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Quantitative Mass Density Image Reconstructed from the Complex X-Ray Refractive Index.

Mukaide T, Iida A, Watanabe M, Takada K, Noma T - PLoS ONE (2015)

Bottom Line: The mass density was obtained from the experimentally observed ratio of the imaginary and real parts of the complex X-ray refractive index.An empirical linear relationship between the X-ray mass attenuation coefficient of the materials and X-ray energy was found for X-ray energies between 8 keV and 30 keV.The reconstructed mass density agrees well with the calculated one.

View Article: PubMed Central - PubMed

Affiliation: Nanomaterials R&D Center, Canon Inc., Ohta-ku, Tokyo, Japan.

ABSTRACT
We demonstrate a new analytical X-ray computed tomography technique for visualizing and quantifying the mass density of materials comprised of low atomic number elements with unknown atomic ratios. The mass density was obtained from the experimentally observed ratio of the imaginary and real parts of the complex X-ray refractive index. An empirical linear relationship between the X-ray mass attenuation coefficient of the materials and X-ray energy was found for X-ray energies between 8 keV and 30 keV. The mass density image of two polymer fibers was quantified using the proposed technique using a scanning-type X-ray microbeam computed tomography system equipped with a wedge absorber. The reconstructed mass density agrees well with the calculated one.

No MeSH data available.


Reconstructed images.Tomographic images of (a) β and (b) δ. The β image is linearly proportional to the μ image as shown in Eq (2). (c) Mass density image in g/cm3, (d) line profiles of mass density along the broken line in (c). The black solid, red dashed, and blue dotted lines show the mass density calculated by the proposed method, conventional approximation, and Eq (3) using a known chemical composition, respectively.
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pone.0131401.g004: Reconstructed images.Tomographic images of (a) β and (b) δ. The β image is linearly proportional to the μ image as shown in Eq (2). (c) Mass density image in g/cm3, (d) line profiles of mass density along the broken line in (c). The black solid, red dashed, and blue dotted lines show the mass density calculated by the proposed method, conventional approximation, and Eq (3) using a known chemical composition, respectively.

Mentions: The reconstructed distributions of β and δ calculated from the tomographic images are shown in Fig 4(a) and 4(b), respectively. These images were reconstructed using the algebraic reconstruction technique (ART) [21] with 100 iterations. In Fig 4(a) and 4(b), the contrast difference between the two polymer fibers can be easily discriminated by eye. The right and left polymer fibers were PET and PE, respectively. It is also possible to see the glue that connects the two polymer fibers from the images in Fig 4(a) and 4(b). Fig 4(c) presents a tomographic ρ image, which was calculated using the reconstructed β and δ images (Fig 4(a) and 4(b), respectively) and a calibration function (Eq (3)). The profile along the broken line indicated on the ρ image is plotted with a black solid line in Fig 4(d). The red dashed line in Fig 4(d) is the ρ value calculated using the conventional approximation, which assumes that ⟨Z + f′⟩/⟨A⟩ is equal to 0.5. The blue dotted lines in Fig 4(d) show the mass density of PE (left) and PET (right) calculated from the δ image using Eq (3) with the known chemical composition. The mass densities of PE and PET obtained were 0.95 ± 0.01 g/cm3 and 1.34 ± 0.02 g/cm3, respectively. This result agrees well with the tabulated value for these polymers (PE: 0.910–0.965 g/cm3, PET: 1.33–1.42 g/cm3) [22]. The mass densities for PE and PET obtained using the proposed method (black solid line in Fig 4(d)) are in agreement with the calculated values (blue dotted lines in Fig 4(d)), while the conventional approximation (red dashed line in Fig 4(d)) shows a large discrepancy in both cases. The average difference in the mass density measured with the present method and the calculated mass density is approximately 2% for PET and 3% for PE. As expected, the large hydrogen content in these materials results in a large error using the conventional approximation (the hydrogen content, based on the number of atoms, of PET and PE are 36% and 67%, respectively).


