To configure correct planar CT imaging geometry

[pingchanglee]

I try to reproduce CT reconstruction in the paper Laminography in the Lab: Imaging planar objects using a conventional x-ray CT scanner
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In this study, the object is tilted and the object stage is rotate along the tilted axis.

Based the TIGRE demo example, DEMO 18: Arbitrary axis of rotation, I tried to reconstruct the LEGO volume.
According to the demo example, it says:

In TIGRE this has been implemented by defining the rotation with 3 angles, specifically the ZYZ configuration of Euler angles.

So, I first converted the rotation angles to Euler angles.

  ### Convert to ZYZ Euler angle 
  rad = np.pi / 180 
  tilt_radian = rad * 30
  unit_vec = np.array((np.sin(tilt_radian) , 0, np.cos(tilt_radian)))
  geo.angles = np.zeros((n_proj, 3))
  
  for i in range(n_proj):
      if i == 0:
          geo.angles[i,:] = np.array((angles[i], tilt_radian, 0))
      else:
          rot = R.from_rotvec( angles[i] * unit_vec)
          euler_angle = rot.as_euler('ZYZ')
          geo.angles[i,:] = euler_angle

But the reconstruction result is totally wrong.

However, when I set the angles this way:

  n_proj = angles.shape[0]
  zeros_array = np.zeros((n_proj, 1), dtype=np.float32)
  tilt_array = np.ones((n_proj, 1), dtype=np.float32) * 30 * np.pi / 180
  geo.angles = np.hstack((angles.reshape(n_proj, 1) , tilt_array, zeros_array))

the reconstruction result seems right!
This result confused me, since this is not ZYZ.

Hopefully, there is someone can help me to figure this out. Thanks!

In all references listed in Further Reading and code, talk very little about the spherical trajectory of both detector and X-ray source. Is it possible to elaborate this part in TIGRE?
Thanks!!!

Both test code and the projection data are available here

[1999kevin]

Hi, do you know if this problem has been solved? I also wonder if it is a ZYZ configuration. If not, what is the configuration? I also try to reconstruct the data while having 2 ratoting axises but te results are not so good

[AnderBiguri]

Sorry @pingchanglee , I had completely missed this. Are you still struggling with it? @1999kevin yes its ZYZ as the demos show. What is the issue?

[1999kevin]

Thank you very much. A new issue has been posted.

[pingchanglee]

@AnderBiguri
It is my bad.
After going over the paper again today, I find that the coordinate system described in the paper is not the same as TIGRE but I carelessly missed it before!
Now, I have no problem about this topic. Thank you guys!