Workshop on "X-ray Science with Coherent Radiation"
Shaping X-Rays by Diffractive Coded Nano-Optics
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- Bu səhifədəki naviqasiya:
- David Paterson, Advanced Photon Source
- Nanometer Imaging with a High Brightness Source
Shaping X-Rays by Diffractive Coded Nano-OpticsE. Di FabrizioTASC-NNL-INFM (National Institute for the Physics of Matter) Elettra Synchrotron Light Source
The current intense interest in extreme ultraviolet and x-ray microscopy is mainly due to the availability of a nearly ideal optical source for nano-optics based on diffraction, that is, a source with low divergence whose wavelength can be tuned over a range of several keV and whose spectrum can be monochromatised with a band pass of less than 10-4. Synchrotrons of the latest generation and free electron lasers (in the near future) are devices that produce x-rays with these characteristics. When a source of electromagnetic radiation is bright enough, that is, point-like and monochromatic, a new world opens for the designer of optical instruments and for a wider community of experimenters and theorists. This happened with the invention of the optical microscope and is still happening with x-ray microscopes of the latest generation. Although available x-ray sources have coherence characteristics very close to those of lasers at visible wavelengths, up to now the design of new optical devices has not proceeded much beyond simple focusing optical elements. In fact the zone plate, that can be now considered a well established focusing element for x-rays, was invented more than hundred years ago but due to technological difficulties, they have been implemented only in the last two decades. In this article we show that it is possible to design, fabricate and easily use new optical elements that, beyond focusing, can perform new optical functions. In particular, the intensity (and polarization for extreme ultraviolet wavelength ) of light in the space beyond the optical elements can be redistributed with almost complete freedom. In other words, already available extreme ultraviolet and x-ray sources are suitable as ideal sources for diffractive optical elements designed to perform new optical functions that can conveniently be summarized under the expression .of. “beam shaping”. To our knowledge this is the first example of design, fabrication and application of novel x-ray optical elements that can perform multi-focusing in a single or multiple focal plane, beam shaping of a generic monochromatic beam into a well defined geometrical and “artistic” shape. These new optical functions, can be used for many applications ranging from microscopy, such as differential interference contrast microscopy, bio-imaging, maskless lithography and chemical vapour deposition induced by extreme ultraviolet and x-ray radiation.
Conventional spatial coherence measurement techniques rely upon a sequential series of measurements to completely map the coherence function of a source. Typically, the separation of slits – for example in a Young’s slits experiment – pinholes or mirrors must be varied. This is time consuming, limiting the parameter space that can be explored in an experiment and makes measurements of pulsed sources very difficult. Invited Abstracts: Friday Afternoon A technique that uses a diffracting mask to achieve the measurement of the entire coherence function with a single recording of a diffraction pattern will be described. The technique is directly applicable to measurement of sources with pulsed or DC nature. The mask is a class of coded apertures called a uniformly redundant array (URA). The technique can be performed with the URA as an absorption diffraction mask or a phase-shifting mask to measure harder x-ray sources. The analysis method and spatial coherence function measurements of 1.1–1.8 keV and 7.9 keV undulator radiation at the Advanced Photon Source will be described.  Uniformly redundant array design
Nanometer Imaging with a High Brightness SourceWenbing YunXradia, Inc., 4075A Sprig Drive, Concord, CA 94520 The future high brightness synchrotron sources will permit development of x-ray imaging techniques with sub-10 nm resolution and unprecedented capabilities, including 3D tomography for imaging biological specimens and studying crack initiation and propagation in materials science, spectromicroscopy for chemical state mapping of soil and environmental samples, and microdiffraction for mapping of crystallography phases and textures. As in the optical spectrum, the development of suitable lenses with the required optical property is of critical importance to realize these capabilities. Zone plate lens has demonstrated 20-nm resolution, which is the highest spatial resolution achieved over the whole electromagnetic spectrum. The inherent high fabrication accuracy by advanced lithography technology means that it has a high degree of the source coherence preservation, as manifested by its diffraction limited focusing demonstrated by many researchers at high spatial resolution. Fabricating high-resolution