between the optic and the sample to allow more degrees of motion for relatively large and irregularly shaped samples, for example, to access high-angle tilts for stress and texture analysis. Further constraints on the design are imposed by in situ high-temperature and high-pressure apparatus, the position of the-detector, video camera, and other devices. These geometric constraints are usually more stringent when retrofitting an optic into an existing system. Optimization of the optic length is best done by simulating the optics performance.
D. Collimating polycapillary optics
The output beam intensity is one of the important performance parameters for both focusing and collimating op-tics. In contrast to focusing optics where the focal spot size is an important performance parameter, the beam divergence is particularly important for collimating optics. The optimization of output beam intensity for a collimating optic is relatively straightforward, but the optimization for beam divergence can be more complicated, involving both the X-ray source as well as the application. The beam divergence of a collimating optic is roughly determined by the critical angle, which is inversely proportional to the X-ray energy, as shown in Equation θc(mrad).
However, beam divergence can be controlled by many other factors such as optic shape, X-ray source dimensions, and source-optic geometry. An extreme case exists when the optic is long enough for the high-angle X-rays to be eventually absorbed after many reflections and those X-rays with small angles will be preferentially transmitted because the absorption of reflected X-rays decreases with decreasing incident angle.
The trade-off between the decrease of intensity, and the concomitant decrease of divergence can be tracked by the intensity-divergence ratio, which is analogous to the flux density used to track the performance of a focusing optic. Figure 9 shows the simulation results for beam intensity and divergence as a function of the length for a particular type of collimating optic.
Although the maximum intensity was obtained at point “A,” the intensity-divergence ratio, which can be an important parameter for some X-ray diffraction (XRD)analysis, has the highest value at point“B.”A collimating optic delivering the highest intensity is not necessarily the optimum design for XRD analysis because some XRD applications require a maximum limit for divergence. Another approach to achieve a small beam divergence is to design the optic so the maximum incident angle of X-rays entering each capillary channel is less than the critical angle.
As the incident angle at each reflection point for the collimating optic decreases, the output beam divergence will be < the critical angle if the X-rays exactly follow the designed trajectories. The maximum incident angle, θmax, into each channel can be estimated by
where D, is the diameter of the source. One can achieve a low maximum incident angle by increasing the IFD and reducing the size of the source spot. The latter provides a large capture angle of the optic. Using a small X-ray source also increases the transmission efficiency of the optic, but if de-creasing the spot size necessitates decreasing the source power, the trade-off becomes more complex. For example, when a polycapillary collimating optic with 10 mm IFD coupled with a microfocus X-ray source of 30 pm in diameter, the maximum incident angle at the input end is estimated from Eq. (4) to be approximately 1.5 mrad, much less than the critical angle of 4 mrad at Cu Ka radiation (8.04 keV). The simulation result in Figure 10 shows how the beam divergence is affected by the X-ray source size.
Because of these multiple factors, the practical optimization of the optic performance is achieved by simulating all the relevant parameters.
Generally, if the X-ray source is small enough for a de-sired beam size, a short IFD allows the possibility of increasing the effective capture angle, which is defined as the solid angle of X-rays collected from the source by the optic multiplied by the transmission efficiency of the optic. The combination of small source and short access distance of the X-rays tube is particularly important when a small, parallel beam is required. This can be clearly seen in the illustration shown in Figure 11.
Integrating the capillary optic to a low-power, microfocus source often provides flux and flux density comparable and higher than from conventional, sealed-tube and rotating-anode sources operating at significantly higher power.
An example of a compact, coupled, source-optic system, the X-BeamTM system (X-Beam is a registered trademark of X-ray Optical Systems,Inc.) is shown in Figure 12.
Either a collimating or a focusing polycapillary optic can be coupled to a source in the X-Beam systems. Nominal characteristics of X-Beam systems are shown in Tables 2 and 3.
Table 2 Typical characteristics of X-Beam systems with focusing poly-capillary optics. The optic length is ~60 mm
|wdt_ID||Output focal distance||4mm||9mm|
|1||Focal spot size, FWHM||< 25 um|
|3||Flux density (cps/um2)||1.6×10^5||9.2×10^2|
|4||Source power||50 kV, 50 W Mo Ka||50 kV, 50 W Mo Ka|
Table 3 Typical characteristics of X-Beam systems with collimating, polycapillary optics for several beam diameters, radiation types, and power settings. The optic length is 30 mm.
|2||Divergence, FWHM (mrad)||1||2||1||2|
|3||Source power||50 kV, 50 W Mo Ka||40 kV, 80 W Mo Ka||50 kV, 50 W Mo Ka||50 kV, 50 W Mo Ka|
3. X-RAY APPLICATION FOR POLYCAPILLARY OPTICS
A. Focused-beam applications
(1) Micro X-ray fluorescence(MXRF)
Polycapillary optics are the most widely used optics for MXRF(Gao et al.,1996)and are an integral part of several commercial MXRF instruments. The small size and low power of these optics enables the development of on-line MXRF sensors for semiconductor, pharmaceutical, and other materials-based industries as well as the development of remote and portable instruments, for example, planetary rovers. MXRF systems can take many different forms, some of which are illustrated in Figures 13-20.
