Evaluation of the Weighted Mean X-ray Energy for an Imaging System Via Propagation-Based Phase-Contrast Imaging
<p>Measurement setup at Gesellschaft für Schwerionenforschung (GSI). The laser beam is split into backlighter and heater. The backlighter is shot at a tungsten wire for generating X-rays. The heater can optionally be shot at an object for generating shock waves or explosions. The inset shows a zoom-in on the tungsten backlighter wire (B) and the titanium wire (T) positions, depicted as green circles. In the presented measurement the heater is not shot at the titanium wire and the cold titanium wire is imaged. The images are obtained with imaging plates. The magnet is used to divert electrons, which occur due to the explosion of the wire and cause noise in the acquired images.</p> "> Figure 2
<p>Measurement of a titanium wire with regions of interest (ROI). <b>Green Rectangle</b>: ROI that is used to reconstruct the wire. <b>Red Rectangle</b>: background.</p> "> Figure 3
<p><b>Left</b>: phase reconstructions for the green marked region of interest in <a href="#jimaging-06-00063-f002" class="html-fig">Figure 2</a> retrieved with the following energies (from top to bottom): <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>=</mo> <mo>[</mo> <mn>2.7</mn> <mo>;</mo> <mn>4.7</mn> <mo>;</mo> <mn>11.8</mn> <mo>;</mo> <mn>22.0</mn> <mo>]</mo> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>. <b>Right</b>: lineplots (blue) of the retrieved phase, which is shown in the <b>Left</b> images, and theoretical phase at the centre of the wire (red).</p> "> Figure 4
<p>Evaluation of the dominant energy. (<b>a</b>) Absolute phase difference between theoretical phase and retrieved mean phase in dependence of the energy. The calculated energy range is between <math display="inline"><semantics> <mrow> <mn>2</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>22</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>. (<b>b</b>) Detailed view on the minimum with a finer step-size (purple). For the finer step-size the evaluated energy range is between <math display="inline"><semantics> <mrow> <mn>11.5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>12.5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>. In blue a section of the plot shown in (<b>a</b>) can be seen. The error is in the regime of <math display="inline"><semantics> <mrow> <mn>0.08</mn> <mspace width="0.166667em"/> <mi>rad</mi> </mrow> </semantics></math>.</p> "> Figure 5
<p>Absolute difference between the mean phase-shift of the green region of interest and the theoretical value depending on the energy. (<b>a</b>) The grey curve results from the reconstruction process with a uniform reference and the orange curve from a noisy reference with <math display="inline"><semantics> <mrow> <mi>NL</mi> <mo>=</mo> <mn>31.81</mn> <mspace width="0.166667em"/> <mi>dB</mi> </mrow> </semantics></math>. (<b>b</b>) Results for different assumed diameters of the titanium wire. The blue curve presents the result shown in <a href="#jimaging-06-00063-f004" class="html-fig">Figure 4</a> for the given value of the diameter of <math display="inline"><semantics> <mrow> <mn>50</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. In green, red and yellow the absolute phase difference for a theoretical phase-shift of a <math display="inline"><semantics> <mrow> <mn>45</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, a <math display="inline"><semantics> <mrow> <mn>55</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and a <math display="inline"><semantics> <mrow> <mn>60</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> wire is shown, respectively. The error is in the regime of <math display="inline"><semantics> <mrow> <mn>0.08</mn> <mspace width="0.166667em"/> <mi>rad</mi> </mrow> </semantics></math>.</p> "> Figure 6
<p>Monochromatic simulations of the propagation signature of a <math display="inline"><semantics> <mrow> <mn>50</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> titanium wire for different energies. Source-blurring is neglected in the simulations. A lineplot of the measurement shown in <a href="#jimaging-06-00063-f002" class="html-fig">Figure 2</a> is plotted in blue for comparative reasons. In yellow the simulation for <math display="inline"><semantics> <mrow> <mn>10</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>, in orange the simulation for <math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and in red the simulation for <math display="inline"><semantics> <mrow> <mn>12</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> is shown. The simulation in orange for <math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> yields the best fit for the measured values at the centre of the wire.</p> "> Figure 7
