Cone-Beam 3-D Reconstruction with Double Circular Trajectory

Rizo, P.; Grangeat, Pierre; Sire, Pascal; Lemasson, Ph.; Delageniere, S.

doi:10.1557/proc-217-117

Cited by 2 publications

(2 citation statements)

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“…We initially introduced this method [2][3][4][5][6][7][8][9][10][11][12][13][14]. The principle is to use the reconstruction of a set of concentric spheres to measure the response of the reconstruction code to particular frequencies.…”

Section: Modula Non Transfer Funciton Measurementsmentioning

confidence: 99%

“…To check the response of the reconstruction code at very low frequencies, like in [2,10] we placed a set of simulated uniform spheres on one of the rotation axis of the system, and we reconstructed it with the Feldkamp code and the Radon code with single circular source trajectory. For Radon, we present one case with linear interpolation of the shadow area and one without interpolation.…”

Section: Level Dlstortionsmentioning

confidence: 99%

See 1 more Smart Citation

X-Ray Cone Beam Tomography with Two Tilted Circular Trajectories

Rizo

Grangeat

Sire

et al. 1992

Review of Progress in Quantitative Nondestructive Evaluation

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Recently 3-D cone-beam tomography has become of interest for the nondestructive evaluation of advanced materials. The main field of application in nondestructive testing is the evaluation of structural ceramics. Study of such materials implies high density resolution and high sensitivity to cracks. In fact, with a single circular source trajectory, when the conebeam aperture increases, density is underestimated and cone shaped artifacts may appear at interfaces in the sampie even at relatively small aperture [1][2][3]. These artifacts limit the thiekness we can ex amine with a planar source trajectory. To maintain optimal reconstruction accuracy with a circular source trajectory, the angular aperture must remain within ±10 0 • However Kudo and Saito [4] showed that this limit can be slightly overcome by using a special interpolation of the shadow area. But to examine greater thicknesses and to maintain resolution, we must widen the cone-beam aperture thereby decreasing accuracy. To overcome these aperture limitations, Tuy [5] introduced the double circular source trajectory idea.Until now, most of the experiments presented in the literature were performed with a planar source trajectory [1,2,3,4,6]. Recently, a new method presented by Smith [7,8] has been applied to nonplanar source trajectories by Kudo and Saito [9]. The inversion presented by Kudo uses the Hilbert transform of the first derivative of the Radon transform. This inversion has been experienced with real data on two circular trajectories at 90° with intersection of the two axis of the trajectories (orthogonal scan).We have presented [10] reconstructions on simulated with double circular source trajectories with an exact reconstruction method using the inversion of the first derivative of the 3-D Radon transform. These simulations were performed with an angle smaller than 90° between the two trajectories. Here we quantify the advantages of this method and we present experimental reconstruction in this implementation. We show also that according to the Radon space sampling, the axes of the two trajectories do not have to intersect, but they must be close enough. MATHEMATICALBACKGROUNDGrangeat [11,12] showed that we can link exactly the X-ray transform of an object and the first derivative of its 3D Radon transform. Given an object function f(M) where M is a given point of the space, let us define the X-ray transform Xf(S,A), as the radiographie reading at point A corresponding to a source position S: +00Xf(S,A)= J f (S + a.u~)da with u~ = a = 0

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