new batch of KIT gratings

delivered in January

phase-shift gratings

thickness variation above 10%

absorption gratings

tried to increase absorption thickness above 100-120 μm

see my report

macroscopic defects in the gold structure

final setup

• G0 from the previous shipping
• G1 most compatible with spec, according to KIT report
• G2 most uniform according to our measurement

~10% visibility

45 keV design, 100 kVp, 6 mA

applications

water diffusion in cement

inspired by Fei Yang's "Dark-field X-ray imaging of unsaturated water transport in porous materials"

the relevant signals

• transmission \(A\)
• dark field \(B\)
• log ratio \(R = \log(A) / \log(B)\)

theoretical introduction

• Lynch et al. \[ B \propto \mu_d = \frac{3\pi}{\lambda^2}f |\Delta n|^2 d \begin{cases} D' & \text{if } D' \leqslant 1\\[2ex] \!\begin{align} D' - \sqrt{D'^2 - 1}\\ (1 + D'^{-2}/2) \\ + (D'^{-1} + D'^{-3} / 4) \\ \log\left(\frac{D' + \sqrt{D'^2 - 1}}{D' - \sqrt{D'^2 - 1}}\right) \end{align} & \text{otherwise} \end{cases} \]
• dark field as a function of sphere diameter and photon energy

sum over the spectrum

\[ R(\energy) = \frac{\log B}{\log A} = \frac{\mu_d}{2k\beta} \]

\[ R = C\frac{\sum_\energy w(\energy)|\Delta n(\energy)|^2 \energy u(\energy)}{\sum_\energy w(\energy) \energy \beta} \]

expect large increase in contrast

\[ R = C\frac{\sum_\energy w(\energy)|\Delta n(\energy)|^2 \energy u(\energy)}{\sum_\energy w(\energy) \energy \beta} \]

• \(u\) depends on the diameter of the pores
• \(\Delta n\) includes \(\delta\)

protocol

• dry cement cylinder at 120 °C for one hour
• isolate sides with water-proof tape
• put the base in contact with water
• repeated radiographs with 20 phase steps x 0.2 s for about two hours

results: absorption

results: ratio \(R\)

first shot

after one hour

contrast-to-noise ratio

contrast-to-noise ratio

quantitative diffusion

thresholding \(\rightarrow\) fraction of wet pixels

conclusions and outline

• critical issues to be considered by in-house fabrication team
• lung experiment would be repeated if we get any emphysematic samples
• expand the cement measurements
  • a complete theoretical treatment is possible by including a beamline micro-CT for the pore-size distribution
  • Fei's input particularly valuable now that she joins the team