Direct measurement of transverse coherence length of hard X rays from interference fringes

Coherent X-ray beam expander based on a multilens interferometer

A coherent X-ray beam expander based on a multilens interferometer is proposed in this paper. The multilens interferometer allows efficient generation of a highly diverging coherent beam up to several milliradians in the hard X-ray energy range. The optical properties of the interferometer were experimentally demonstrated at the ESRF ID13 undulator beamline (Grenoble, France), using 12.4 keV X-rays. The beam expander allowed us to control the angular size and photon flux density of the formed beam and enabled operation in both coherent and incoherent modes. The experimental results were fully consistent with the theoretical concepts and appropriate computer simulations. Future design improvements and related applications are also discussed.

X-ray phase-sensitive imaging using a bilens interferometer based on refractive optics

The phase-sensitive X-ray imaging technique based on the bilens interferometer is developed. The essence of the method consists of scanning a sample, which is set upstream of the bilens across the beam of one lens of the interferometer by recording changes in the interference pattern using a high-resolution image detector. The proposed approach allows acquiring the absolute value of a phase shift profile of the sample with a fairly high phase and spatial resolution. The possibilities of the imaging technique were studied theoretically and experimentally using fibres with different sizes as the test samples at the ESRF ID06 beamline with 12 keV X-rays. The corresponding phase shift profile reconstructions and computer simulations were performed. The experimental results are fully consistent with theoretical concepts and appropriate numerical calculations. Applications of the interferometric imaging technique are discussed, as well as future improvements.

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.

Visualization of protein crystals by high-energy phase-contrast X-ray imaging

High-energy phase-contrast X-ray microscopy and tomography of protein crystals in an optically opaque matrix is demonstrated with micrometre resolution on the macromolecular crystallography beamline P14 at PETRA III.

For the extraction of the best possible X-ray diffraction data from macromolecular crystals, accurate positioning of the crystals with respect to the X-ray beam is crucial. In addition, information about the shape and internal defects of crystals allows the optimization of data-collection strategies. Here, it is demonstrated that the X-ray beam available on the macromolecular crystallo­graphy beamline P14 at the high-brilliance synchrotron-radiation source PETRA III at DESY, Hamburg, Germany can be used for high-energy phase-contrast microtomography of protein crystals mounted in an optically opaque lipidic cubic phase matrix. Three-dimensional tomograms have been obtained at X-ray doses that are substantially smaller and on time scales that are substantially shorter than those used for diffraction-scanning approaches that display protein crystals at micrometre resolution. Adding a compound refractive lens as an objective to the imaging setup, two-dimensional imaging at sub-micrometre resolution has been achieved. All experiments were performed on a standard macromolecular crystallography beamline and are compatible with standard diffraction data-collection workflows and apparatus. Phase-contrast X-ray imaging of macromolecular crystals could find wide application at existing and upcoming low-emittance synchrotron-radiation sources.

X-ray reflecto-interferometer based on compound refractive lenses

An X-ray amplitude-splitting interferometer based on compound refractive lenses, which operates in the reflection mode, is proposed and realized. The idea of a reflecto-interferometer is to use a very simplified experimental setup where a focused X-ray beam reflected from parallel flat surfaces creates an interference pattern in a wide angular range. The functional capabilities of the interferometer were experimentally tested at the European Synchrotron Radiation Facility (ESRF) ID06 beamline in the X-ray energy range from 10 keV to 15 keV. The main features of the proposed approach, high spatial and temporal resolution, were demonstrated experimentally. The reflections from free-standing Si3N4 membranes, gold and resist layers were studied. Experimentally recorded interferograms are in good agreement with our simulations. The main advantages and future possible applications of the reflecto-interferometer are discussed.

Focus characterization of the NanoMAX Kirkpatrick-Baez mirror system

The focusing and coherence properties of the NanoMAX Kirkpatrick-Baez mirror system at the fourth-generation MAX IV synchrotron in Lund have been characterized. The direct measurement of nano-focused X-ray beams is possible by scanning of an X-ray waveguide, serving basically as an ultra-thin slit. In quasi-coherent operation, beam sizes of down to 56 nm (FWHM, horizontal direction) can be achieved. Comparing measured Airy-like fringe patterns with simulations, the degree of coherence |μ| has been quantified as a function of the secondary source aperture (SSA); the coherence is larger than 50% for SSA sizes below 11 µm at hard X-ray energies of 14 keV. For an SSA size of 5 µm, the degree of coherence has been determined to be 87%.

