US 2026/0219211 A1 · X-RAY DIFFERENTIAL PHASE CONTRAST NANO CT SYSTEM AND IMAGING METHOD THEREFOR

Abstract

Disclosed are an X-ray differential phase contrast nano CT system and an imaging method therefor. The X-ray differential phase contrast nano CT system mainly comprises: an annular inclined grid-shaped cone beam X-ray source (9), a sample table (5), an objective lens (6), an analysis grating (7) and an imaging detector. The X-ray differential phase contrast nano CT imaging method specifically includes an image collection method, a refraction angle imaging method, a linear absorption coefficient imaging method and a linear diffusion coefficient imaging method. The annular inclined grid-shaped cone beam illumination X-ray source is introduced, such that the defect of incomplete refraction angle sampling is overcome, thereby significantly improving the quality of a refraction angle reconstruction image. Meanwhile, a linear diffusion coefficient reconstruction image in two dimensions is provided, thus providing richer imaging information than traditional nano CT.

An imaging method for an X-ray differential phase contrast nano CT system, wherein the X-ray differential phase contrast nano CT system comprises an annular inclined grid-shaped cone beam X-ray source, a sample table, an objective lens, an analysis grating and an imaging detector, and the annular inclined grid-shaped cone beam X-ray source comprises a grid-shaped structure;

