Reconstruction of the complex refractive index in nonlinear phase contrast tomography

Figures & data

Figure 1. Experimental set-up in propagation-based phase contrast tomography from a single propagation-based phase contrast image per projection showing the coordinate system.

Table 1. Values of the $\mathit{\delta }$ and $\mathit{\mu }$ values for the materials in the object, for 24 keV X-rays, from http://henke.lbl.gov/optical_constants.

Material	$\mathit{\delta }({10}^{-7})$	$\mathit{\mu }({\mathrm{m}}^{-1})$
PMMA	4.628	41.2
Al	9.396	502.6

Figure 2. Horizontal section of the true $\mathit{\beta }$ and $\mathit{\delta }$ maps.

Figure 3. Horizontal section of the initial blurred $\mathit{\beta }$ and $\mathit{\delta }$ maps.

Figure 4. Section of the reconstructed $\mathit{\beta }$ and $\mathit{\delta }$ maps for a PPSNR of 24 dB.

Figure 5. Diagonal profiles of the $\mathit{\beta }$ map:intial map (blue), true map (red), reconstructed map (Black) (PPSNR $=$ 24 dB).

Figure 6. Diagonal profiles of the $\mathit{\delta }$ map:intial map (blue), true map (red), reconstructed map (black) (PPSNR $=$ 24 dB).

Figure 7. Evolution of the partial data term corresponding to the selected projection angle as a function of the iterations number without noise (full line) and with noise (dotted line) for a $\mathrm{PPSNR}=24$ dB.

Figure 8. Evolution of the normalized mean square error on $\mathit{\delta }$ as a function of the iterations number without noise (full line) and with noise (dotted line) for a PPSNR $=$ 24 dB.

Figure 9. Evolution of the normalized mean square error on $\mathit{\beta }$ as a function of the iterations number without noise (full line) and with noise (dotted line) for a PPSNR $=$ 24 dB.