A real-time phase-space beam emittance monitoring system

An electron beam position and angle monitoring system, ps-BPM, has been shown to be able to measure the electron source position and angle at a single location in a beamline at a synchrotron source. This system uses a monochromator to prepare a photon beam whose energy is at that of the K-edge of an absorber filter. The divergence of the beam from the source gives an energy range that will encompass the K-edge of the filter. A measurement of the centre of the monochromatic beam and the K-edge location through the absorber filter gives the position and angle of the electron source. Here, it is shown that this system is also capable of measuring the source size and divergence at the same time. This capability is validated by measurement as the beam size in the storage ring was changed and by ray-tracing simulations. The system operates by measuring the photon beam spatial distribution as well as a K-edge filtered beam distribution. These additional measurements result in the ability to also determine the electron source size and divergence.

Probing the spatial coherence of wide X-ray beams with Fresnel mirrors at BL25SU of SPring-8

Probing the spatial coherence of X-rays has become increasingly important when designing advanced optical systems for beamlines at synchrotron radiation sources and free-electron lasers. Double-slit experiments at various slit widths are a typical method of quantitatively measuring the spatial coherence over a wide wavelength range including the X-ray region. However, this method cannot be used for the analysis of spatial coherence when the two evaluation points are separated by a large distance of the order of millimetres owing to the extremely narrow spacing between the interference fringes. A Fresnel-mirror-based optical system can produce interference patterns by crossing two beams from two small mirrors separated in the transverse direction to the X-ray beam. The fringe spacing can be controlled via the incidence angles on the mirrors. In this study, a Fresnel-mirror-based optical system was constructed at the soft X-ray beamline (BL25SU) of SPring-8. The relationship between the coherence and size of the virtual source was quantitatively measured at 300 eV in both the vertical and horizontal directions using the beam. The results obtained indicate that this is a valuable method for the optimization of optical systems along beamlines.

Rocking curve and spatial coherence properties of a long X-ray compound refractive lens

Semi-analytical theory of a long set of X-ray compound refractive lenses (CRLs) based on recurrence relations is developed further. The geometrical aperture, angular divergence of incident radiation and source size were accurately taken into account. Using this theory it is possible to calculate the width of the rocking curve of a long (40.7 cm) Be CRL which coincides with experimental data obtained earlier. By this approach the transverse coherence length for the X-ray beam after passing a set of CRLs of arbitrary complexity has been estimated. It is shown that at the focus this coherence length is equal to a diffraction-limited beam size (beam size in the case of a point source) and has minimal difference with the real beam size.

Coherent X-ray beam metrology using 2D high-resolution Fresnel-diffraction analysis

Direct metrology of coherent short-wavelength beamlines is important for obtaining operational beam characteristics at the experimental site. However, since beam-time limitation imposes fast metrology procedures, a multi-parametric metrology from as low as a single shot is desirable. Here a two-dimensional (2D) procedure based on high-resolution Fresnel diffraction analysis is discussed and applied, which allowed an efficient and detailed beamline characterization at the SACLA XFEL. So far, the potential of Fresnel diffraction for beamline metrology has not been fully exploited because its high-frequency fringes could be only partly resolved with ordinary pixel-limited detectors. Using the high-spatial-frequency imaging capability of an irradiated LiF crystal, 2D information of the coherence degree, beam divergence and beam quality factor M² were retrieved from simple diffraction patterns. The developed beam metrology was validated with a laboratory reference laser, and then successfully applied at a beamline facility, in agreement with the source specifications.

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.

Lens coupled tunable Young's double pinhole system for hard X-ray spatial coherence characterization

We have implemented a modified Young's double slit experiment using pinholes with tunable separation distance coupled with compound refractive lens for hard X-ray spatial coherence characterization. Varying distance between the apertures provides a high sensitivity to the determination of spatial coherence across a wide range of experimental parameters. The use of refractive lenses as a Fourier transformer ensures far field registration conditions and allows the realization of a very compact experimental setup in comparison with the classical Young technique and its derivatives. The tunable double aperture interferometer was experimentally tested at the ESRF ID06 beamline in the energy range from 8 to 25 keV. The spatial coherence and the source size were measured by evaluating the visibility of the interference fringes at various separation distances between the apertures and this value agrees very well with the data obtained by other techniques. The proposed scheme can be used for comprehensive characterization of the coherence properties of the source on low emittance synchrotrons in the hard X-ray region.

