## 3 Experimental Results  
Experimental X-ray imaging data were collected using the Xradia(r) micro XCT200 (Carl Zeiss X-ray Microscopy, Inc., Pleasanton, CA, USA) polychromatic X-ray laboratory source combined with the PiXirad detector system, as shown in Figure 6. X-ray spectra were recorded using the XR-100T-CdTe AMPTEK detector designed to characterize X-ray tubes and for X-ray spectroscopy applications. The source was a closed X-ray tube (Hamamatsu) consisting of a tungsten target and operated at a tube voltage of 40 kVp at a power of 10 W. The PiXirad detector was cooled down to an operating temperature of \(-20\)\({}^{\circ}\)C using a combination of water cooling and nitrogen gas. A Galili motion controller was added to the system and was connected between the PiXirad detector and the rotation stage in order to synchronize their communication during the tomography scan. The effective image pixel size is defined by the physical detector pixel size divided by the geometric magnification factor, \(M\), where \(M=\frac{R_{1}+R_{2}}{R_{1}}\). Here, \(R_{1}\) is the source-to-sample distance, which is equal to 125 cm, and \(R_{2}\) is the sample-to-detector distance equal to 115 cm. In this experiment \(M=1.9\), giving an effective pixel size of 30 \(\upmu\)m. The phantom sample (QRM GmbH) consisted of a 10 mm diameter cylinder of epoxy resin with three inserts (of 2 mm diameter each) of HA400, HA800 and HA1200. The phantom sample composition in the experiment was identical to that used in the simulation. Figure 5: Calculated \(\chi^{2}\) error plots as a function of the energy bandwidth in the absence of noise (left-hand column) and with 1% noise included (right-hand column), showing the separation of (**a**,**b**) HA400, (**c**,**d**) HA800, and (**e**,**f**) HA1200 from the surrounding epoxy matrix. The PiXirad detector system simultaneously outputs 4 images, each corresponding to a different energy threshold. Whilst there is significant flexibility over the choice of energy threshold, due to the finite energy resolution of the detector they cannot be chosen arbitrarily and are restricted to certain ranges as determined by the PiXirad control software [16]. When setting energy thresholds in the control software for the PiXirad detector the software takes into account the finite energy resolution of the detector and automatically limits the minimum separation allowed between thresholds. The energy resolution values (and hence minimum separation) for each of the thresholds used in this paper are shown in Figure S2. Based on the possible energy thresholds, the following threshold values were used for the experiment: \(E_{1}=16\) keV and \(E_{2}=21.1\) keV, and \(E_{3}=23.9\) keV and \(E_{4}=29.7\) keV resulting in energy bandwidths of 5.1 keV and 5.8 keV, respectively. Note that the small discrepancy between the experimental energy threshold values and the simulated threshold values is well below the energy resolution of the PiXirad. Experimental 2D projection data was first collected from a well-characterized phantom sample comprising a HA400 insert embedded in epoxy (identical to Figure 2a). The detector exposure time was set to 3.5 s which was determined by the dynamic range of the detector at the lowest energy threshold (where the flux was greatest). The total time for the X-ray \(\upmu\)CT experiment was 2 h including sample preparation and alignment; with 45 min for actual data collection which was required in order to build up sufficient statistics for analysis. Correction of the measured intensity to account for the effect of charge-sharing was applied according to Equation (S1) (see Supplementary Material) and the procedure summarised in Figure 3 was used to separate the HA400 insert from the epoxy. The experimental results are shown in Figure 7a,b. Note that in Figure 7b transmission through half of the resin matrix was blocked due to the presence of additional inserts (HA800 and HA1200) within the phantom sample.