Polycapillary x-ray optics provide an innovative new way to control x-ray beams. Placing these optics after the object to be imaged provides very efficient rejection of Compton scatter, while allowing image magnification without loss of resolution, image demagnification, or image shaping to match with digital detectors. An extensive study of the effects of surface and profile defects have greatly enhanced the understanding of the manufacturing process and lead to improved reproducibility and manufacturability of the optics. Measurements were performed on magnifying tapers. The optics had measured primary transmissions greater than 50% and scatter transmission of less than 1%. For a 5-cm thick Lucite phantom, this resulted in a contrast enhancement compared to a conventional grid of nearly a factor of two. The magnification from the tapered capillary optics improved the MTF at all frequencies out to 1.9 times the original system resolution. Increases below the system resolution are most important because clinically relevant structures generally occupy lower spatial frequencies.

Alternatively, placing a collimating optic and diffracting crystal before the patient provides sufficient monochromatic beam intensity for medical imaging. Contrast, resolution, and intensity measurements were performed with both high and low angular acceptance crystals. At 8 keV, contrast enhancement was a factor of 5 relative to the polychromatic case, in good agreement with theoretical values. At 17.5 keV, monochromatic subject contrast was more than a factor of 2 times greater than the conventional polychromatic contrast. An additional factor of two increase in contrast is expected from the removal of scatter obtained from using the air gap which is allowable rom the parallel beam. The measured angular resolution after the crystal was 0.4 mrad for a silicon crystal.

The realization of these applications has been advanced by the recent marked improvement in available optic quality and reproducibility. Manufacturing progress has been assisted by the development of simulation analyses which allow for increasingly accurate assessment of optics defects. Optics performance over the whole range of energy from 10 to 80 keV can often be matched with one or two fitting parameters. Continuing optics manufacturing challenges include the advance of applications at energies above 40 keV and the production of optics for imaging which are of adequate clinical size. Multioptic jigs designed to increase imaging area have been tested.

Polycapillary x-ray optics are bundles of hollow glass capillary tubes. X rays can be transmitted down a curved hollow tube as long as the tube is small enough and bent gently enough to keep the angles of incidence less than the critical angle for total reflection. A polycapillary fiber is a single fiber created from hundreds or thousands of capillary tubes. A fiber cross section is shown in Figure 1.

Fig. 1 Cross-sectional SEM picture of polycapillary fiber, which has 10-µm channel diameter

Typical capillary channel sizes are between 2 and 12 um. Thousands of such fibers are strung through lithographically produced metal grids to produce a multifiber lens. Alternatively, a larger diameter polycapillary fiber can be shaped into a one-piece, monolithic, optic as sketched in Figure 2.

Fig. 2 Sketch of the interior channels of a tapered monolithic polycapillary optic

The development and study of polycapillary optics and its applications in x-ray lithography, x-ray astronomy, diffraction analysis, x-ray fluorescence, and medicine have been pursued since 1990.

The angular selectivity provided by the small critical angles make polycapillary optics well suited for removal of Compton scattered photons in imaging. The efficient capture of x-ray source emission by the thousands of independent channels in polycapillary collimating optics provides two or three orders of magnitude of intensity gain for monochromatic applications.

2.1.1. Polycapillary Fiber Measurements and Numerical Simulations

Extensive modeling programs used to describe the propagation of x rays along capillaries with complex geometries have been developed. These computer codes are based on Monte Carlo simulations of geometrical optics trajectories and provide essential information on performance, design and potential applications of capillary optics. The geometric algorithm for the simulations is approximated in two dimensions by projecting the trajectory onto the local fiber cross section. Reflectivities are computed from standard tables. The simulation also allows for the roughness and waviness of the capillary walls to be taken into account. Capillary surface oscillations with wavelengths shorter than the capillary length and longer than the wavelength of the roughness are called waviness. The detailed shape of the channel walls is unknown, but waviness is modeled as a random tilt of the glass wall. The tilt angles are assumed to have a Gaussian distribution with width σ.

For high quality glass σ is much smaller than the critical angle, θ_c. Consideration is taken of the fact that the surface tilt angle will affect the probability of x-ray impact on that surface. The effect of waviness on fiber transmission is shown in Figure 3.

