Underneath the Arches, no. 61, October 24, 1968

Underneath the Arches was Grand Valley State\u27s faculty and staff newsletter, published from 1963 to 1971. It was a precursor to the Forum

Principle of the reverse projection method.

<p>Starting from the phase stepping curve (a) that is recorded without sample (reference scan), the sample is measured with grating positions corresponding to the two linear regions of the stepping curve. The two recorded intensities can then be used to obtain the attenuation of the sample as well as its differential phase shift Δ<i>φ</i>_<i>s</i>. Panel (b) shows the histogram of the differential phase-contrast projections of a tomographic scan of a biomedical sample. The red lines mark the region where the error of the linear approximation is less than 5%. Only 0.1% of all pixels lie outside of this region.</p

Root mean squared error and structure similarity of the tomographic reconstructions displayed in Figs 6 and 7 compared to the reference scan.

<p>Root mean squared error and structure similarity of the tomographic reconstructions displayed in Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0184217#pone.0184217.g006" target="_blank">6</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0184217#pone.0184217.g007" target="_blank">7</a> compared to the reference scan.</p

Comparing the tomographic reconstructions of a high statistic scans obtained by widely-used phase stepping approach and the reverse projection method.

<p>(a) Tomographic reconstructions of the differential phase contrast projections, obtained with the PS approach (left) and the RP method (right). (b) Line plot at the position marked by the dashed lines in (a). Both images appear very similar, which is also apparent in the line plot. The contrast in the RP image is slightly weaker, since high values are underestimated by this method.</p

Image quality and quantitative accuracy of the RP method in a low-dose scenario.

<p>Comparison of the reconstructions obtained with the PS method (a, 111 counts/pixel/projection) and the RP method (b, 44.4 mean counts) with a reference scan (c). Remarkably, the RP reconstruction shows superior image quality compared to the PS method, even though only 2 of the 5 steps of the PS approach are used to generate the RP reconstruction. Panel (d) shows a difference image of (b) and (c), which is dominated by noise. That implies a good quantitative accuracy of the RP method. This finding is confirmed by line plot in panel (e) which shows plots along the lines displayed in panels (b) and (c). Note that the values for the RP method were averaged over 4 slices and 4 pixels in direction perpendicular to the line for improved readability.</p

Dark-field/scattering signal strength.

<p>(a) Exemplary dark-field projection of the measured biological sample. The sample shows a smooth dark-field signal close to unity, a prerequisite for successful application of the reverse projection method. (b) Histogram of dark-field values in all projections of one tomographic scan. The peak of the sample’s dark-field is narrow and close to unity. Further, there are next to no pixels with extreme values, which could hinder the applicability of the RP method.</p

Mean values and the corresponding standard deviation of the refractive index decrement <i>δ</i> relative to water, exemplary for the materials formalin (fluid inside the tube), PMMA and the Falcon tube.

<p>Mean values and the corresponding standard deviation of the refractive index decrement <i>δ</i> relative to water, exemplary for the materials formalin (fluid inside the tube), PMMA and the Falcon tube.</p

Lipid, protein, and water analysis of different human soft tissue types.

<p>(A and B) Axial tomographic slices in attenuation and phase contrast, respectively, through the measured plastic cylinder containing tendon, muscle, fat, and skin tissues. (C–E) Decomposed images of the region marked by the white box in (B).</p

Concept illustration for three-dimensional (3D) characterization of lipid, protein, and water concentrations.

<p>(A) Schematic drawing of the three-grating Talbot-Lau interferometer used for the measurements in this study. (B and C) Exemplary tomographic imaging results of a porcine fat and rind sample in attenuation and phase contrast, respectively. The obtained 3D datasets represent the distribution of the linear attenuation coefficient <i>μ</i> and the refractive index decrement <i>δ</i> within the object and can be converted to quantitative Hounsfield units (HU and HUp). (D) Theoretically calculated HU and HUp values for fictive mixtures of varying protein and lipid concentrations. The results span a triangle, and every (experimentally evaluated) HU-HUp-pair can be assigned to exactly one specific protein and lipid content.</p

Experimental lipid, protein and water concentrations (exp.) of the examined dairy products (dp) in comparison to the contents stated by the manufacturers (pack.).

<p>Experimental lipid, protein and water concentrations (exp.) of the examined dairy products (dp) in comparison to the contents stated by the manufacturers (pack.).</p