Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Comparison of the average measured height of the grating structures, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document} h 1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document} h 2 , with the designed heights, for MPG7 and MPG8. Uncertainties shown are the standard deviation. The heights were measured by the manufacturer, Microworks, GmbH.

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques: Comparison, Standard Deviation

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Modulated phase grating parameters used in visibility measurements. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document} h 1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document} h 2 are listed as their corresponding phase-shift in radians.

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques:

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Theoretical visibility vs. grating-to-detector distance, z , for ( a ) an ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\pi , 0)$$\end{document} ( π , 0 ) RectMPG and an ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\pi /2, \pi /8)$$\end{document} ( π / , π / 8 ) RectMPG and ( b ) an ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\pi /2, \pi /8)$$\end{document} ( π / , π / 8 ) RectMPG compared with theoretical simulations of the measured heights of MPG7 and MPG8, with heights shown in Table . All parameters are the same between the simulations except for the phase heights of the grating envelope function, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document} h and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document} h 1 .

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques:

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Comparison of visibility vs. grating-to-detector distance, z , for MPG7, MPG8, and the presented theory. The visibility was measured as as function of grating-to-detector distance, z for a fixed source-to-detector distance, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L = 110 \, cm$$\end{document} L = 110 c m . Notice that the two theory lines are the same as in Figure b. The experimental visibility was calculated near the center of the grating and the mean is shown. The error bars represent the standard deviation.

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques: Comparison, Standard Deviation

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Comparison of the average measured height of the grating structures, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document} h 1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document} h 2 , with the designed heights, for MPG7 and MPG8. Uncertainties shown are the standard deviation. The heights were measured by the manufacturer, Microworks, GmbH.

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques: Comparison, Standard Deviation

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Modulated phase grating parameters used in visibility measurements. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document} h 1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document} h 2 are listed as their corresponding phase-shift in radians.

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques:

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Theoretical visibility vs. grating-to-detector distance, z , for ( a ) an ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\pi , 0)$$\end{document} ( π , 0 ) RectMPG and an ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\pi /2, \pi /8)$$\end{document} ( π / , π / 8 ) RectMPG and ( b ) an ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\pi /2, \pi /8)$$\end{document} ( π / , π / 8 ) RectMPG compared with theoretical simulations of the measured heights of MPG7 and MPG8, with heights shown in Table . All parameters are the same between the simulations except for the phase heights of the grating envelope function, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document} h and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document} h 1 .

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques:

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Comparison of visibility vs. grating-to-detector distance, z , for MPG7, MPG8, and the presented theory. The visibility was measured as as function of grating-to-detector distance, z for a fixed source-to-detector distance, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L = 110 \, cm$$\end{document} L = 110 c m . Notice that the two theory lines are the same as in Figure b. The experimental visibility was calculated near the center of the grating and the mean is shown. The error bars represent the standard deviation.

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques: Comparison, Standard Deviation

Journal: Scientific Reports

Article Title: Theoretical and experimental analysis of the modulated phase grating X-ray interferometer

doi: 10.1038/s41598-024-78133-8

Figure Lengend Snippet: Anchovy images acquired using MPG7. Images were acquired at a source-to-detector distance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L = 110 \, cm$$\end{document} L = 110 c m , a source-to-grating distance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1 = 20 \, cm$$\end{document} L 1 = 20 c m , and a grating-to-object distance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{GO} = 13.5 \, cm$$\end{document} D GO = 13.5 c m , for an autocorrelation length of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ACL = 57.5 \, nm$$\end{document} A C L = 57.5 n m . The zoomed regions are ROI1 (yellow) and ROI2 (magenta). Note colorbar differences in original and zoomed images.

Article Snippet: The gratings, referred to as MPG7 and MPG8, were manufactured by Microworks, GmbH.

Techniques: