To demonstrate the influence of the extended source on the device response, the ray locations at the device output are shown in for different anode point positions. The ray output locations are strongly influenced by the anode point location, demonstrating that an experimentally significant anode size has been chosen. The ray locations are similar to those shown in previous simulation studies [27
]. It is noteworthy that the ray locations alone do not provide the wavefield intensity and do not enable the evaluation of spatial coherence properties.
Fig. 2 Simulation results showing the spatial distribution of ray locations at the polycapillary device output plane with varying input anode source point locations. The panels show (from left to right) the anode source point locations (−6.4 μ (more ...)
The intensity of the simulated output wavefield, computed in step 3, containing responses from all anode points is shown in . Additionally, the intensity of wavefields propagated away from the output plane, as computed in step 4 with a conventional Fresnel propagation operator, are shown. As the wavefields propagate away from the device, the intensity from the individual capillaries begins to diverge and overlap somewhat while the response from the overall device remains relatively collimated. This general behavior corresponds well with experimental results in the literature [37
Finally, the spectral degree of coherence, computed in step 5 from the wavefield responses of individual anode source points, or modes, is shown in . The two-point spectral degree of coherence is shown in each frame as an image with reference to a point r1 in the output plane. The simulated optic has a highly structured coherence response that, in the output plane, is characterized by several “bright spots” corresponding to a high spatial degree of correlation with r1. As the wavefields propagate away from the device, the structured spatial response begins to disperse, causing a more uniform effective spectral degree of coherence of approximately μeff = 0.3, especially when referenced to r1 = (0,0).
Fig. 4 Simulation results showing the spectral degree of coherence of the polycapillary device output wavefield. The spectral degree of coherence is a two-point quantity, and these data are shown as a function of r2 with r1 = (0, 0) on the left (
Media 2) and (more ...)
This framework for the analysis of polycapillary device spatial coherence properties opens the door for more comprehensive investigations of the influence of device parameters on the coherence response and optimization of these parameters for specific applications. One potential application for collimating x-ray optics generally is in phase-contrast imaging techniques. In-line phase contrast methods, specifically, suffer from a trade-off between the source coherence necessary for generation of phase-contrast features and the source flux. Collimating optics can potentially alter this relationship by capturing a larger solid angle of an x-ray tube’s output than would be possible otherwise. A key question, however, is how the wavefield coherence properties are changed due to propagation through the polycapillary device and the effect on image quality. The framework described here could potentially be used to evaluate the suitability of these devices for phase-contrast imaging. In addition, the simulation methods presented here may be useful for investigation of the wavefield output from polycapillary devices. Experimental measurements of these devices have demonstrated that the output intensity of certain devices contains ringing features that are strongly suggestive of the Fraunhofer diffraction patterns found due to light propagation through an aperture [17
]. These effects are best characterized when the phase of propagating rays are accounted for in the output, especially as capillary devices are manufactured at smaller diameters where these patterns are most evident [18
]. Interference effects, which are well known to occur in multiple-reflection optics [8
], may also be investigated with access to simulations of the wavefield without the need for an analytic solution to the wave equation.
The framework presented in this work consists of an adaptable five-step process. In future work, these steps may be altered to address specific topics of interest. For example, enhanced polycapillary device simulation methods may be incorporated into step 2. Specifically, the effects of capillary waviness and surface roughness have not been included here and may potentially have a substantial effect on the coherence properties of a device. In addition, a number of methods exist to perform the wavefield construction in step 3, the accuracy of which could form the basis of future studies. The methods presented here form the basis for improved understanding of the properties of polycapillary devices and provide a framework for future investigations into the effects of polycapillary optical devices on spatial coherence properties.