zone plates for multikeV x-rays is very challenging because it requires producing precise nanometer scale structures with a high aspect ration (defined as thickness/feature-size). The challenge increases with x-ray energy because the aspect ratio required for maintaining a reasonable focusing efficiency increases with x-ray energy. Currently, Xradia is producing some of the Invited Abstracts: Friday Afternoon best performing x-ray zone plates for multikeV x-rays. With a focusing efficiency exceeding 10% for 3-10 keV x-rays, Xradia’s zone plate has an outermost zone width of 50-nm. This zone plate has a spatial resolution of 60-nm using its first order diffraction and 20-nm with a reduced efficiency using its third order diffraction. In principle, there is no fundamental limit to the resolution of a zone plate and the practical limitation is the fabrication of precise and accurate nanostructures with extreme high aspect ratio. While the challenge is substantial to develop zone plates with improving spatial resolution, the available resources are limited for research labs as well as companies like Xradia. We will discuss some exciting possibilities of some synchrotron-based x-ray imaging techniques, including high spatial resolution sub-10 nm resolution and spectromicroscopy capable of chemical state mapping and elemental specific imaging at high spatial resolution. We will also present the development of zone plate lenses for coherent hard x-ray applications. Dr. Wenbing Yun Xradia, Inc., 4075A Sprig Drive, Concord, CA 94520, Phone 925-288-1818, Fax 925-288-0310. E-mail wyun@xradia.com. Invited Abstracts: Saturday Morning Coherence and x-ray microscopy Chris Jacobsen Department of Physics & Astronomy, Stony Brook University Microscopy with coherent x-ray beams can take many forms. The coherent beam can be focused to a diffraction-limited spot which is then scanned through a specimen. If a large area detector is used, the resulting imaging process is incoherent, whereas if a spatially segmented detector is used one can carry out partially coherent imaging. With Brookhaven Lab and MPI Garching, our group has developed a segmented detector (1) that can be used for delivering both amplitude and phase contrast images from a single scan of the specimen (2). Absorption contrast is particularly favorable for soft x-ray spectromicroscopy studies of chemical heterogeneities in biological and environmental science specimens (in particular when clustering or pattern matching approaches are used for data analysis (3)), but efforts to extend chemical analysis to phase contrast imaging will also be discussed. The coherent beam can also directly illuminate the specimen, with the exit wave carrying information about the specimen. X-ray holography provides one means for recording and reconstructing this exit wave (4, 5), and this can be extended to three dimensions using diffraction tomography (6-8), as will be discussed by Cloetens. The characteristics of holography will be compared with other approaches such as far-field diffraction reconstruction and transport of intensity equation reconstruction. With any of these methods, the information that can be obtained about the specimen is ultimately limited by radiation damage. The effects of radiation damage can be minimized by maintaining the specimen at cryogenic temperatures. This approach works very well for preserving specimen mass and structure at larger spatial scales (9); however, it appears to provide less protection to near-edge absorption resonances used for chemical state imaging (10). 1. M. Feser et al., in X-ray micro- and nano-focusing: applications and techniques II I. McNulty, Ed. (SPIE, Bellingham, WA, 2001), vol. 4499, pp. 117-125. 2. M. Feser, C. Jacobsen, P. Rehak, G. De Geronimo, Journal de Physique IV 104, 529-534 (2003). 3. C. Jacobsen et al., Journal de Physique IV 104, 623-626 (2003). 4. M. Howells et al., Science 238, 514--517 (1987). 5. I. McNulty et al., Science 256, 1009--1012 (1992). 6. A. J. Devaney, IEEE Transactions on Image Processing 1, 221--228 (1992). 7. W. Leitenberger, T. Weitkamp, M. Drakopoulos, I. Snigireva, A. Snigirev, Optics Communications 180, 233-238 (2000). 8. T. Beetz, C. Jacobsen, A. Stein, Journal de Physique IV 104, 31-34 (2003). 9. J. Maser et al., Journal Of Microscopy 197, 68-79 (2000). 10. T. Beetz, C. Jacobsen, Journal of Synchrotron Radiation 10, 280-283 (2003).
In this talk we consider the real-space ideas in the context of the diffraction of fields containing phase curvature, which we term astigmatic fields. We show that astigmatic diffraction patterns allow unique recovery of structural information from diffracted intensities in reciprocal space. We demonstrate an algorithm that allows the phase to be recovered uniquely and reliably. We then go on to consider the next level of complexity, which is the recovery of the correlations in the wavefield. We outline a technique by which complete coherence information may be recovered from a beam and we present some experimental results recently obtained at the Advanced Photon Source.
