Achieving diffraction-limited resolution in soft-X-ray Fourier-transform holography

The spatial resolution of microscopic images acquired via X-ray Fourier-transform holography is limited by the source size of the reference wave and by the numerical aperture of the detector. We analyze the interplay between both influences and show how they are matched in practice. We further identify, how high spatial frequencies translate to imaging artifacts in holographic reconstructions where mainly the reference beam limits the spatial resolution. As a solution, three methods are introduced based on numerical post-processing of the reconstruction. The methods comprise apodization of the hologram, refocusing via wave propagation, and deconvolution using the transfer function of the imaging system. In particular for the latter two, we demonstrate that image details smaller than the source size of the reference beam can be recovered up to the diffraction limit of the hologram. Our findings motivate the intentional application of a large reference-wave source enhancing the image contrast in applications with low photon numbers such as single-shot experiments at free-electron lasers or imaging at laboratory sources.BMBF, 05K10KTB, Verbundprojekt: FSP 301 - FLASH: Nanoskopische Systeme. Teilprojekt 1.1: Universelle Experimentierkammer für Streuexperimente mit kohärenten Femtosekunden-Röntgenpulsen Multi Purpose Coherent Scattering Chamber for FLASH and XFEL 'MPscatt

Mask-based dual-axes tomoholography using soft x-rays

We explore tomographic mask-based Fourier transform x-ray holography with respect to the use of a thin slit as a reference wave source. This imaging technique exclusively uses the interference between the waves scattered by the object and the slit simplifying the experimental realization and ensuring high data quality. Furthermore, we introduce a second reference slit to rotate the sample around a second axis and to record a dual-axes tomogram. Compared to a single-axis tomogram, the reconstruction artifacts are decreased in accordance with the reduced missing data wedge. Two demonstration experiments are performed where test structures are imaged with a lateral resolution below 100 nm

Reduced order multirate schemes in industrial circuit simulation

AbstractIn this paper the industrial application of Reduced Order Multirate (ROMR) schemes is presented. This paper contains the mathematical foundations of the ROMR schemes and elaborates on the construction of these schemes using specific Model Order Reduction (MOR) techniques. Especially the Maximum Entropy Snapshot Sampling method for generating a reduced basis and reduction by Gauß–Newton with Approximated Tensors (GNAT). This basis generation method is also used for generating the basis for the gappy hyper-reduction method used for nonlinear function evaluation. For the multirate integration part, a Backward Differentation Formula approach to integration is used in conjunction with a coupled-slowest-first multirate approach. After introducing the numerical approach to industrial circuit simulation validation experiments are performed. First a simple academic model is used, and then an industrial test case is simulated as presented by STMicroelectronics. A significant speedup in simulation time is achieved whilst accuracy and convergence is kept

Experimental evaluation of signal-to-noise in spectro-holography via modified uniformly redundant arrays in the soft x-ray and extreme ultraviolet spectral regime

We present dichroic x-ray lensless magnetic imaging by Fourier transform holography with an extended reference scheme via a modified uniformly redundant array (mURA). Holographic images of magnetic domains simultaneously generated by a single pinhole reference as well as by a mURA reference are compared with respect to the signal-to-noise ratio (SNR) as a function of exposure time. We apply this approach for spectro-holographic imaging of ferromagnetic domain patterns in Co/Pt multilayer films. Soft x-rays with wavelengths of 1.59 nm (Co L 3 absorption edge) and 20.8 nm (Co M 2,3 absorption edges) are used for image formation and to generate contrast via x-ray magnetic circular dichroism. For a given exposure time, the mURA-based holography allows to decouple the reconstruction SNR from the spatial resolution. For 1.59 nm wavelength, the reconstruction via the extended reference scheme shows no significant loss of spatial resolution compared to the single pinhole reference. In contrast, at 20.8 nm wavelength the single pinhole reveals some very intricate features which are lost in the image generated by the mURA, although overall a high-quality image is generated. The SNR-advantage of the mURA scheme is most notable when the hologram has to be encoded with few photons, while errors associated with the increased complexity of the reconstruction process reduce the advantage for high-photon-number experiments.BMBF, 05K13KT3, Verbundprojekt 05K2013 - DynaMaX: Messplatz für ultraschnelle Dynamik bei BESSY II. Teilprojekt

Dynamic Phase Transitions in Cell Spreading

We monitored isotropic spreading of mouse embryonic fibroblasts on fibronectin-coated substrates. Cell adhesion area versus time was measured via total internal reflection fluorescence microscopy. Spreading proceeds in well-defined phases. We found a power-law area growth with distinct exponents a_i in three sequential phases, which we denote basal (a_1=0.4+-0.2), continous (a_2=1.6+-0.9) and contractile (a_3=0.3+-0.2) spreading. High resolution differential interference contrast microscopy was used to characterize local membrane dynamics at the spreading front. Fourier power spectra of membrane velocity reveal the sudden development of periodic membrane retractions at the transition from continous to contractile spreading. We propose that the classification of cell spreading into phases with distinct functional characteristics and protein activity patterns serves as a paradigm for a general program of a phase classification of cellular phenotype. Biological variability is drastically reduced when only the corresponding phases are used for comparison across species/different cell lines.Comment: 4 pages, 5 figure

Multi-Color Imaging of Magnetic Co/Pt Multilayers

We demonstrate for the first time the realization of a spatial resolved two color, element-specific imaging experiment at the free-electron laser facility FERMI. Coherent imaging using Fourier transform holography was used to achieve direct real space access to the nanometer length scale of magnetic domains of Co/Pt heterostructures via the element-specific magnetic dichroism in the extreme ultraviolet spectral range. As a first step to implement this technique for studies of ultrafast phenomena we present the spatially resolved response of magnetic domains upon femtosecond laser excitation