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Principle of Straight Line Trajectory Translation CT

Principle of Straight Line Trajectory Translation CT

In industrial non-destructive inspection for inspecting defects of electronic components, particularly in the line of automatic inspection apparatus for inspecting substances, the most commonly applied method is straight line type rather than the circumference type.

Our proposed Translation CT which is our proposed straight track technical methods can obtain the 3D tomographic data in line inspection of linear movement that does not add the rotation of X-ray source, rotation of the camera and rotation of the sample. Translation CT technical component can be used in HT Edition Series. This page discuss the basic principles of Translation CT.

1. Translation Parallel Beam and Projection Slice Theorem

For each projection angle θ of the translation of parallel beam, next equation can be applied for projection data.

ht_para_ct_proj_equa0

Fourier transform can be applied to the above equation.

ht_para_ct_proj_equa2

ht_para_ct_proj_equa3

ht_para_ct_proj_Eng

Formula of CT projection intercept theorem is as follows.

ht_para_ct_proj_slice_theorem

 

2. Translation Parallel Beam (Parallel-beam) CT Reconstruction

From CT projection intercept theorem, an accurate image reconstruction formula(see below) will be derived.

ht_para_ct_proj_recon

 

3. Translation Fan-beam (Fan-beam) CT Reconstruction

From the reconstruction formula of accurate parallel beam(see above), the accurate fan-beam CT reconstruction formula will be derived.

ht_fan_ct_proj_Eng

ht_fan_ct_proj_recon

 

4. Translation Cone Beam (Cone-beam) CT Reconstruction

Extend to conventional FDK type from re-constitutive equation of the translation fan-beam CT. Then, re-constitutive equation of translation cone beam CT reconstruction can be obtained.

 

5. Translation Parallel Fan-beam (Parallel-fan-beam) CT Reconstruction

Extend to conventional FDK type from re-constitutive equation of the translation parallel beam CT. Then, re-constitutive equation of translation parallel fan beam CT reconstruction can be obtained.

6. Examples of Translation CT Reconstruction

Next images show examples of Translation CT Reconstruction.

ht_recon_VR_0

ht_recon_VR_1

 

Please feel free to inquire.

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