Variable zoom X-ray computed tomography method for composites
View Patent ↗A variable zoom X-ray CT method can significantly improve resolution for structures with large in-plane dimensions, for example to detect complex structural damage due to low-velocity impact in large thin composite laminate panels. The variable zoom method comprises emitting an X-ray beam from an X-ray source to project a region of interest (ROI) of a specimen within a field of view (FOV) onto a detector. Projections of the ROI are scanned with the detector while rotating the specimen about a rotational axis of a specimen stage and translating the specimen stage along an acquisition trajectory between the X-ray source and the detector. The acquisition trajectory specifies a source-to-object distance (SOD) between the X-ray source and the rotational axis of the specimen stage at each rotation angle of the specimen stage. A reconstruction computer reconstructs a three-dimensional volume of the specimen from the projections scanned by the detector.
1. A variable zoom method of an X-ray computed tomography (CT) scanner, the method comprising:
emitting an X-ray beam from an X-ray source to project a region of interest (ROI) of a specimen within a field of view (FOV) onto a detector;
obtaining projections of the ROI of the specimen with the detector while rotating the specimen about a rotational axis of a specimen stage and translating the specimen stage along an acquisition trajectory between the X-ray source and the detector; and
reconstructing, by a reconstruction computer, a three-dimensional volume of the specimen from the projections scanned by the detector, wherein the acquisition trajectory specifies a source-to-object distance (SOD) between the X-ray source and the rotational axis of the specimen stage at each rotation angle of the specimen stage.
2. The method of claim 1 , wherein the X-ray source and the detector are stationary while rotating and translating the specimen.
3. The method of claim 1 , wherein the ROI is projected onto a central area of the detector.
4. The method of claim 1 , wherein the acquisition trajectory translates the rotational axis of the specimen stage along a center of the FOV.
5. The method of claim 1 , wherein an initial SOD along the acquisition trajectory is SOD ROI , wherein the SOD ROI is a closest SOD at which the ROI is fully within the FOV.
6. The method of claim 5 , wherein the SOD ROI is a closest SOD at which the ROI remains within the FOV while a rotation angle of the specimen stage is less than a threshold angle.
7. The method of claim 6 , wherein the SOD at each rotation angle of the specimen stage is:
SOD(θ)=max{SOD ROI ,S 0 +½( T p +( S p −T p )|sin θ|)},
where θ is the rotation angle of the specimen stage, SOD(θ) is the SOD at each rotation angle of the specimen stage, SOD ROI is the initial SOD, S 0 is a safety offset, S P is a specimen width, and T P is a specimen thickness.
8. The method of claim 7 , wherein SOD(θ)=SOD ROI while the rotation angle of the specimen stage is less than the threshold angle.
9. The method of claim 1 , wherein reconstructing the three-dimensional volume comprises:
weighting a backprojection of a set of filtered radiographs with a weighting factor based on the SOD at each rotation angle of the specimen stage.
10. The method of claim 9 , wherein the weighting factor comprises:
w
v
z
(
θ
)
=
S
O
D
(
θ
)
S
D
D
,
where w vz is the weighting factor, SOD(θ) is the SOD at each rotation angle of the specimen stage, and SDD is a source-to-detector distance.
11. The method of claim 9 , wherein reconstructing the three-dimensional volume further comprises:
calculating a projection to volume transformation for each projection angle and the SOD to produce the backprojection of the set of filtered radiographs; and
adding weighted backprojected pixel values to voxels in the three-dimensional volume based on an interpolation method to produce the reconstruction of the three-dimensional volume.
12. The method of claim 11 , wherein reconstructing the three-dimensional volume further comprises:
calculating a ramp filter in the frequency domain;
calculating weighted and filtered radiographs based on the ramp filter and applying a periodic-smooth decomposition to produce the set of filtered radiographs.
13. The method of claim 12 , wherein calculating the ramp filter in the frequency domain comprises calculating a one-dimensional direct Fourier Transform on:
h
[
n
p
x
]
=
1
(
2
p
x
)
2
{
1
,
n
=
0
0
,
n
even
-
1
/
(
π
n
/
2
)
2
,
n
odd
,
where n is and integer n∈[−n x zp ,n x zP ), p x is a row pixel spacing, n x zp =(2n x −1) 2 rounded to the next power of two, and n x is a number of pixels in a projection row.
14. The method of claim 11 , wherein when calculating the projection to volume transformation, projection coordinates are different for each projection angle according to varying SOD(θ).
15. The method of claim 14 , wherein calculating the projection to volume transformation comprises:
calculating a three-dimensional coordinate transformation (x, y, z) T =R(θ)R V ·(t, s, r) T , where (t, s, r) are reconstructed volume coordinates, (x, y, z) are projection coordinates, R V is a volume transformation matrix and R θ is a matrix of specimen rotation.
16. The method of claim 11 , wherein the interpolation method is a distance-driven method or a separable footprints method.
17. The method of claim 11 , wherein the weighted and filtered radiographs are weighted to account for different ray lengths in a cone X-ray beam.
18. The method of claim 17 , wherein calculating the weighted and filtered radiographs and applying the periodic-smooth decomposition comprises calculating:
S
θ
(
x
,
y
k
)
=
[
P
θ
′
(
x
,
y
k
)
*
h
(
x
)
]
=
p
x
IFFT
{
FFTP
θ
′
(
x
,
y
k
)
Z
P
·
FFTh
[
n
p
x
]
shift
}
,
and
P
θ
′
(
x
,
y
k
)
=
P
S
[
P
θ
(
x
,
y
k
)
1
+
(
x
2
+
y
k
2
)
/
S
O
D
2
(
θ
)
]
,
where FFT is a one-dimensional direct Fourier transform, IFFT is a one-dimensional inverse discrete Fourier transform, h[np x ] shift is a half-spaces of the ramp filter h[np x ] swapped using a fftshift method, n x zp is a zero-padded radiograph to avoid inter-period artefacts, and PS is the periodic-smooth decomposition such that only a periodic part of a weighted radiograph boundary is used.
19. The method of claim 11 , wherein adding the weighted backprojected pixel values to voxels in the three-dimensional volume based on an interpolation method comprises calculating:
v ( t,s,r )=Σ θ w vz (θ) z d 2 (θ) S θ ( xz d ,yz d ),
where
z
d
(
θ
)
=
1
1
-
z
/
S
O
D
(
θ
)
,
v(t, s, r) is a reconstruction volume value, the summation is calculated for all coordinate triads (t, s, r), interpolated values v(t, s, r) are obtained using the interpolation method, w vz (θ) is the weighting factor, and S θ (xz d , yz d ) are filtered radiographs.