<p>Monochromatic simulation of the propagation signature of titanium wires with varying diameter of <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>10</mn> <mo>%</mo> </mrow> </semantics></math> of the supposed diameter of <math display="inline"><semantics> <mrow> <mn>50</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. The results for the best fitting energies are shown for each diameter. Source-blurring is included in the simulations. A lineplot of the measurement shown in <a href="#jimaging-06-00063-f002" class="html-fig">Figure 2</a> is plotted in blue for comparative reasons. In yellow the simulation of a wire with <math display="inline"><semantics> <mrow> <mn>45</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> diameter for <math display="inline"><semantics> <mrow> <mn>10.5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>, in orange the simulation of a wire with <math display="inline"><semantics> <mrow> <mn>50</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> diameter for <math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and in red the simulation of a wire with <math display="inline"><semantics> <mrow> <mn>55</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> diameter for <math display="inline"><semantics> <mrow> <mn>11.5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> is shown.</p> "> Figure 8
<p>Simulation of the propagation signature of a titanium wire of <math display="inline"><semantics> <mrow> <mn>50</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> diameter. On the left (<b>a</b>,<b>c</b>,<b>e</b>), three toy spectra with different weighted mean energies (red line) and with different energy distributions are assumed. Three monochromatic lines (green) at <math display="inline"><semantics> <mrow> <mn>5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>20</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> ((<b>b</b>)) or <math display="inline"><semantics> <mrow> <mn>5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>15</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>20</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> (c/d and e/f), respectively, are used to illustrate the spectra. On the right (<b>b</b>,<b>d</b>,<b>f</b>), the corresponding simulated propagation signatures of a <math display="inline"><semantics> <mrow> <mn>50</mn> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> titanium wire are shown in orange. Source-blurring is neglected in the simulations. The blue line shows a lineplot of the measurement of the wire. From top to bottom the weighted mean energy of the spectra is <math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> (a/b), <math display="inline"><semantics> <mrow> <mn>13</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> (c/d) and <math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> (e/f). The maximal contributing energy bin of the spectra is <math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> (a/b), <math display="inline"><semantics> <mrow> <mn>15</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> (c/d) and <math display="inline"><semantics> <mrow> <mn>15</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> (e/f).</p> "> Figure 9
<p>(<b>a</b>) Detector read-out of the propagation signatures of three carbon wires acquired at Diamond Light Source (DLS). (<b>b</b>) Reconstructed thickness of the carbon wires at the correct energy of <math display="inline"><semantics> <mrow> <mn>10</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>. (<b>c</b>,<b>d</b>) Absolute difference between mean phase-shift of the region marked with the red line in (<b>a</b>) and theoretical value depending on the energy. (<b>c</b>) Whole energy range between <math display="inline"><semantics> <mrow> <mn>2</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>22</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math>. (<b>d</b>) Energy range around the minimum between <math display="inline"><semantics> <mrow> <mn>9.5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>10.5</mn> <mspace width="0.166667em"/> <mi>keV</mi> </mrow> </semantics></math> in finer steps (purple). In blue the corresponding section of the plot in (<b>c</b>) is shown. The error is in the range of <math display="inline"><semantics> <mrow> <mn>0.01</mn> <mspace width="0.166667em"/> <mi>rad</mi> </mrow> </semantics></math>.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Measurement Setup at GSI
2.2. Measurement Setup at DLS
2.3. Propagation-Based Phase-Contrast
2.4. Computer Simulation
2.5. Energy Evaluation for GSI Data
3. Results
3.1. Evaluation of the Dominant X-ray Energy
3.2. Validation of the Evaluated Dominant X-ray Energy
3.3. Validation of the Evaluation Method with Monochromatic Images
4. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Seifert, M.; Weule, M.; Cipiccia, S.; Flenner, S.; Hagemann, J.; Ludwig, V.; Michel, T.; Neumayer, P.; Schuster, M.; Wolf, A.; et al. Evaluation of the Weighted Mean X-ray Energy for an Imaging System Via Propagation-Based Phase-Contrast Imaging. J. Imaging 2020, 6, 63. https://doi.org/10.3390/jimaging6070063
Seifert M, Weule M, Cipiccia S, Flenner S, Hagemann J, Ludwig V, Michel T, Neumayer P, Schuster M, Wolf A, et al. Evaluation of the Weighted Mean X-ray Energy for an Imaging System Via Propagation-Based Phase-Contrast Imaging. Journal of Imaging. 2020; 6(7):63. https://doi.org/10.3390/jimaging6070063
Chicago/Turabian StyleSeifert, Maria, Mareike Weule, Silvia Cipiccia, Silja Flenner, Johannes Hagemann, Veronika Ludwig, Thilo Michel, Paul Neumayer, Max Schuster, Andreas Wolf, and et al. 2020. "Evaluation of the Weighted Mean X-ray Energy for an Imaging System Via Propagation-Based Phase-Contrast Imaging" Journal of Imaging 6, no. 7: 63. https://doi.org/10.3390/jimaging6070063