Contents

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 Straight line trajectory 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. Straight line trajectory translation CT’s technical component can be used in HT Edition Series. Typical types of Straight line trajectory translation CT are Translation parallel beam CT, Translation fan-beam CT, Translation cone-beam CT and Translation parallel fan-bam CT. This page discuss the flow that leads the theorem of each CT for using the principle of Straight line trajectory CT used in the TomoShop®: HT Edition series.

The examples of Straight Line Trajectory Translation CT Reconstruction

To begin with, before stating the theorem of each CT for using the principle of Straight line trajectory CT, it discusses Translation parallel beam theorem and Projection slice theorem.

Principle Theorems (Translation Parallel Beam Theorem and Projection Slice Theorem)

The principles that used by HT Edition series includes Translation parallel beam theorem and Projection slice theorem as the basic components. Therefore, those are discussed here.

Translation Parallel Beam Theorem 

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.

Projection Slice Theorem

Formula of CT projection intercept theorem is as follows.

In the next, it would be discussed the each CT theorem by using the formulas discussed in here.

Translation Parallel Beam CT Reconstruction

From Translation parallel beam theorem, an accurate image reconstruction formula (see below) will be derived.

Translation Fan-beam CT Reconstruction

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

Translation Cone-beam CT Reconstruction

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

Translation Parallel Fan-beam CT Reconstruction

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