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Quantitative high-energy phase measurements

High-energy ratio independent of the material

Progress towards the new setup

  • gratings
  • source
  • motors
  • detector

Grating fabrication at KIT

Detailed progress on the issue tracker

First overplated mask (June)

Second mask, wrong duty cycle (August)

First irradiation attempt (October)

The resist is too sensitive

New 225 kV source

  • source
  • high-voltage generator
  • controller
  • authorization

Mythen detector

  • energy threshold >20 keV
  • special module with fan geometry
  • 24 bits (was 16)
  • 50 µm pixel size (was 80µm)
  • More about the SNR in Maria's report

Improved visibility by 50%

average from 5% to 7.5%

Improved visibility by 50%

average from 5% to 7.5%

Quantitative phase experiments

  • noise: is \(\sigma_P\) reliable?
  • signal: can we measure \(\delta\)?

Wedge samples

Constant differential phase value proportional to \(\delta\)

  • PMMA - Polymethyl methacrylate
  • PS - Polystyrene
  • HDPE - High-density polyethylene

\(R \approx 2\)

Noise properties of the phase

\[\begin{align*} \sigma_P &= \frac{2}{v_0\sqrt{N_0}}\\ \end{align*} \]
\[\begin{align*} v &= \text{visibility}\\ N &= \text{number of photons}\\ _0 &= \text{without sample} \end{align*} \]

\[ \sigma_P = 2(v_0 \sqrt{N_0})^{-1}\]

\[\text{prediction error} = \frac{\sigma_\text{predicted} - \sigma_\text{observed}}{\sigma_{\text{predicted}}}\]

Measuring \( \delta \)

geometrical inputs + measured dpc value P:

\[ \delta = \frac{2 \pi p \tan \theta}{D}P \]

\( p \) period of the grating
\( D \) distance \(G_1-G_2\)
\( \theta \) wedge angle
\( P \) measured DPC value

Absolute \( \delta \)

material NIST table \( \delta (\cdot 10^{-9}) \) experimental \( \delta (\cdot 10^{-9}) \)
PMMA \(102\) \(92 \pm 19\)
PS \(90\) \(81 \pm 21\)
HDPE \(88\) \(87 \pm 14\)

No fit, no calibration, real absolute experimental values!

theoretical values for an energy of 50 keV, which is the average of the simulated spectrum

Relative \( \delta \)

Accounts for energy calibration, universally used in publications

material NIST table \( \delta/\delta_\text{PMMA} \) experimental \( \delta/\delta_\text{PMMA} \)
PS \(0.89\) \(0.88 \pm 0.30\)
HDPE \(0.87\) \(0.95 \pm 0.25\)

Note the large uncertainty, even after 50 hours exposure per sample

Conclusions

New setup

  • only official authorization is missing
  • excellent performance of the new motors and detector
  • gratings still unavailable

Noise: sensitivity prediction

  • no free parameters, reasonable agreement within 50%
  • important constraints for applications
  • missing link \(R \leftrightarrow \) geometry and energy
  • \(R < \text{ or } > 1 \) should be particularly important

Signal: quantitative phase

  • very good agreement, even without calibration
  • measurement requires many long exposures