Computer simulations of X-ray six-beam diffraction in a perfect silicon crystal. I

This paper reports computer simulations of the transmitted-beam intensity distribution for the case of six-beam (000, 220, 242, 044, -224, -202) diffraction of X-rays in a perfect silicon crystal of thickness 1 mm. Both the plane-wave angular dependence and the six-beam section topographs, which are usually obtained in experiments with a restricted beam (two-dimensional slit), are calculated. The angular dependence is calculated in accordance with Ewald's theory. The section topographs are calculated from the angular dependence by means of the fast Fourier transformation procedure. This approach allows one to consider, for the first time, the transformation of the topograph's structure due to the two-dimensional slit sizes and the distance between the slit and the detector. The results are in good agreement with the results of other works and with the experimental data. This method of calculation does not require a supercomputer and it was performed on a standard laptop. A detailed explanation of the main features of the diffraction patterns at different distances between the slit and the detector is presented.

Measurement of power spectral density of broad-spectrum visible light with heterodyne near field scattering and its scalability to betatron radiation

We exploit the speckle field generated by scattering from a colloidal suspension to access both spatial and temporal coherence properties of broadband radiation. By applying the Wiener-Khinchine theorem to the retrieved temporal coherence function, information about the emission spectrum of the source is obtained in good agreement with the results of a grating spectrometer. Experiments have been performed with visible light. We prove more generally that our approach can be considered as a tool for modeling a variety of cases. Here we discuss how to apply such diagnostics to broad-spectrum betatron radiation produced in the laser-driven wakefield accelerator under development at SPARC LAB facility in Frascati.

Analogical optical modeling of the asymmetric lateral coherence of betatron radiation

By exploiting analogical optical modeling of the radiation emitted by ultrarelativistic electrons undergoing betatron oscillations, we demonstrate peculiar properties of the spatial coherence through an interferometric method reminiscent of the classical Young's double slit experiment. The expected effects due to the curved trajectory and the broadband emission are accurately reproduced. We show that by properly scaling the fundamental parameters for the wavelength, analogical optical modeling of betatron emission can be realized in many cases of broad interest. Applications to study the feasibility of future experiments and to the characterization of beam diagnostics tools are described.

Numerical analysis of partially coherent radiation at soft x-ray beamline

A new model for numerical analysis of partially coherent x-ray at synchrotron beamlines is presented. The model is based on statistical optics. Four-dimensional coherence function, Mutual Optical Intensity (MOI), is applied to describe the wavefront of the partially coherent light. The propagation of MOI through optical elements in the beamline is deduced with numerical calculation. The coherence of x-ray through beamlines can be acquired. We applied the model to analyze the coherence in the STXM beamline at SSRF, and got the coherence length of the beam at the endstation. To verify the theoretical results, the diffraction experiment of a single slit was performed and the diffraction pattern was simulated to get the coherence length, (31 ± 3.0) µm × (25 ± 2.1) µm (H × V), which had a good agreement with the theoretical results, (30.7 ± 0.6) µm × (31 ± 5.3) µm (H × V). The model is applicable to analyze the coherence in synchrotron beamlines.

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.

Evaluation of partial coherence correction in X-ray ptychography

Coherent X-ray Diffraction Imaging (CDI) and X-ray ptychography both heavily rely on the high degree of spatial coherence of the X-ray illumination for sufficient experimental data quality for reconstruction convergence. Nevertheless, the majority of the available synchrotron undulator sources have a limited degree of partial coherence, leading to reduced data quality and a lower speckle contrast in the coherent diffraction patterns. It is still an open question whether experimentalists should compromise the coherence properties of an X-ray source in exchange for a higher flux density at a sample, especially when some materials of scientific interest are relatively weak scatterers. A previous study has suggested that in CDI, the best strategy for the study of strong phase objects is to maintain a high degree of coherence of the illuminating X-rays because of the broadening of solution space resulting from the strong phase structures. In this article, we demonstrate the first systematic analysis of the effectiveness of partial coherence correction in ptychography as a function of the coherence properties, degree of complexity of illumination (degree of phase diversity of the probe) and sample phase complexity. We have also performed analysis of how well ptychographic algorithms refine X-ray probe and complex coherence functions when those variables are unknown at the start of reconstructions, for noise-free simulated data, in the case of both real-valued and highly-complex objects.