These applications, as well as most of the other applications discussed in this section, make use of the broad energy bandwidth accommodated by polycapillary optics. The broad energy transmission of polycapillary optics distinguishes them from diffractive optics such as flat and curved crystal optics, and multilayer thin-film optics.
Nominal characteristics for focusing polycapillary optics are listed in Table 4.
Table 4 Characteristics of focusing polycapillary optics.
|1||Small focal spots: 25 m m for Cu Ka 15 m m for Mo Ka|
|2||Capture angle: up to 20°|
|3||Transmission effificiency: up to 30%, depending on geometry and energy|
Only monolithic optics are shown in Table IV because they provide focal spots much smaller than multifiber, focusing optics, which have a spot size limited by the polycapillary fiber width.
Table 5 Characteristics of collimating polycapillary optics.
|1||Output beam size||10×10, 20×20, 30×30 mm2||0.5, 1.5, 4, 6 mm|
|2||Output divergence||～4 mrad Cu Ka||～ 1 mrad Mo Ka , ～ 2 mrad Cu Ka|
|3||Capture angle||4.2°, 7°, 8.8°||up to 20°|
|4||Axial and planar divergence||are identical|
|5||Transmission effificiency||Up to 30% transmission effificiency||up to 30%, depending on geometry and energy|
In special cases, for example, neutron focusing, multifiber focusing optics can be used because of their larger collecting area.
Focusing optics can be utilized as a spatial filter for all applications where background radiation from areas not in the region of interest interferes with the signal of interest. Havirilla and Gao (2001) have developed a MXRF method using dual polycapillary focusing optics consisting of an ex-citation optic to focus a small beam on the specimen and a detection optic for collecting fluorescent X-rays (Figure 14).
This method can be used to detect elements within radioactive materials (Figure 15).
MXRF analysis of radioactive materials is hampered because the X-rays from radioactive emission usually swamp the energy-dispersive detector. Their results show the spontaneous radiation background was practically eliminated from the spectrum and, therefore, the detection sensitivity and accuracy was greatly improved. The dual optics geometry opens new application opportunities for MXRF analysis of radioactive materials.
(2) Partial-pressure scanning electron microscopy The compact size and flexibility of capillary optics facilitates their incorporation into existing processing and diagnostic instruments. An application in a low-vacuum scanning electron microscope (LV-SEM) and an environmental SEM (ESEM) is shown in Figure 16.
The electron beam spreads in the high-pressure environmental chamber and fluorescent X-rays generated outside the area of interest are detected by the detector and reduce the image contrast. A polycapillary optic collects X-rays from an area defined by the optic spot size and focuses them on the detector, reducing the background and enhancing the image contrast (Gao and Rohde, 2001) (Figure 17).
(3) Electron-excited spectroscopy
High-resolution spectroscopy not only greatly increases the elemental discrimination and detection sensitivity, but, in some cases, can give chemical as well as compositional information. This can be done by wavelength-dispersive spectroscopy with a collimating optic to increase the diffracted-beam intensity as shown in Figure 18 (Soejima and Narusawa, 2000).
Using parallel-beam geometry with capillary optics makes it possible to discriminate wavelengths with a flat-crystal monochromator by a simple rotation of the crystal rather than a more complex motion required when using a curved crystal. For ultrahigh resolution spectroscopy, an energy-dispersive microcalorimeter detector (Wollman et al.,1997a) can be used with collimating optics (Figure 19).
An example of the fluorescence spectrum from such a measurement is shown in Figure 20 (Wollman et al., 1997b).
B. Collimated-beam applications 1.X-ray powder diffraction(XRPD)
Collimating polycapillary optics convert a highly diver-gent beam (up to 20°) into a quasiparallel beam with divergence of 1 to 4 mrad (0.06°-0.23°)(Table III and V). The parallel-beam XRPD geometry (Figure 21) greatly reduces and removes many sources of errors in peak position and intensity inherent to the parafocusing (for example, Bragg-Brentano) geometry (Figure 22) such as sample position, shape, roughness, flatness, and transparency.
