Characterization of spatial coherence of synchrotron radiation with non-redundant arrays of apertures

FOCUS: fast Monte Carlo approach to coherence of undulator sources

FOCUS (Fast Monte CarlO approach to Coherence of Undulator Sources) is a new GPU-based simulation code to compute the transverse coherence of undulator radiation from ultra-relativistic electrons. The core structure of the code, which is written in the language C++ accelerated with CUDA, combines an analytical description of the emitted electric fields and massively parallel computations on GPUs. The combination is rigorously justified by a statistical description of synchrotron radiation based on a Fourier optics approach. FOCUS is validated by direct comparison with multi-electron Synchrotron Radiation Workshop (SRW) simulations, evidencing a reduction in computation times by up to five orders of magnitude on a consumer laptop. FOCUS is then applied to systematically study the transverse coherence in typical third- and fourth-generation facilities, highlighting peculiar features of undulator sources close to the diffraction limit. FOCUS is aimed at fast evaluation of the transverse coherence of undulator radiation as a function of the electron beam parameters, to support and help prepare more advanced and detailed numerical simulations with traditional codes like SRW.

Fast and reliable technique for spatial coherence measurement with a temporally modulated nonredundant slit array

We propose a method of measuring the spatial coherence of light by means of a temporally modulated nonredundant slit array implemented on a digital micromirror device. We first formulate the theory of the spatial coherence measurement to incorporate a general case when the observation plane is not necessarily placed in the far field of the slit array. We then demonstrate experimentally that a single measurement determines the spatial coherence for 15 different slit separations accurately, even if background light is unavoidable, under the condition that a nonredundant array of six slits is illuminated evenly. These results clearly show that fast and highly reliable spatial coherence measurement is achievable with the proposed method without any difficulties.

Direct 2D spatial-coherence determination using the Fourier-analysis method: multi-parameter characterization of the P04 beamline at PETRA III

We present a systematic 2D spatial-coherence analysis of the soft-X-ray beamline P04 at PETRA III for various beamline configurations. The influence of two different beam-defining apertures on the spatial coherence properties of the beam is discussed and optimal conditions for coherence-based experiments are found. A significant degradation of the spatial coherence in the vertical direction has been measured and sources of this degradation are identified and discussed. The Fourier-analysis method, which gives fast and simple access to the 2D spatial coherence function of the X-ray beam, is used for the experiment. Here, we exploit the charge scattering of a disordered nanodot sample allowing the use of arbitrary X-ray photon energies with this method.

Coherence properties of the high-energy fourth-generation X-ray synchrotron sources

An analysis of the coherence properties of the fourth-generation high-energy storage rings with emittance values of 10 pm rad is performed. It is presently expected that a storage ring with these low emittance values will reach diffraction limit at hard X-rays. Simulations of coherence properties were performed with the XRT software and an analytical approach for different photon energies from 500 eV to 50 keV. It was demonstrated that a minimum photon emittance (diffraction limit) reached at such storage rings is λ/2π. Using mode decomposition it is shown that, for the parameters of the storage ring considered in this work, the diffraction limit will be reached for soft X-ray energies of 500 eV. About ten modes will contribute to the radiation field at 12 keV photon energy and even more modes give a contribution at higher photon energies. Energy spread effects of the electron beam in a low-emittance storage ring were analysed in detail. Simulations were performed at different relative energy spread values from zero to 2 × 10^-3. A decrease of the degree of coherence with an increase of the relative energy spread value was observed. This analysis shows that, to reach the diffraction limit for high photon energies, electron beam emittance should go down to 1 pm rad and below.

Quantitative ptychographic bio-imaging in the water window

Coherent X-ray ptychography is a tool for highly dose efficient lensless nano-imaging of biological samples. We have used partially coherent soft X-ray synchrotron radiation to obtain a quantitative image of a laterally extended, dried, and unstained fibroblast cell by ptychography. We used data with and without a beam stop that allowed us to measure coherent diffraction with a high-dynamic range of 1.7·10⁶. As a quantitative result, we obtained the refractive index values for two regions of the cell with respect to a reference area. Due to the photon energy in the water window we obtained an extremely high contrast of 53% at 71 nm half-period resolution. The dose applied in our experiment was 9.5·10⁴ Gy and is well below the radiation damage threshold. The concept for dynamic range improvement for low dynamic range detectors with a beam stop opens the path for high resolution nano-imaging of a variety of samples including cryo-preserved, hydrated and unstained biological cells.

