Fig 1.
The scanning geometry of nano-CT at BSRF.
(a) is the simplified scanning geometry and x-ray optical layout is here ignored. (b) depicts three Cartesian coordinate systems: (X, Y, Z) for projection image acquisition, (x, y, z) for image reconstruction and (x′, y′, z′) for the stage.
Fig 2.
The plane integral curves of the sample with the shift along vertical axis z.
Fig 3.
The trajectory of the center of mass of the sample.
(a) depicted the rotation trajectory of the center of mass of the sample in the two dimensional plane without the horizontal shift along x. (b) shows the position shift of the mass of center when the horizontal shift along x happens.
Fig 4.
The influence of the geometry misalignment on the CT images.
(a) and (b) are two projections under two different view angles. (c)-(g) are the projection sinograms and (h)-(l) the reconstructed CT images. (c) and (h) correspond to the case without jittering, (d) and (i) with shift along axis x, (e) and (j) with shift along axis y, (f) and (k) with shift along axis z and (g) and (l) with shifts along x, y and z simultaneously.
Fig 5.
The correction procedure and results for the vertical shift.
(a) shows how to produce the plane integral curve at the first view angle. (b) depicts the vertical shift between two view angles by the plane integral curves. (c) is the cross correlation curve of the two signals in (b). (d) compares the calibrated curve with the simulated shift curve. (e) shows how to form the sinogram from the recorded two dimensional projection image sequence. (f) is the calibrated sinogram. (g) and (h) are the reconstructed CT images by the algorithm in Eq (1) with the sinogrms in (e) and (f) respectively. (i) provides the grey value profiles of the 200th row of the images in (g), (h) and the phantom.
Fig 6.
The correction procedure and results for the horizontal shift.
(a) shows the actual trajectory of the center of mass of the phantom. (b) presents the fitted trajectory using Matlab function “lsqcurvefit”. (c) compares the calibrated curve with the simulated shift curve. (d) is the corrected trajectory of the center of mass of the phantom. (e) and (f) are the reconstructed CT images by the algorithm in Eq (1) with the sinogrms in (a) and (d) respectively. (i) provides the grey value profiles of the 200th row of the images in (e), (f) and the phantom.
Fig 7.
The TXM nano-CT projection images of ZrB2/SiC nanocomposite ceramic.
The first row is the original images recorded by CCD camera under five view angles. The second row is the ones after logarithm operation.
Fig 8.
The correction procedure and results for the vertical shift with the TXM nano-CT experimental data.
(a) is one of the two dimensional projection images after logarithm operation. (b) depicts the plane integral curve at the first view angle marked by the solid blue line and the one at other view angle marked by the dashed red line. (c) shows the cross correlation result of these two curves in (b). (d) is the correction curve. (e) and (h) are the sinogram and the CT image of the 690th row of the projection before correction. (f) and (i) are after correction. (g) shows the difference between (e) and (f). (j) shows the difference between (h) and (i). (k) and (n) are the sinogram and the CT image of gold particles before correction. (l) and (o) are after correction. (m) shows the difference between (k) and (l). (p) shows the difference between (n) and (o).
Fig 9.
The correction procedure and results for the horizontal shift with the TXM nano-CT experimental data.
(a) is the sinogram of the 690th row of the projection with a size 360 × 1024 after the vertical shift correction. (b) depicts the actual trajectory of the center of mass and the fitted one. (c) is the calibrated sinogram and the trajectory of the center of mass using the correction curve in (d). (e) and (h) are the sinogram and the CT image before correction. (f) and (i) are after correction. (g) and (j) show the differences of sinograms and CT images before and after correction. (k) and (m) are the sinogram and the CT image of gold particles before correction. (l) and (n) are after correction.
Fig 10.
The false color map of the typical slice in Fig 9i.