Figure 23 shows diffraction scans for peaks displayed by silicon (Bates, 1998) and alumina powder (Schields and Huang, 2002) as a function of severe sample-displacement. Peak shifts and reduction of intensity are eliminated using parallel beam diffraction.
The number of crystals in a powder satisfying the Bragg condition depends on the volume irradiated by the beam and the crystal size (Smith, 2002). An additional benefit of using a collimated beam for XRPD is to spread the incident beam over a large region, allowing many more crystals to be in diffracting condition compared to the area typically irradiated with a parafocusing instrument (～6×10mm2). Indeed, Smith demonstrates that increasing intensities to increase counting statistics increases the absolute accuracy by only ~2% for the parafocusing geometry. Figure 24 compares diffraction patterns displayed by the same basalt specimen using a 2 kW sealed tube source with parallel-beam produced by conventional parallel-plate optics and a 20 W microfocus source with collimating capillary optics.
The dramatic efficiency generated by the capillary optic coupled to a low-power source is striking (Haller, 2000). Another example of enhanced diffracted intensity provided by a capillary optic for a 222 pole figure collected from a 100 A silver thin-film on a silicon crystal is shown in Figure 25 (Matney et al., 1999).
The signal-to-noise is increased by ～10 to 20 times. Multifiber collimating optics are often selected for applications requiring a large cross-section, parallel-beam as for large-area, thin-film texture studies (Kardiawarman et al.,1995) and X-ray lithography(Chen et al.,1999). The flexibility in sample presentation is provided by the parallel beam was shown by Yamanoi and Nakazawa(2000) in Figure 26 which shows a schematic for a powder diffraction set up which eliminates preferred orientation errors.
The elimination of multiple sources of error and the potential for reducing the power, size, weight, and cost of an instrument makes parallel beam X-ray systems natural candidates for on-line diffraction systems for quality control and feedback in manufacturing and process environments. Such systems are under development for implementation for the semiconductor, steel, pharmaceutical, and cement industries among others.
(2) Single-crystal X-ray diffraction
Many of the benefits of parallel-beam powder diffraction described previously also apply to single crystal diffraction applications. Perhaps the most important and most studied application to date has been application of a collimated X-ray beam to protein crystallography (Owens et al.,1996). Figure 27 is a schematic representation of such a system, and a diffraction pattern for lysozyme is shown in Figure 28.
The diffracted-beam intensity obtained with a polycapillary monolithic optic with a slightly convergent (～0.5°)beam and a 50 W microfocus source was equal or greater to that from a 5 kW rotating anode source equipped with the most advanced confocal optics, with resolution<2 A and Rmerge <6% for lysozyme (Guberev et al.,2000a, b). At the present time the local divergence (divergence of X-rays from each capillary channel) of ~0.12°, limits the unit-cell size of molecular crystals that can be successfully analyzed to <200 A. A similar X-ray system which includes a graphite monochromator has recently become available commercially (Foundling et al., 2001). By using more strongly convergent beams (up to～2°) Owens et al. (1997) obtained even higher X-ray density on smaller beam spots. Together with special software developed by Ho et al. (1998) for analysis of convergent-beam diffraction pattems, convergent beam systems can be used for screening very small protein crystals (Huang et al., 2001), microdiffraction measurements with a very low-power source (e.g., a 2 W source for planetary rovers), and for neutron diffraction from small crystals for macromolecular structure, high pressure, and low-temperature studies (Gibson et al., 2001a).
(3) Medical applications A potential major area of application for polycapillary optics is in medicine (Gibson et al,1991, MacDonald and Gibson 1995). Used as angular filters to magnify X-ray images, they have demonstrated significant and important increase in contrast and resolution for mammography (Kruger et al., 1996) and are under active investigation for other soft tissue imaging and for cancer therapy. These also represent enabling applications of polycapillary optics but are not reviewed in this paper because of limited space and because they are at an earlier stage of general acceptance and application than the other examples provided. Also, they were reviewed in papers in the Denver X-ray Conference 2001 proceedings(Gibson et al.,2001b; Sugiro et al., 2001).
Polycapillary optics have gained broad acceptance and are now being used in a broad variety of applications. Beginning as optics custom integrated into individual research setups, they then were used as standard options to enhance the performance of existing X-ray analytical instruments, and are now widely used as essential components in X-ray spectrometers and diffractometers. The development of compact X-ray sources, matched to the capillary optic input requirements, have allowed a large reduction of the size, power, and weight of X-ray systems allowing the development of compact X-ray sensors for portable, remote, and in-line applications in industry, science, and medicine.