Recovering atomic-scale chemistry from fused multi-modal electron microscopy
Systems and methods for fused multi-modal electron microscopy are provided to generate quantitatively accurate 2D maps or 3D volumes with pixel/voxel values that directly reflect a sample's chemistry. Techniques are provided for combining annular dark field detector (ADF), annular bright field (ABF) and/or pixelated detector image data and energy dispersive X-rays (EDX) data and/or electron energy loss spectroscopy (EELS) data for a sample and generating chemical 2D and 3D maps by applying minimization optimization process.
1 . A method for chemical sample imaging, the method comprising:
receiving energy dispersive X-ray (EDX) image data corresponding to a chemical sample, the EDX image data containing one or more measured chemical maps;
receiving annular dark field (ADF) image data or annular bright field (ABF) or pixelated detector (PD) image data corresponding to the chemical sample;
correlating the EDX image data and the ADF image data or the ABF or the PD image data using an optimization process that performs a minimization between each of the EDX image data and the ADF image data or the ABF image data and one or more recovered chemical maps of the chemical sample; and
in response to the optimization process, generating and displaying and/or storing the one or more recovered chemical maps corresponding to the chemical sample.
2 . A method for chemical sample imaging, the method comprising:
receiving electron energy loss spectroscopy (EELS) image data corresponding to a chemical sample, the EELS image data containing one or more measured chemical maps corresponding to the chemical sample;
receiving annular dark field (ADF) image data or annular bright field (ABF) or pixelated detector (PD) image data corresponding to the chemical sample;
correlating the EELS image data and the ADF image data or the ABF image data using an optimization process that performs a minimization between each of the EELS image data and the ADF image data or the ABF or PD image data and one or more recovered chemical maps of the chemical sample; and
in response to the optimization process, generating and displaying and/or storing the one or more recovered chemical maps corresponding to the chemical sample.
3 . The method of any of claim 1 or 2 , wherein the optimization process comprises applying an optimization expression as follows:
arg
min
x
λ
1
2
b
H
-
∑
i
(
Z
i
x
i
)
γ
2
2
+
λ
2
∑
i
(
x
i
-
b
i
log
(
x
i
)
)
+
λ
3
∑
i
x
i
TV
where b H is the annular or pixelated detector image data, λ i and γ are weighting coefficients, b i and x i are the measured chemical maps and recovered chemical maps, respectively, i is an element, Z i is a scaling factor, and TV is channel-wise total variation regularization.
4 . The method of any of claim 1 or 2 , wherein the optimization process comprises applying an optimization expression as follows:
arg
min
x
λ
1
2
b
H
-
∑
i
(
Z
i
x
i
)
γ
2
2
+
λ
2
2
b
i
-
x
i
2
2
+
λ
3
∑
i
x
i
TV
where b H is the annular or pixelated detector image data, λ i and γ are weighting coefficients, b i and x i are the measured chemical maps and recovered chemical maps, respectively, i is an element, Z i is a scaling factor, and TV is channel-wise total variation regularization.
5 . The method of any of claim 1 or 2 , wherein the optimization process comprises applying an optimization expression as follows:
x
^
=
arg
min
x
λ
1
2
A
h
∑
i
(
Z
i
x
i
)
γ
-
b
h
2
2
+
λ
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∑
i
(
A
c
x
i
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b
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log
(
A
c
x
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+
λ
3
∑
i
x
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TV
where b H is the annular or pixelated detector image data, A h and A c are forward projection operators for the annular detector image data and chemical maps, λ and γ are weighting coefficients, b i is the measured chemical image data across a range of specimen projection angles, and x i is the recovered chemical volume for element i, respectively, Z i is a scaling factor, and TV is channel-wise total variation regularization.
6 . The method of any of claim 1 or 2 , wherein the optimization process comprises applying an optimization expression as follows:
arg
min
x
λ
1
2
A
h
∑
i
(
Z
i
x
i
)
γ
-
b
h
2
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A
c
x
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b
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log
(
A
c
x
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2
2
+
λ
3
∑
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x
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TV
where b H is the annular or pixelated detector image data, A h and A c are forward projection operators for the annular detector image data and chemical tilts, λ and γ are regularization parameters, b i and x i are the measured and recovered chemical maps for element i, respectively Z i is a scaling factor, and TV is channel-wise total variation regularization.
7 . The method of any of claim 1 or 2 , wherein the EDX image data comprises measured chemical maps of a plurality of different chemical compounds.
8 . The method of any of claim 1 or 2 , wherein the EELS image data comprises measured chemical maps of a plurality of different chemical compounds.
9 . The method of any of claim 1 or 2 , wherein generating and displaying and/or storing the one or more recovered chemical maps comprises: overlaying the measured chemical maps on the recovered chemical maps wherein the EDX image data comprises chemical maps of a plurality of different chemical compounds.
10 . The method of any of claim 1 or 2 , wherein the EDX image data or the EELS image data comprises a plurality of measured chemical maps and a plurality of recovered chemical maps are generated, the method further comprising:
determining a stoichiometric concentration of the chemical sample by comparing the plurality of recovered chemical maps to one another, of the plurality of recovered chemical maps corresponding to a different chemical composition; and
determining a concentration of each of the different chemical compositions.
11 . A method for chemical sample imaging, the method comprising:
receiving electron energy loss spectroscopy (EELS) image data and receiving energy dispersive X-ray (EDX) image data corresponding to a chemical sample, the EDX image data and the EELS image data containing one or more measured chemical maps corresponding to the chemical sample;
receiving annular dark field (ADF) and/or annular bright field (ABF) and/or pixelated detector (PD) image data corresponding to the chemical sample;
correlating the EELS image data, the EDX image data, and the ADF or the ABF or the PD image data using an optimization process that performs a minimization between each of the EELS image data and the EDX image data, and the ADF, the ABF, or the PD image data and one or more recovered chemical maps of the chemical sample; and
in response to the optimization process, generating and displaying and/or storing the one or more recovered chemical maps corresponding to the chemical sample.