the imaging method comprises refraction angle imaging and linear diffusion coefficient imaging, and the refraction angle imaging comprises the following steps:
S10:
determining whether sample scattering is ignored;
S11:
when the sample scattering is not ignored, calculating a refraction image horizontal component of a sample under an object plane grating coordinate, when a rotation angle of the sample is φ, a refraction angle image of the sample on an image plane being
θ
x
″
(
X
,
Y
,
φ
)
=
p
2
⁢
π
⁡
(
d
i
-
s
i
)
⁢
arctan
⁢
I
U
(
X
,
Y
,
φ
)
-
I
D
(
X
,
Y
,
φ
)
I
V
(
X
,
Y
,
φ
)
-
I
P
(
X
,
Y
,
φ
)
,
a refraction angle image of the sample under the object plane grating coordinate being
θ
x
″
(
x
,
y
,
φ
)
=
ps
∘
2
⁢
π
⁡
(
s
o
-
d
o
)
⁢
s
i
⁢
arctan
⁢
I
U
(
X
,
Y
,
φ
)
-
I
D
(
X
,
Y
,
φ
)
I
V
(
X
,
Y
,
φ
)
-
I
P
(
X
,
Y
,
φ
)
;
S12:
when the sample scattering is not ignored, calculating a refraction image vertical component of the sample under the object plane grating coordinate, when the rotation angle is φ+π, the refraction angle image of the sample on the image plane being
θ
y
″
(
X
,
Y
,
φ
)
=
p
2
⁢
π
⁡
(
d
i
-
s
i
)
⁢
arctan
⁢
I
U
(
-
X
,
Y
,
φ
+
π
)
-
I
D
(
-
X
,
Y
,
φ
+
π
)
I
V
(
-
X
,
Y
,
φ
+
π
)
-
I
P
(
-
X
,
Y
,
φ
+
π
)
,
the refraction angle image of the sample under the object plane grating coordinate being
θ
y
′′
(
x
,
y
,
φ
)
=
p
⁢
s
o
2
⁢
π
⁡
(
s
o
-
d
o
)
⁢
s
i
⁢
arc
⁢
tan
⁢
I
U
⁢
(
-
X
,
Y
,
φ
+
π
)
-
I
D
(
-
X
,
Y
,
φ
+
π
)
I
V
(
-
X
,
Y
,
φ
+
π
)
-
I
P
(
-
X
,
Y
,
φ
+
π
)
;
S13:
when the sample scattering is ignored, calculating the refraction image horizontal component of the sample under the object plane grating coordinate, when the rotation angle is φ, the refraction angle image of the sample on the image plane being capable of being expressed as the following formula by an ascending amplified image and a descending amplified image:
θ
x
′′
(
X
,
Y
,
φ
)
=
p
2
⁢
π
⁡
(
d
i
-
s
i
)
⁢
arc
⁢
sin
⁢
I
U
⁢
(
X
,
Y
,
φ
)
-
I
D
(
X
,
Y
,
φ
)
I
U
(
X
,
Y
,
φ
)
+
I
D
(
X
,
Y
,
φ
)
·
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
R
ma
⁢
x
-
R
m
⁢
i
⁢
n
,
the refraction angle image of the sample under the object plane grating coordinate being
θ
x
′′
(
x
,
y
,
φ
)
=
p
⁢
s
o
2
⁢
π
⁡
(
s
o
-
d
o
)
⁢
s
i
⁢
arc
⁢
sin
⁢
I
U
⁢
(
X
,
Y
,
φ
)
-
I
D
(
X
,
Y
,
φ
)
I
U
(
X
,
Y
,
φ
)
+
I
D
(
X
,
Y
,
φ
)
·
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
R
ma
⁢
x
-
R
m
⁢
i
⁢
n
;
S14:
when the sample scattering is ignored, calculating the refraction image vertical component of the sample under the object plane grating coordinate, when the rotation angle is φ+π, the refraction angle image of the sample on the image plane being capable of being expressed as the following formula by the ascending amplified image and the descending amplified image:
θ
y
′′
(
X
,
Y
,
φ
)
=
p
2
⁢
π
⁡
(
d
i
-
s
i
)
⁢
arc
⁢
sin
⁢
I
U
(
-
X
,
Y
,
φ
+
π
)
-
I
D
(
-
X
,
Y
,
φ
+
π
)
I
U
(
-
X
,
Y
,
φ
+
π
)
+
I
D
(
-
X
,
Y
,
φ
+
π
)
·
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
R
ma
⁢
x
-
R
m
⁢
i
⁢
n
,
the refraction angle image of the sample under the object plane grating coordinate being