Fig. 3 Simulations of transmission spectra for a fiber with waviness alone compared with the experimental data. The maximum waviness to avoid underestimation at mid range energies is less than 0.25 mrad. The simulations do not include the roughness or bending. Bending primarily reduces the transmission at high energies, and roughness reduces the transmission for large incident angles

Waviness is primarily responsible for reduction of transmission at mid-range energies, and additionally, for a further reduction of transmission in geometries which result in large incident angles, for example if the source is moved off axis. A simulation fit including waviness and bending for a single 0.5 mm diameter fiber with 10 µm channels is shown in Figure 4.

Fig. 4 Transmission of a single fiber of the type used for the lens in Fig. 5, compared to simulation analysis with fitting parameters waviness=0.15 mrad, unintentional bending radius R=125 m, and open area 64.5%

Most borosilicate and lead glass optics have simulation fitting parameters which give a Gaussian width for the waviness of 0.12 -0.15 mrad. This is in agreement with slope error data of the Cornell group.

2.1.2.Lens Quality Analysis

The output of a collimating lens at 20 keV is shown in Figure 5.

Fig. 5 Comparison of experimental and simulated transmission of a multifiber collimating lens as a function of energy. An image of the x-ray output of the lens is shown in the inset at upper right. The non-ideal simulation includes a waviness of 0.15 mrad and an unintentional bend with a radius of 125 m for the center fibers.

The nonuniformity was less than 3 % at 8 keV. The transmission of that lens as a function of photon energy is shown in Figure 5. Using the waviness and bending determined from the single fiber simulation of Figure 4, the simulation fits the measured value well. This implies that other effects, such as fiber misalignment or blocked channels, are minimal.

The simulation shown in Figure 4 did not include roughness. Roughness only slightly decreases the specular reflectivity at low angles, and so has almost no impact on the transmission spectra there or in Figure 5, but becomes increasingly important under circumstances in which the angle and number of reflections increases. It can be seen that surface roughness must also be considered to model the effects of moving the source away from the focal point in Figure 6.

Fig. 6 Measured and simulated transmission as the source is moved along the optic axis at 20 keV

2.2.1. Practical Monochromatic Radiography

Some routine imaging applications, such as screening mammography, are extremely challenging in that dose, contrast, resolution and cost are all critically important. Already low subject contrasts are further reduced in a conventional system by averaging over relatively large energy bandwidths. Image contrast is also degraded by scattered radiation. Synchrotron measurements using monochromatic beams have demonstrated higher contrast, but synchrotrons are not clinically available. Using monochromator crystals with a conventional source without an optic is not practicable because the low intensity of the diffracted beam will not allow imaging in vivo before motion blur occurs. Polycapillary collimating optics can allow sufficient diffracted beam intensity to make laboratory or clinical monochromatic imaging possible without a synchrotron.

A preliminary test study using a 1 cm x 1 cm multifiber optic demonstrated the use of polycapillary optics to produce monochromatic images. A schematic of the contrast test object, and the resulting images, are shown in Figure 7 and Figure 8.

Fig. 7 Side view of the polypropylene step contrast object used for Fig. 8

Fig. 8 X-ray image of plastic with 6.6 mm step, obtained with monochromatic beam (left), and conventional beam (right). The step is readily apparent with the monochromatic beam.

The measured contrast of the 6.6 mm step was a factor of 5 higher for monochromatic 8 keV x rays than for the polychromatic case. This was in agreement with theoretical calculations based on the variation of attenuation coefficients with photon energy. Similar enhancements were seen for objects with compositional variation. Preliminary measurements with a very low power source at 17.5 keV showed subject contrast enhancement of a factor of 2, also in agreement with theoretical calculations. This contrast enhancement is in addition to that expected from the reduction of scattered radiation.

The presence of photons that have been Compton scattered out of the primary beam creates an additive background fog which significantly reduces contrast. The parallel beam produced by the crystal would allow removal of scattered radiation by introducing a simple air gap between the patient and the detector.

With conventional tube sources, allowable air gap sizes are limited by geometrical blurring due to the finite source size, as shown in the top of Figure 9. Implementation of a parallel beam would reduce geometrical blur and therefore allow a larger air gap. As shown, the output divergence of the collimating optic degrades the resolution.