Coherent X-ray diffraction imaging and characterization of strain in silicon-on-insulator nanostructures

Coherent X-ray diffraction imaging (CDI) has emerged in the last decade as a promising high resolution lens-less imaging approach for the characterization of various samples. It has made significant technical progress through developments in source, algorithm and imaging methodologies thus enabling important scientific breakthroughs in a broad range of disciplines. In this report, we will introduce the principles of forward scattering CDI and Bragg geometry CDI (BCDI), with an emphasis on the latter. BCDI exploits the ultra-high sensitivity of the diffraction pattern to the distortions of crystalline lattice. Its ability of imaging strain on the nanometer scale in three dimensions is highly novel. We will present the latest progress on the application of BCDI in investigating the strain relaxation behavior in nanoscale patterned strained silicon-on-insulator (sSOI) materials, aiming to understand and engineer strain for the design and implementation of new generation semiconductor devices.

X-ray multilens interferometer based on Si refractive lenses

We report a multilens X-ray interferometer consisting of six parallel arrays of planar compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. Overlapping such coherent beams produces an interference pattern demonstrating substantially strong longitudinal functional dependence. The interference fringe pattern produced by multilens interferometer was described by Talbot imaging formalism. Theoretical analysis of the interference pattern formation was carried out and corresponding computer simulations were performed. The proposed multilens interferometer was experimentally tested at ID06 ESRF beamline in the X-ray energy range from 10 to 30 keV. The experimentally recorded fractional Talbot images are in a good agreement with computer simulations.

Retrieval of the atomic displacements in the crystal from the coherent X-ray diffraction pattern

The retrieval of spatially resolved atomic displacements is investigated via the phases of the direct(real)-space image reconstructed from the strained crystal's coherent X-ray diffraction pattern. It is demonstrated that limiting the spatial variation of the first- and second-order spatial displacement derivatives improves convergence of the iterative phase-retrieval algorithm for displacements reconstructions to the true solution. This approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.

Measurement of coherence length and incoherent source size of hard x-ray undulator beamline at Pohang Light Source-II

We measured the spatial coherence length and incoherent source size of a hard x-ray undulator beamline at Pohang Light Source-II, the stored electron energy of which has been increased from 2.5 GeV to 3 GeV. The coherence length was determined by single-slit measurement of the visibility of the Fresnel diffraction pattern. The correlated incoherent source size was cross-checked for three different optics: the single slit, beryllium parabolic compound refractive lenses, and the Fresnel zone plate. We concluded that the undulator beamline has an effective incoherent source size (FWHM) of 540 μm (horizontal) × 50 μm (vertical).

A robust tool for photon source geometry measurements using the fractional Talbot effect

A reliable measurement of beam coherence is important for optimal performance of a number of coherence methods being utilized at third-generation synchrotrons and free-electron lasers. Various approaches have been proposed in the past for determining the source size, and hence the degree of coherence; however they often require complex setups with perfect optics and suffer from undefined uncertainties. We present a robust tool for X-ray source characterization with a full quantitative uncertainty analysis for fast on-the-fly coherence measurements. The influence of three multilayer monochromator crystals on the apparent source size is evaluated using the proposed method.

Full optical characterization of coherent x-ray nanobeams by ptychographic imaging

Scanning coherent diffraction microscopy (ptychography) is an emerging hard x-ray microscopy technique that yields spatial resolutions well below the lateral size of the probing nanobeam. Besides a high resolution image of the object, the complex wave field of the probe can be reconstructed at the position of the object. By verifying the consistency of several independent wave field measurements along the optical axis, we address the question of how well the reconstruction represents the nanobeam. With a single ptychogram the wave field can be properly determined over a large range along the optical axis, also at positions inaccessible otherwise.

Experimental characterization of the coherence properties of hard x-ray sources

The experimental characterization of the coherence properties of hard X-ray sources is reported and discussed. The source is described by its Mutual Optical Intensity (MOI). The coherent-mode decomposition is applied to the MOI described by a Gaussian-Schell model. The method allows for a direct, quantitative characterization of the degree of coherence of both synchrotron and laboratory sources. The latter represents the first example of characterizing a low coherence hard x-ray source.

Manipulating atomic fragmentation processes by controlling the projectile coherence

We have measured the scattering angle dependence of cross sections for ionization in p+H2 collisions for a fixed projectile energy loss. Depending on the projectile coherence, interference due to indistinguishable diffraction of the projectile from the two atomic centers was either present or absent in the data. This shows that, due to the fundamentals of quantum mechanics, the preparation of the beam must be included in theoretical calculations. The results have far-reaching implications on formal atomic scattering theory because this critical aspect has been overlooked for several decades.