θ
y
′′
(
x
,
x
,
φ
)
=
p
2
⁢
π
⁡
(
s
o
-
d
o
)
⁢
s
i
⁢
arc
⁢
sin
⁢
I
U
(
-
X
,
Y
,
φ
+
π
)
-
I
D
(
-
X
,
Y
,
φ
+
π
)
I
U
(
-
X
,
Y
,
φ
+
π
)
+
I
D
(
-
X
,
Y
,
φ
+
π
)
·
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
R
ma
⁢
x
-
R
m
⁢
i
⁢
n
;
S15:
calculating a refraction image horizontal component of the sample under an object plane natural coordinate;
the refraction image horizontal component under the natural coordinate being capable of being expressed as the following formula by the collected refraction angle component under the grating coordinate:
θ
x
(
x
,
y
,
φ
)
=
θ
x
′′
(
x
,
y
,
φ
)
-
θ
y
′′
(
x
,
y
,
φ
)
2
⁢
cos
⁢
ω
=
θ
x
′′
(
x
,
y
,
φ
)
-
θ
x
′′
(
-
x
,
y
,
φ
+
π
)
2
⁢
cos
⁢
ω
;
S16:
calculating a refraction image vertical component of the sample under the object plane natural coordinate;
the refraction image vertical component under the natural coordinate being capable of being expressed as the following formula by the collected refraction angle component under the grating coordinate:
θ
y
(
x
,
y
,
φ
)
=
θ
x
′′
(
x
,
y
,
φ
)
+
θ
y
′′
(
x
,
y
,
φ
)
2
⁢
sin
⁢
ω
=
θ
x
′′
(
x
,
y
,
φ
)
+
θ
x
′′
(
-
x
,
y
,
φ
+
π
)
2
⁢
sin
⁢
ω
;
S17:
reconstructing a gradient of a reduction of a real part of a refractive index of the sample under the object plane natural coordinate,
∇
δ
⁡
(
x
′
,
y
′
,
z
′
)
=
ℛ
-
1
[
-
θ
→
(
x
,
y
,
φ
)
]
=
∫
0
π
d
⁢
φ
⁢
∫
-
∞
∞
ℱ
x
-
1
⁢
❘
"\[LeftBracketingBar]"
ρ
❘
"\[RightBracketingBar]"
⁢
ℱ
x
[
-
θ
→
(
x
,
y
,
φ
)
]
δ
^
(
x
′
⁢
cos
⁢
φ
+
z
′
⁢
sin
⁢
φ
-
x
)
⁢
dx
;
S18:
reconstructing the reduction of the real part of the refractive index of the sample under the object plane natural coordinate,
δ
⁡
(
x
′
,
y
′
,
z
′
)
=
-
∫
0
π
d
⁢
φ
⁢
∫
-
∞
∞
ℱ
y
-
1
⁢
ℱ
x
-
1
⁢
❘
"\[LeftBracketingBar]"
ρ
❘
"\[RightBracketingBar]"
2
⁢
π
⁡
(
ρ
2
+
v
2
)
⁢
(
ρ
⁢
ℱ
x
⁢
ℱ
y
⁢
θ
x
(
x
,
y
,
φ
)
+
v
⁢
ℱ
x
⁢
ℱ
y
⁢
θ
y
(
x
,
y
,
φ
)
)
⁢
δ
^
(
x
′
⁢
cos
⁢
φ
+
z
′
⁢
sin
⁢
φ
-
x
)
⁢
dx
;
the linear diffusion coefficient imaging comprises the following steps:
S31:
calculating a scattering variance image of a sample on an image plane, when the sample is on the sample table of X-ray differential phase contrast nano CT and a rotation angle is φ, the scattering variance image of the sample on the image plane being
σ
x
′′
2
(
X
,
Y
,
φ
)
=
p
2
2
⁢
π
2
(
d
i
-
s
i
)
2
⁢
ln
⁢
R
m
⁢
ax
-
R
m
⁢
i
⁢
n
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
[
I
v
(
X
,
Y
,
φ
)
-
I
P
(
X
,
Y
,
φ
)
I
V
(
X
,
Y
,
φ
)
+
I
P
(
X
,
Y
,
φ
)
]
2
+
[
I
U
(
X
,
Y
,
φ
)
-
I
D
(
X
,
Y
,
φ
)
I
U
(
X
,
Y
,
φ
)
+
I
D
(
X
,
Y
,
φ
)
]
2
;
S32:
calculating a horizontal scattering variance image of the sample under an object plane grating coordinate, the horizontal scattering variance image of the sample under the object plane grating coordinate being
σ
x
′′
2
(
x
,
y
,
φ
)
=
[
s
o
(
d
i
-
s
i
)
(
s
o
-
d
o
)
⁢
s
i
]
2
⁢
σ
x
′′
2
(
X
,
Y
,
φ
)
=
p
2
2
⁢
π
2
[
s
o
(
s
o
-
d
o
)
⁢
s
i
]
2
ln
⁢
R
m
⁢
ax
-
R
m
⁢
i
⁢
n
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
[
I
V
(
X
,
Y
,
φ
)
-
I
P
(
X
,
Y
,
φ
)
I
V
(
X
,
Y
,
φ
)
+
I
P
(
X
,
Y
,
φ
)
]
2
+
[
I
U
(
X
,
Y
,
φ
)
-
I
D
(
X
