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Lensless Imaging Results

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High-Resolution Extreme Ultraviolet Microscopy

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Abstract

The achieved imaging results are presented and discussed in this chapter. Using digital in-line holography amplitude and phase-contrast imaging in the extreme ultraviolet on cell-like specimen is presented. This is followed by experiments on coherent diffraction imaging at the Abbe limit demonstrating unprecedented relative resolution. Experiments carried out in reflection geometry, which allow for much more applications, and the introduction of an award-winning cancer cell classification method conclude that chapter.

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Notes

  1. 1.

    The water window is a range of wavelengths between the K-edge of oxygen at 2.34 nm and the K-edge of carbon at 4.4 nm, where biological materials become transparent.

  2. 2.

    A 3 mm diameter silicon disk with 200 \(\upmu \)m thickness in this case.

  3. 3.

    With simulated hologram \(|U_\mathrm{{det}}(x,y)|^2\) at the end of the reconstruction is denoted. Visual and numerical comparison with the measured hologram \(I(x,y)\) allows to judge whether or not the reconstruction was successful.

  4. 4.

    The refractive index of \(\mathrm {Si}_3\mathrm {N}_4\) is \(n=1.24-0.17\mathrm {i}\) at 39 nm wavelength [5]. Hence, \(\triangle \phi =2\pi \cdot 0.24d /\lambda \) is the phase shift of a wave passing through a \(\mathrm {Si}_3\mathrm {N}_4\) layer of thickness \(d\) relative to the wave propagating through the open space of the burst window in the presented case.

  5. 5.

    Compare to Fig. 3.8 where the distances between pinhole and sample were larger.

  6. 6.

    For the DIH reconstructions presented in this thesis the computation grid was typically between \(4000\times 4000\) and \(7000\times 7000\) pixels large, demanding a high amount of memory.

  7. 7.

    If the measured diffraction pattern in CDI is highly oversampled one can even reduce the computation grid further by binning pixels together without losing resolution in the reconstructed object, as was done in Sect. 4.3.

  8. 8.

    A processor operating at 3.1 GHz having four cores and 8 GB random access memory.

  9. 9.

    For very special sample geometries providing sparsity sub-wavelength CDI was demonstrated for visible light [10].

  10. 10.

    The bare 200 nm silicon nitride has a residual transmission of \(0.02\,\%\) [5].

  11. 11.

    From a first estimate by mechanically measuring the distance it was clear that the distance between sample and CCD was in the order of 10 mm.

  12. 12.

    Maximum detectable momentum transfer refers to the highest measurable modulus of the projected momentum transfer vector \(\mathbf {q}\) for all angles \(\phi \) (Fig. 3.9) with respect to the center of the CCD, e.g. at the CCD’s midpoints of the edges.

  13. 13.

    The conservative value of \(\mathrm {PRTF}=0.5\) as threshold is used.

  14. 14.

    The \(90\,\%\)/\(10\,\%\) of the modulus of the electron density \(\rho \) criterion is used to determine the resolution of the experimental data [11].

  15. 15.

    The different hue is due to a constant phase offset compared to Fig. 4.6c, which is one of the remaining ambiguities in a CDI reconstruction.

  16. 16.

    Please refer to Fig. 3.11 for the coordinate definition in this section.

  17. 17.

    Success in this case is measured by the error metric, which was mentioned in Sect. 2.3.

  18. 18.

    More precisely these are ellipses in the stretched pattern.

  19. 19.

    Note that the NA should in principle allow a resolution of \(\triangle r\approx 0.63\,\upmu \)m. This is effectively reduced here due to the projection.

  20. 20.

    Carbon and gold have a comparable reflectivity at used wavelength and angle of incidence [5]. Hence, one probes the surface and silhouette of the specimen at the same time to acquire a maximum of spatial information.

  21. 21.

    For convenience the whole measured intensity distribution will be denoted as diffraction pattern in the remainder of this section, regardless of the fact that the center represents actually a hologram.

  22. 22.

    A comparable Fourier transform based approach was proposed by Lendaris and Stanley for classifying photographic transparencies [29].

  23. 23.

    Of course this method will also work with pure CDI setups and is not limited to the presented geometry, just the data collection then becomes more problematic due to the need for a beam stop etc.

  24. 24.

    Here image refers to the measured raw data from the CCD. Each image was normalized to a common level.

  25. 25.

    The measured power of a single harmonic at 1 kHz repetition rate behind the pinhole is \(\approx \)1 nW. Together with \(\lambda =39\) nm this yields a number of photons per pulse on target \(n_\mathrm{{ph}}\approx 6\times 10^6\) \({\mathrm {photons}}/{\mathrm {pulse}}\). Together with the exposure time \(t_\mathrm{{exp}}=1{,}500\)s and the values and formulas given in [33] it allows an estimate of the dose.

  26. 26.

    Unit: 1 [Gy] = 1 [J/kg] is the unit of the dose called Gray.

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  1. Institute of Optics and Quantum Electronics, Friedrich Schiller University Jena, Jena, Germany

    Michael Werner Zürch

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Zürch, M.W. (2015). Lensless Imaging Results. In: High-Resolution Extreme Ultraviolet Microscopy. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-12388-2_4

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