X-ray propagation microscopy of biological cells using waveguides as a quasipoint source

We have used x-ray waveguides as highly confining optical elements for nanoscale imaging of unstained biological cells using the simple geometry of in-line holography. The well-known twin-image problem is effectively circumvented by a simple and fast iterative reconstruction. The algorithm which combines elements of the classical Gerchberg-Saxton scheme and the hybrid-input-output algorithm is optimized for phase-contrast samples, well-justified for imaging of cells at multi-keV photon energies. The experimental scheme allows for a quantitative phase reconstruction from a single holographic image without detailed knowledge of the complex illumination function incident on the sample, as demonstrated for freeze-dried cells of the eukaryotic amoeba Dictyostelium discoideum. The accessible resolution range is explored by simulations, indicating that resolutions on the order of $20$ nm are within reach applying illumination times on the order of minutes at present synchrotron sources.

Figure 1

Experimental setup. The x-ray beam is focused by two KB mirrors onto the system of two crossed planar WGs with a layered guiding core structure for optimized transmission. Two-dimesional-beam confinement is achieved by crossing a horizontally confining planar waveguide (HPWG) upstream with a second, vertically confining waveguide (VPWG) downstream. The sample holder (S) with freeze-dried D. discoideum cells attached to a thin polyimide film is placed at a distance $z_1$ from the WG system. The cells (for an optical micrograph, see inset on the upper right, scale bar $5\mathrm{\hspace{0.5em}}\mathrm{\mu }\mathrm{m}$) can be visualized during the experiment using an optical video microscope (V) with a drilled lens to allow for the passage of the x-ray beam. An area detector is placed at a distance $z_2\gg z_1$ away from the sample to collect the intensity diffracted from the sample.

Figure 2

Holographic intensity diffracted from freeze-dried D. discoideum cells, normalized by the empty WG intensity (a). Iterative reconstruction of the object phase, obtained after 200 GS iterations (b). Phase reconstruction obtained with a modified HIO scheme for pure phase objects as described in the main text (c). The boundary of the support area was determined from a holographic reconstruction and is marked here by a dashed blue line. The color bar is scaled in rad and also $\mathrm{mg}/{\mathrm{cm}}^2$, indicating the projected effective mass density of the cells [21]. A line scan through a globular region of higher density is indicated in the upper cell by a thin black line and reproduced in the inset on the lower left (open circles), along with a model curve (red solid line; see main text).

Figure 3

Phase map (a) of a simulated object transmission function for an unstained biological cell with parameters as used in the real experiment and (b) iterative reconstruction obtained with the modified HIO scheme described in the main text. The angular averaged power spectral density (PSD) of the simulated phase map is shown as a red line in panel (c). For comparison, the PSD of the reconstruction from the simulated data is plotted (blue line) along with a PSD of a reconstruction from modeled data with 10 times more simulated flux (black line). The HIO scheme successfully recovers the spatial frequency component marked by an arrow, where there is a zero in the phase-contrast transfer function (PCTF) (d). Notably, an increase in simulated flux results in the recovery of more unconstrained frequencies.

Figure 4

The power spectral density (PSD) of a simulated object transmission function for a weakly scattering Siemens star test pattern is shown in comparison to the PSD of the holographic and the iterative reconstruction from the simulated data, based on the modified HIO scheme (a). See Fig. 5 for the corresponding real-space images. Although the zeros of the contrast transfer function have a strong influence on the holographic reconstruction, in this case the iterative reconstruction is essentially free of such artifacts, and the object transmission function is recovered for nearly all spatial frequencies. The phase-contrast transfer function corresponding to the simulated experimental geometry is shown in panel (b).

Figure 5

Original phase map from a simulated Siemens star test pattern with a phase difference of $0.03$ rad between the light and dark stripes (a), together with the holographic (b) and iterative reconstruction (c), using a modified HIO scheme. Scale bars indicate $250$ nm.