,
Y
,
φ
)
I
U
(
X
,
Y
,
φ
)
+
I
D
(
X
,
Y
,
φ
)
]
2
S33:
calculating a vertical scattering variance image of the sample under the object plane grating coordinate, when the rotation angle is φ+π, a scattering variance image of the sample on an image plane being
σ
y
′′
2
(
X
,
Y
,
φ
)
=
σ
x
′′
2
(
-
X
,
Y
,
φ
+
π
)
=
p
2
2
⁢
π
2
(
d
i
-
s
i
)
2
ln
⁢
R
ma
⁢
x
-
R
m
⁢
i
⁢
n
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
[
I
V
(
-
X
,
Y
,
φ
+
π
)
-
I
P
(
-
X
,
Y
,
φ
+
π
)
I
V
(
-
X
,
Y
,
φ
+
π
)
+
I
P
(
-
X
,
Y
,
φ
+
π
)
]
2
+
[
I
U
(
-
X
,
Y
,
φ
+
π
)
-
I
D
(
-
X
,
Y
,
φ
+
π
)
I
U
(
-
X
,
Y
,
φ
+
π
)
+
I
D
(
-
X
,
Y
,
φ
+
π
)
]
2
the vertical scattering variance image of the sample under the object plane grating coordinate being
σ
y
′′
2
(
x
,
y
,
φ
)
=
σ
x
′′
2
(
-
x
,
y
,
φ
+
π
)
=
[
s
o
(
d
i
-
s
i
)
(
s
o
-
d
o
)
⁢
s
i
]
2
⁢
σ
x
′′
2
(
-
X
,
Y
,
φ
+
π
)
=
p
2
2
⁢
π
2
[
s
o
(
s
o
-
d
o
)
⁢
s
i
]
2
ln
⁢
R
m
⁢
ax
-
R
m
⁢
i
⁢
n
R
m
⁢
ax
+
R
m
⁢
i
⁢
n
[
I
V
(
-
X
,
Y
,
φ
+
π
)
-
I
P
(
-
X
,
Y
,
φ
+
π
)
I
V
(
-
X
,
Y
,
φ
+
π
)
+
I
P
(
-
X
,
Y
,
φ
+
π
)
]
2
+
[
I
U
(
-
X
,
Y
,
φ
+
π
)
-
I
D
(
-
X
,
Y
,
φ
+
π
)
I
U
(
-
X
,
Y
,
φ
+
π
)
+
I
D
(
-
X
,
Y
,
φ
+
π
)
]
2
S34:
reconstructing a horizontal linear diffusion coefficient of the sample under the object plane grating coordinate, a three-dimensional reconstruction formula of the horizontal linear diffusion coefficient being
ω
x
′′
(
x
′
,
y
′
,
z
′
)
=
ℛ
-
1
[
σ
x
′′
2
(
x
,
y
,
φ
)
]
=
∫
0
π
d
⁢
φ
⁢
∫
-
∞
∞
ℱ
x
-
1
⁢
❘
"\[LeftBracketingBar]"
ρ
❘
"\[RightBracketingBar]"
2
⁢
π
⁢
i
⁢
ρ
⁢
ℱ
x
[
σ
x
′′
2
(
x
,
y
,
φ
)
]
δ
^
(
x
′
⁢
cos
⁢
φ
+
z
′
⁢
sin
⁢
φ
-
x
)
⁢
dx
;
S35:
reconstructing a vertical linear diffusion coefficient of the sample under the object plane grating coordinate, a three-dimensional reconstruction formula of the vertical linear diffusion coefficient being
ω
y
′′
(
x
′
,
y
′
,
z
′
)
=
ℛ
-
1
[
σ
y
′′
2
(
x
,
y
,
φ
)
]
=
∫
π
2
⁢
π
d
⁢
φ
⁢
∫
-
∞
∞
ℱ
x
-
1
⁢
❘
"\[LeftBracketingBar]"
ρ
❘
"\[RightBracketingBar]"
2
⁢
π
⁢
i
⁢
ρ
⁢
ℱ
x
[
σ
y
′′
2
(
x
,
y
,
φ
)
]
δ
^
(
x
′
⁢
cos
⁢
φ
+
z
′
⁢
sin
⁢
φ
-
x
)
⁢
dx
;
wherein p is a period of the analysis grating, do is an object distance of the sample relative to the objective lens, and di is an image distance of the imaging detector relative to the objective lens;
So is an object distance of the grid-shaped structure relative to the objective lens, and Si is an image distance of the analysis grating relative to the objective lens;
I0 is an incident light intensity of the sample, Rmax and Rmin are a maximum value and a minimum value of an angle signal response curve respectively, and IV(X, Y, φ), IU(X, Y, φ), IP(X, Y, φ) and ID(X, Y, φ) represent a valley amplified image, an ascending amplified image, a peak amplified image and a descending amplified image respectively.

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X-ray differential phase contrast nano ct system and imaging method therefor

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X-ray differential phase contrast nano ct system and imaging method therefor

Life of this patent

Abstract

Claims7