- 1 Principle of Straight Line Trajectory Translation CT
- 1.1 1. Translation Parallel Beam and Projection Slice Theorem
- 1.2 2. Translation Parallel Beam (Parallel-beam) CT Reconstruction
- 1.3 3. Translation Fan-beam (Fan-beam) CT Reconstruction
- 1.4 4. Translation Cone Beam (Cone-beam) CT Reconstruction
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.
For each projection angle θ of the translation of parallel beam, next equation can be applied for projection data.
Fourier transform can be applied to the above equation.
Formula of CT projection intercept theorem is as follows.
From CT projection intercept theorem, an accurate image reconstruction formula(see below) will be derived.
From the reconstruction formula of accurate parallel beam(see above), the accurate fan-beam CT reconstruction formula will be derived.
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.
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.
Next images show examples of Translation CT Reconstruction.