Fig. 9 Air gap magnification showing degradation of image due to finite source size

For the monochromatic measurement, good angular resolution was achieved even with a large spot source. The exit divergence from the optic was measured by rotating a high quality crystal in the beam. The rocking curves for the Kα copper line measured with the three different crystals are shown in Figure 10. For the narrowest bandwidth crystal, silicon, the entire rocking curve width is due to the optic divergence. When the measurement is repeated with mica, the width is a combination of the divergence and the crystal width. For graphite, the crystal dominates.

Fig. 10 Rocking curves of three crystals in the output beam of the collimating optic: silicon (left) with FWHM 4.0 mrad, dominated by the optic; mica (middle) with FWHM 4.4 mrad; and graphite (right) with FWHM 42.5 mrad, dominated by the crystal

Resolution was measured by measuring the shadow of a knife edge with an image plate. The resultant intensity profiles, displayed in Figure 11 showed the resolved Mo Kα doublet. The Gaussian fit width of the derivative peak for the Kα₁ line is given in Table 1.

Table 1 Rocking curves and resolution measurements using three different crystals. The rocking curve widths are due to the combined effects of the angular bandwidth of the crystal and the 4-mrad output divergence of the optic. The energy width for graphite is taken to include the whole Kα doublet.

Fig. 11 Knife edge resolution profiles obtained with silicon (left), mica (middle) and graphite (right) crystals

For a perfect crystal and parallel monochromatic input beam, the knife -edge image would be ideally sharp (with a perfect detector). For a crystal with a large bandwidth, such as graphite, the angular width is determined by the optic divergence, since the crystal can accommodate the full range (of angles output from the optic. For a crystal with a bandwidth narrower than the optic divergence, a monochromatic beam would give a width equal to the crystal bandwidth. The 3-eV energy width of the Kα₁ emission line produces an additional angular spread of

Combining the effects of the crystal, lens divergence, and energy spread, the angular distribution of intensity off the crystal can be approximated as a Gaussian distribution,

where ∆θ is the deviation of the output angle from the normal Bragg angle, I(φ) is the angular distribution from the optic, assumed to be a Gaussian of width σ_optic, I(E) is the spectral distribution of the K_α1 line, also assumed Gaussian of width σ_E, ρ(β) is the probability distribution of the planes at angle β from the surface of the crystal, which has a width α given by the crystal bandwidth, the delta function insures that the incidence angle equals the reflection angle, and finally, the output width is given by

The theoretical width is additionally broadened in quadrature by the detector resolution which is 50 µm at 300 mm or 0.2 mrad. The experimental angular resolutions agree fairly well with the calculated resolutions. The theoretical angular resolution from the lens/crystal system would give a spatial resolution for an object on the front side of a 50-mm thick patient of 23 lp/mm with an ideal detector and the silicon crystal. The efficiency η of a crystal can be calculated as

The intensity reflected by the crystal is the input intensity times η multiplied by the reflectivity, R, of the crystal itself. For silicon, the calculated η is 0.005, R is approximately unity, and the measured efficiency is 0.003 ± 0.001. Mica, with a larger bandwidth, α, gives a much higher efficiency, but similar resolution, since for silicon the resolution is limited not by α but by the energy width of the Kα₁ line. Thus, mica should be preferable for rapid imaging.

As mentioned in the previous section, contrast is degraded by scattered radiation. In a conventional polychromatic medical imaging system scatter is removed by inserting a grid with lead ribbons parallel to the incoming beam. Alternatively, scatter can be removed by inserting a capilllary optic between the object and the detector. Because capillary optics have an angular acceptance that is limited by the critical angle (1.5 mrad at 20 keV), scattered photons are not transported down optics channels, but are largely absorbed by the glass walls of the capillary optic. Measured transmission for scattered photons are typically less than 1%. This leads to measured contrast enhancements of around a factor of two at 20 keV.

The tested prototype optics were also tapered and elongated to also provide image magnification, as shown in Figure 12.

Fig. 12 Magnification with a long tapered polycapillary optic showing no increased blurring
after the entrance plane of the optic, as compared to air gap magnification in Fig. 9

Using a tapered prototype optic with an output to input diameter ratio of 1.8, the resolution was increased by the same factor. Further, the modulation transfer function (MTF)was increased at all spatial frequencies, including the diagnostically important lower frequencies. The resolution was not degraded by the capillary structure, which was on a smaller scale (20 μm channel size) than the desired resolution. The results were very promising, but the early optics suffered from low transmission efficiency. Defect analysis indicated that a serious defect was localized glass inclusions.