The coherent radiation fraction of low-emittance synchrotrons

In this work the coherence properties of the synchrotron radiation beam from an X-ray undulator in a fourth-generation storage ring are analyzed. A slightly focused X-ray beam is simulated using a wavefront propagation through a non-redundant array of slits and the mutual coherence function is directly obtained and compared with the Gaussian-Schell approximation. The numerical wave propagation and the approximate analytical approaches are shown to agree qualitatively, and it is also shown that, when the coherent fraction is selected by a finite aperture before the focusing element, even achromatic focusing systems like total reflection mirrors become slightly chromatic. This effect is also well accounted for in the Gaussian-Schell model. The wavefront propagation simulation through the non-redundant array was repeated with an imperfect mirror demonstrating that, although the wavefront is distorted, its coherent length is practically unchanged.

Two-dimensional mapping of the asymmetric lateral coherence of thermal light

We report in this work the first experimental verification of the asymmetric lateral coherence which is a measurement of the spatio-temporal coherence by using a wide-band Young interference experiment with a fixed off-axis slit. We demonstrate the coherence properties through the measurement of the real part of the coherence factor of thermal light. We extend our recent results obtained for betatron and undulator radiations providing a robust experimental method for the two-dimensional mapping of the two-point correlation function of broadband radiation preserving the phase information. The proposed method can be used as a high-sensitivity alternative to traditional interferometry with quasi-monochromatic radiation.

Spatial coherence determination from the Fourier analysis of a resonant soft X-ray magnetic speckle pattern

We present a method to determine the two-dimensional spatial coherence of synchrotron radiation in the soft X-ray regime by analyzing the Fourier transform of the magnetic speckle pattern from a ferromagnetic film in a multidomain state. To corroborate the results, a Young's double-pinhole experiment has been performed. The transverse coherence lengths in vertical and horizontal direction of both approaches are in a good agreement. The method presented here is simple and gives a direct access to the coherence properties of synchrotron radiation without nanostructured test objects.

Characterizing transverse coherence of an ultra-intense focused X-ray free-electron laser by an extended Young's experiment

Characterization of transverse coherence is one of the most critical themes for advanced X-ray sources and their applications in many fields of science. However, for hard X-ray free-electron laser (XFEL) sources there is very little knowledge available on their transverse coherence characteristics, despite their extreme importance. This is because the unique characteristics of the sources, such as the ultra-intense nature of XFEL radiation and the shot-by-shot fluctuations in the intensity distribution, make it difficult to apply conventional techniques. Here, an extended Young's interference experiment using a stream of bimodal gold particles is shown to achieve a direct measurement of the modulus of the complex degree of coherence of XFEL pulses. The use of interference patterns from two differently sized particles enables analysis of the transverse coherence on a single-shot basis without a priori knowledge of the instantaneous intensity ratio at the particles. For a focused X-ray spot as small as 1.8 µm (horizontal) × 1.3 µm (vertical) with an ultrahigh intensity that exceeds 10(18) W cm(-2) from the SPring-8 Ångstrom Compact free-electron LAser (SACLA), the coherence lengths were estimated to be 1.7 ± 0.2 µm (horizontal) and 1.3 ± 0.1 µm (vertical). The ratios between the coherence lengths and the focused beam sizes are almost the same in the horizontal and vertical directions, indicating that the transverse coherence properties of unfocused XFEL pulses are isotropic. The experiment presented here enables measurements free from radiation damage and will be readily applicable to the analysis of the transverse coherence of ultra-intense nanometre-sized focused XFEL beams.

Water window ptychographic imaging with characterized coherent X-rays

A ptychographical coherent diffractive imaging experiment in the water window with focused soft X-rays at 500 eV is reported. An X-ray beam with high degree of coherence was selected for ptychography at the P04 beamline of PETRA III synchrotron radiation source. The beam coherence was measured with the newly developed non-redundant array method, and a coherence length of 4.1 µm and global degree of coherence of 35% at 100 µm exit slit opening in the vertical direction were determined. A pinhole, 2.6 µm in size, selected the coherent part of the beam that was used to obtain ptychographic reconstruction results of a lithographically manufactured test sample and a fossil diatom. The achieved resolution was 53 nm for the test sample and was only limited by the size of the detector. The diatom was imaged at a resolution better than 90 nm.