Quantitative Mass Density Image Reconstructed from the Complex X-Ray Refractive Index.

Mukaide T, Iida A, Watanabe M, Takada K, Noma T - PLoS ONE (2015)

Reconstructed images.Tomographic images of (a) β and (b) δ. The β image is linearly proportional to the μ image as shown in Eq (2). (c) Mass density image in g/cm3, (d) line profiles of mass density along the broken line in (c). The black solid, red dashed, and blue dotted lines show the mass density calculated by the proposed method, conventional approximation, and Eq (3) using a known chemical composition, respectively.
© Copyright Policy
Related In: Results  -  Collection

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pone.0131401.g004: Reconstructed images.Tomographic images of (a) β and (b) δ. The β image is linearly proportional to the μ image as shown in Eq (2). (c) Mass density image in g/cm3, (d) line profiles of mass density along the broken line in (c). The black solid, red dashed, and blue dotted lines show the mass density calculated by the proposed method, conventional approximation, and Eq (3) using a known chemical composition, respectively.
Mentions: The reconstructed distributions of β and δ calculated from the tomographic images are shown in Fig 4(a) and 4(b), respectively. These images were reconstructed using the algebraic reconstruction technique (ART) [21] with 100 iterations. In Fig 4(a) and 4(b), the contrast difference between the two polymer fibers can be easily discriminated by eye. The right and left polymer fibers were PET and PE, respectively. It is also possible to see the glue that connects the two polymer fibers from the images in Fig 4(a) and 4(b). Fig 4(c) presents a tomographic ρ image, which was calculated using the reconstructed β and δ images (Fig 4(a) and 4(b), respectively) and a calibration function (Eq (3)). The profile along the broken line indicated on the ρ image is plotted with a black solid line in Fig 4(d). The red dashed line in Fig 4(d) is the ρ value calculated using the conventional approximation, which assumes that ⟨Z + f′⟩/⟨A⟩ is equal to 0.5. The blue dotted lines in Fig 4(d) show the mass density of PE (left) and PET (right) calculated from the δ image using Eq (3) with the known chemical composition. The mass densities of PE and PET obtained were 0.95 ± 0.01 g/cm3 and 1.34 ± 0.02 g/cm3, respectively. This result agrees well with the tabulated value for these polymers (PE: 0.910–0.965 g/cm3, PET: 1.33–1.42 g/cm3) [22]. The mass densities for PE and PET obtained using the proposed method (black solid line in Fig 4(d)) are in agreement with the calculated values (blue dotted lines in Fig 4(d)), while the conventional approximation (red dashed line in Fig 4(d)) shows a large discrepancy in both cases. The average difference in the mass density measured with the present method and the calculated mass density is approximately 2% for PET and 3% for PE. As expected, the large hydrogen content in these materials results in a large error using the conventional approximation (the hydrogen content, based on the number of atoms, of PET and PE are 36% and 67%, respectively).

Bottom Line: The mass density was obtained from the experimentally observed ratio of the imaginary and real parts of the complex X-ray refractive index.An empirical linear relationship between the X-ray mass attenuation coefficient of the materials and X-ray energy was found for X-ray energies between 8 keV and 30 keV.The reconstructed mass density agrees well with the calculated one.

View Article: PubMed Central - PubMed

Affiliation: Nanomaterials R&D Center, Canon Inc., Ohta-ku, Tokyo, Japan.

ABSTRACT
We demonstrate a new analytical X-ray computed tomography technique for visualizing and quantifying the mass density of materials comprised of low atomic number elements with unknown atomic ratios. The mass density was obtained from the experimentally observed ratio of the imaginary and real parts of the complex X-ray refractive index. An empirical linear relationship between the X-ray mass attenuation coefficient of the materials and X-ray energy was found for X-ray energies between 8 keV and 30 keV. The mass density image of two polymer fibers was quantified using the proposed technique using a scanning-type X-ray microbeam computed tomography system equipped with a wedge absorber. The reconstructed mass density agrees well with the calculated one.

No MeSH data available.