Partly as a result of the understanding developed from defect analysis, there have been significant advances in the manufacturing of long tapered monolithic optics. Transmission of one of a recent batch of similar tapers is shown in Figure 13.

Fig. 13 Measured and simulated transmission of a 24 cm long tapered optic. Simulated transmission is calculated using an extended single fiber simulation assuming an unintentional bending radius of 188 m at the outermost channels

The transmission is about 70% at 20 keV, and close to 30% at 40 keV. The drop in transmission at higher energies is due to bending of the outer channels of the optic. The simulated transmission in figure 6 was determined using a single fiber simulation with bending which increased gradually from the central to outermost channels. The simulation was fit to a bending radius of the outermost channel of R=188 m. This taper was one of a batch of initial prototypes for placement in a multi-optic jig designed to increase the image area to a value which can be of clinical use. The output of the multi-optic jig is shown in Figure 14.

Fig. 14 Output of multi-optic structure at 20 keV

The transmission is still 41% even when including the interoptic gaps and misalignment between the optics.

The MTF of the triad and various pairs of optics were measured. Simulation analysis showed that the optics must be aligned within 50um to keep the MTF degradation to less than 10 % out 100 to 3 lp/mm and within 25μm to keep the MTF degradation less than 6% out to 5 lp/mm.

Scatter rejection depends on absorption of high angle x rays which do not reflect down the channels. The measured high angle transmission of the optic is very low, about 1% at 40 keV, as shown in Table 2, indicating that there is good absorption.

Table 2. High angle transmission and scatter transmission of the tapered optic. The energy window for the angle transmission measurement was 1 keV using the HPGe detector. The scatter transmission measurements were performed with an image plate and 10 keV wide spectrum.

The high angle transmission was measured by moving the source away from the optic axis such that all x rays are incident at larger angles than the critical angle. The theoretical high angle transmission is calculated using

where
L is the optic length,
μ is the mass attenuation coefficient of the optic,
ρ is the mass density of the glass of the optic, and
f is the fractional open area of the optic, which is 72±3%.
The scatter fraction was measured with and without optic for a 6 cm thick plastic block. For the no optic case, the source-phantom distance was 24 cm and the phantom-imaging plate distance was 0.5 cm. For the optic case, a 2.5 mm tantalum aperture was also attached to the input end of the optic.A Fuji imaging plate was used to record the data. Energy sensitivity was obtained by changing the tube potential and filter, to produce narrow energy spectrum. A lead strip was placed on the source side of the optic. The scatter intensity,Is, which is the intensity measured with the detector aligned behind the strip, and the total intensity near the strip, were recorded at 20 keV and 40 keV. The ratio of these intensities is plotted as a function of lead strip width. The extrapolation of the linear fit to zero strip width is the scatter fraction,

where
I_p is the primary intensity in the absence of scatter and
I_s+I_p is the total intensity.
The scatter fractions, with and without the optic, at 20 keV and 40 keV, are listed in Table . The optic reduces the scatter fraction by nearly a factor of 8 even at 40 keV. The scatter transmission of the optic, calculated using

where
T_p is the primary transmission of the optic,
SF is the scatter fraction of the phantom without the optic, and
SF^op is the scatter fraction of the phantom with the optic, is listed in Table 2.
The scatter transmission should be equal to the high angle transmission if both measurements were performed using the same energy windows.
Contrast measurements show the enhancement due to the removal of scatter by the optic are shown in Table 3.

Table 3. Contrast resulting from holes of increasing depth in a 5 cm thick plastic object. The contrast measured at 20 and 40 keV, with and without the optic are all in good agreement with theory. The contrast ratios range from nearly a factor of two for the lower energy to a factor of three for the higher energy, where the scatter fraction is larger.

The contrast is a factor of three higher at 40 keV with the optic. For higher energy applications, or for cases where shorter optics are desirable, the scatter rejection optics should be made of lead glass. Short lead glass scatter rejection optics could also be used for imaging radioactive sources, in a manner similar to gamma cameras.

Marked improvement in simulation accuracy and optic quality have emerged in the last five years. Systematic measurements allow the separate assessment of curvature, waviness, roughness, channel blockage, and channel misalignment on input and output.Improvements in optic quality have lead to practical implementation of many new applications and the potential development of a number of others. Microdiffraction using focused beams and high contrast mammography are emergent new areas.