## 1 Introduction
The X-ray energy of the beam will be defined by the pitch position of both multilayers. In practice, the energy calibration must be performed during the hot commissioning stage in order to achieve the true X-ray energy for user operation. PDS vacuum section #3 consists of a diagnostic screen, white beam slit B, and VBM. The substrate material of the VBM is also single-crystal silicon. There are two stripes in the VBM with the coating material of Rh and Pt. The choice of the stripe and the pitch position of the VBM will define the cut off X-ray energy at the high-energy end. Lastly, PDS vacuum section #4 consists of another diagnostic screen, white beam slit C, photon shutter, and safety shutter. Figure 1: Four different beam modes in MCT beamline: (**a**) white beam, (**b**) pink beam, (**c**) monochromatic beam, and (**d**) monochromatic beam without a third harmonic contribution. There are two granite tables each in experiment hutch B and C, respectively. The first table (Table 1) in experiment hutch B is the work horse table for absorption-contrast and propagation-based phase-contrast imaging. The sample stage and detector stage is mounted in Table 1 in the early stage of user operation with movable sample-to-detector distance. A robot for rapid sample exchange is also mounted in this table. In future operation, the detector stage can be moved to other tables for other imaging modality. Table 2 (the second table in hutch B) will be used for a nano CT-based system with the detector in Table 2. The grating-based system and speckle-based system will be mounted in Table 2.  
The MCT beamline has been designed in response to the needs of the user community (including industry) for high-resolution imaging applications and characterization of materials. This will provide enormous benefit to many 3D X-ray imaging applications [15; 16; 17] such as industrial inspection, medicine, material science, chemistry, and biomedical imaging. There will be two imaging modalities offered by the MCT beamline in the early stages of its operation. These are absorption-contrast and phase-contrast modes. In the phase-contrast mode, we will use a propagation-based phase-contrast imaging set-up. Propagation-based phase-contrast imaging has a simple experimental set-up that does not require any additional optical elements. This method merely allows a spatially coherent wave field to propagate far enough distance from the sample so that the diffraction fringes can be detected by the detector. Due to its simplicity, this propagation-based phase-contrast modality is readily applied to 3D computed tomography (CT) imaging [18; 19; 20]. Meanwhile, the absorption-contrast mode is attained when the sample-to-detector distance is very small. In this way, the phase-contrast is easily achieved by moving the detector away from the sample. The interaction between the X-ray beam and the sample can be generally described by the complex refractive index, \(n=1-\delta+i\beta\), where \(\delta\) is related to the phase shift and \(\beta\) is related to the attenuation. The contrast in conventional X-ray projection images primarily depends on the linear attenuation coefficient, \(\mu(\lambda)=4\pi\beta(\lambda)/\lambda\), where \(\lambda\) is the X-ray wavelength. The X-rays traverse point \(\mathbf{r}\) as a specific location in an object, travel along a straight line \(L(x,\theta)\), indicated by the path length, \(t\), and are distinctively defined by the rotation angle, \(\theta\), and the end-point, \(x\), at the projection (detector) plane. Hence, \(\mu(\mathbf{r},\,\lambda)\) can be written as \(\mu(\mathbf{r},\,\lambda)=\mu(x,\theta,t,\lambda)\). The output intensity, \(I\), in the single wavelength case is provided by integrating the attenuation through the sample, as follows:  
\[I(x,\theta,\lambda)=I_{0}.e^{-\int_{L(x,\theta)}\mu(x,\theta,\lambda)dt}=I_{0 }.e^{-(\mathbf{\mathcal{R}}\mu)(x,\theta,\lambda)} \tag{1}\]  
where \(I_{0}\) is the incident intensity and \(\mathbf{\mathcal{R}}\) is the Radon transform [21].