Coherence and wavefront characterization of Si-111 monochromators using double-grating interferometry

A study of the coherence and wavefront properties of a pseudo-channel-cut monochromator in comparison with a double-crystal monochromator is presented. Using a double-grating interferometer designed for the hard X-ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel-cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.

Probing the transverse coherence of an undulator x-ray beam using brownian particles

We present a novel method to map the two-dimensional transverse coherence of an x-ray beam using the dynamical near-field speckles formed by scattering from colloidal particles. Owing to the statistical nature of the method, the coherence properties of synchrotron radiation from an undulator source is obtained with high accuracy. The two-dimensional complex coherence function is determined at the sample position and the imaging optical scheme further allowed us to evaluate the coherence factor at the undulator output despite the aberrations introduced by the focusing optics.

X-ray nanointerferometer based on si refractive bilenses

We report a novel type of x-ray interferometer employing a bilens system consisting of two parallel compound refractive lenses, each of which creates a diffraction limited beam under coherent illumination. By closely overlapping such coherent beams, an interference field with a fringe spacing ranging from tens of nanometers to tens of micrometers is produced. In an experiment performed with 12 keV x rays, submicron fringes were observed by scanning and moiré imaging of the test grid. The far field interference pattern was used to characterize the x-ray coherence. Our technique opens up new opportunities for studying natural and man-made nanoscale materials.

Phase-space reconstruction of focused x-ray fields

We apply the method of phase-space tomography to reconstruct x-ray beams focused using a compound refractive lens. We show that it is possible to decouple the effect of aberrations in the optical system from the field and hence measure both them and the original field. We recover the complex coherence function and find that it is consistent with expectations.

Shearing interferometer for quantifying the coherence of hard x-ray beams

We report a quantitative measurement of the full transverse coherence function of the 14.4 keV x-ray radiation produced by an undulator at the Swiss Light Source. An x-ray grating interferometer consisting of a beam splitter phase grating and an analyzer amplitude grating has been used to measure the degree of coherence as a function of the beam separation out to 30 microm. Importantly, the technique provides a model-free and spatially resolved measurement of the complex coherence function and is not restricted to high resolution detectors and small fields of view. The spatial characterization of the wave front has important applications in discovering localized defects in beam line optics.

Determination of the size and structure of an X-pinch x-ray source from the diffraction pattern produced by microfabricated slits

X-pinch plasma emits subnanosecond bursts of x rays in the 3-10-keV energy range from a small source. As such, it has been used for high-resolution point-projection imaging of small, dense, rapidly changing plasmas as well as for submillimeter-thick biological samples. In addition to the effect of source size on geometric resolution, a small source size can also provide high spatial coherence of x rays, enabling the rays to be used for imaging weakly absorbing objects with excellent spatial resolution by a method called phase-contrast imaging. To determine the source size, we microfabricated gold slits and imaged them in a point-projection radiography configuration. The shape of the shadow image pattern depends on the source size and energy band of the x rays, the shape and material used for the slits, and the geometry of the experiment. Experimental results have been compared with wave-optics calculations of the expected image pattern as a function of all the parameters listed above. For example, assuming a Gaussiansource distribution, an effective source size in 2.5-4.1 A radiation (1 A = 0.1 nm) of 1.2 +/- 0.5 microm (full width at half-maximum) was determined for a 20-microm Mo wire X pinch. Characterization of the size and structure of the x-ray bursts from X pinches by the use of different wire materials and different slit structures is made.

Synchrotron beam coherence: a spatially resolved measurement

We report a precise and spatially resolved measurement of the complex degree of coherence of a one-dimensional 1.5-keV beam produced by a third-generation synchrotron source. The method of phase-space tomography is used, which requires only measurements of the x-ray intensity. We find that the field is statistically stationary to within experimental error, the correlations are very well approximated by a Gaussian distribution, and the measured coherence length is in excellent agreement with expectations.

Characterization of the transverse coherence of hard synchrotron radiation by intensity interferometry

The transverse coherence of x rays was measured with an intensity interferometer using a 120-microeV-bandwidth monochromator operating at 14.41 keV. By analyzing the transverse coherence profiles, a vertical source profile of a 25-m long undulator of SPring-8, as well as the coherence degradation by a phase object in the beam path, were quantitatively characterized.