## 3 Experimental Results
The application of this mask results in the sudden drop in transmission but does not otherwise impact the separation of the insert. The tube voltage was then increased to 80 kVp to retrieve the denser (HA800, epoxy and HA1200, epoxy) material inserts as shown in Figure 7c-f. The thickness of the material pairs (HA400, epoxy), (HA800, epoxy) and (HA1200, epoxy) retrieved using the combined energy-resolved detector and matrix method are observed to be in very good agreement with the known component thicknesses (supplied by the manufacturer). The calculated \(\chi^{2}\) error inside the range indicated by the black arrows can be seen on each plot. Figure 6: The experimental set-up consisting of the X-ray source, sample stage, and the PiXirad detector. Following a successful proof-of-concept with the phantom, the matrix approach using the PiXirad detector was applied to 3D material separation of a'real-world' biological sample comprising a mouse hand (with dimensions of 5 mm (H) \(\times\) 14 mm (V)). The sample was provided by Dr. [PERSON] (based at the Walter and Eliza Hall Institute of Medical Research) [52]. The sample was stored in formalin but removed from solution during the measurement and placed inside a plastic container to prevent dehydration. The same experimental conditions (e.g., energy thresholds and exposure time) were used for tomographic imaging of the mouse hand. In the present case the attenuation coefficient values used for bone were \(\mu_{bone}(\Delta E_{a})=1109\) m\({}^{-1}\) and \(\mu_{bone}(\Delta E_{b})=392\) m\({}^{-1}\) and the attenuation coefficient values for soft tissue are \(\mu_{diss}(\Delta E_{a})=102\) m\({}^{-1}\) and \(\mu_{diss}(\Delta E_{b})=47\) m\({}^{-1}\). These attenuation coefficients were derived from the X-ray properties of HA400, which has similar X-ray attenuation characteristics to mouse bone [53] and water, which is commonly used to represent hydrated soft tissue. The variation of these coefficients as a function of the X-ray energy were obtained from the National Institute of Standards and Technology (NIST) database [50]. In the case that the X-ray attenuation properties of the sample components are not known a priori, they can be measured in a separate experiment using a coupon of  
Figure 7: Comparison of the retrieved thickness (red solid lines) to the ‘actual’ thickness (blue dashed lines) determined from the manufacturer’s specifications for the separation of (**a**,**b**) HA400, (**c**,**d**) HA800, and (**e**,**f**) HA1200 from the surrounding epoxy matrix. The sudden drop in intensity in (**b**,**d**,**f**) are due to the application of a mask at the detector plane to remove the transmission due to the other inserts. Note that 100 vertical pixels were binned to improve the experimental SNR. The calculated \(\chi^{2}\) error inside the indicated distance range shown by black arrows, can be seen on each plot. The experimental data of (**c**–**f**) were taken at a tube voltage of 80 kVp. known thickness and measurements of the incident and transmitted X-ray intensity [54]. The attenuation coefficients within the energy ranges of \(\Delta E_{a}\) and \(\Delta E_{b}\) can then be calculated using Equation (3). The HA400 calibration data was used to correct for the effects of charge-sharing (see Equation (S1) and Figure S1 in Supplementary Material). For the tomography scan, 360 projections were collected by rotating the sample in 0.5 degrees steps between \(-90^{\circ}\) and \(+90^{\circ}\). An example of the corrected projection showing the four energy threshold images is presented in Figure 8a-d. The matrix equation method using the PiXirad detector yielded the results shown in Figures 7f and 8e (with 2 \(\times\) 2 binning applied). This step was repeated for each projection resulting in two tomographic datasets, one for the soft tissue and the other for the bone. A filtered back projection (FBP) reconstruction algorithm together with ring artefact correction was used to obtain the final 3D reconstruction (Figure 9).