School of Physics, The University of Melbourne, Vic., 3010, Australia Undergraduate optics courses treat waves as if they are completely coherent and have a well-defined and continuous phase. It is now well accepted that most waves are not coherent and so it is necessary to take partial coherence effects into account. It is less well-established that phase distributions are rarely continuous. Indeed, the visible coherent optics community is only now coming to terms with the phenomena associated with phase discontinuities through the new field of “singular optics”. It is to be anticipated that x-ray “singular optics” is also an area of potential importance to the coherent x-ray optics community. Singularities in the phase of a wavefield arise whenever the field amplitude is zero. In particular, these discontinuities in the phase can always be analysed in terms of a combination of edge discontinuities and vortex discontinuities (where the phase spirals around a point singularity with an integer multiple of 2 increase in the phase for each turn). In the optics community, singular optics has found application in the development of optical vortex solitons and in optical trapping (the optical spanner). It is also interesting to note that a wave structure containing a phase vortex carries orbital angular momentum in addition to the spin angular momentum associated with polarization. The role of singular optics in coherent x-ray optics is not yet clear. At the University of Melbourne, we are interested in these structures in the context of phase recovery, where discontinuities play a critical role. It can be shown that propagation-based phase recovery is only able to yield a unique solution when it is known that phase singularities are absent. We speculate that singularities also play a significant, but not yet understood, role in methods to recover correlations in the wavefield. Techniques that use only measurements of intensity will fail when there is a rotational symmetry in the phase. The key issue being that the intensity distribution of a vortex wave structure is independent of the direction of rotation of the vortex. In this context, we have recently begun an exploration of vortex phenomena at x-ray wavelengths. While vortices are expected to be ubiquitous at all wavelengths, we have recently demonstrated the surprising fact that it is particularly easy to create these objects in a controlled way at x-ray wavelengths. I will describe these experimental results and discuss the concepts and role of phase discontinuities in phase recovery methods, as well as in measurements of the phase space properties of a wave. Invited Abstracts: Saturday Morning Diffractive Optics and Shearing Interferometry C. David a, T. Weitkamp a, B. Nöhammer a, H.H. Solak a, A. Diaz a, M. Stampanoni b, E. Ziegler c, J.F. v.d. Veen a Laboratory for Micro- and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland b Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland c European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble Cedex, France The dramatical increase of coherence that will be available from the planned fourth generation x-ray sources gives rise to the question as to what extend optical elements in the beam can preserve this high level of coherence. The deformations of the x-ray wave fronts should be much below one wavelength. In the case of diffractive x-ray optics operated in transmission, this directly translates into a placement accuracy of the diffractive structures of much better than one structure width. State-of-the-art lithography tools are capable of placement accuracies in the range of nanometers, meaning that the above condition can be met in most practical cases. In consequence, diffractive optics have a significant advantage over refractive or reflective x-ray optics in terms of aberrations that may deteriorate the degree of coherence of an x-ray beam. This is of special importance in context with future hard x-ray sources with transverse coherence lengths in the millimeter scale. To make effective use of such a beam, optical elements should be of similar size and simultaneously control the wave fronts with sufficient precision. At the Laboratory for Micro and Nanotechnology we have been developing a large number of diffractive x-ray optics for a wide range of photon energies and applications. The areas of these elements cover, in some cases, many square millimeters. In addition to Fresnel lenses for micro-focusing applications, we have recently developed diffractive hard x-ray optical elements made by wet chemical etching of single crystal silicon. These elements serve as beam splitters and analysers in interferometer set-ups. The applications of such interferometers include phase contrast imaging, wave front sensing and metrology of x-ray mirrors. Although the above-mentioned devices are at the moment optimised for use with radiation from third generation sources, the majority of the developed technological processes could be applied to produce optical elements tailored to the requirements of fourth generation sources. Furthermore, the presented interferometry techniques could be used in interesting novel applications taking advantage of the dramatically increased coherence lengths and flux levels.  
Left: Silicon diffraction grating for interferometry applications. Right: Hard x-ray interferogram of polymer spheres. Invited Abstracts: Saturday Morning Fourier Transform Holography Anatoly Snigerev European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble Cedex, France (Abstract missing) Two-photon interferometry Makina Yabashi SPring-8/JASRI Characterization of x-ray coherence is very important for performing a number of applications based on coherence, as well as for diagnosing high-quality synchrotron sources. Two-photon interferometry originally introduced by Hanbury-Brown and Twiss [1] has a potential to determine spatial and temporal coherence (first-order coherence) and the photon statistics (higher-order coherence) with a very fast resolution. For present synchrotron sources, twophoton interference can be measured as an enhancement of coincidence probability of photoelectric pulses from a single bunch. A high-resolution monochromator must be used in order to get a reasonable enhancement of the coincidence probability [2]. We have developed a system for two-photon interferometry at SPring-8. As a key optics a high-resolution monochromator (HRM) based on 4-bounced asymmetric diffractions has been developed. The device enables to produce monochromatic x-rays with an extremely small bandwidth E = 120 µeV at E = 14.41 keV [3]. First we have measured a spatial coherence profile, particularly along the vertical direction, at the 27-m undulator beamline (19LXU) of SPring-8. Enhancement of coincidence probability was measured as a function of vertical slit width. The large enhancement (~ 30% max.) allowed us to determine spatial coherence profile with high accuracy [4]. Recently we have performed a similar experiment at the beamline 29XU of SPring-8, equipped with a 4.5-m undulator called a SPring-8 standard undulator. From the coherence length and the betatron function, we have determined a vertical source size and emittance, which are in good agreement with estimation by the accelerator group. We have also proved that the method can be applied to diagnose coherence propagation by optical elements. For temporal domain, we have succeeded in determination of pulse width (32 ps in FWHM) from measurement of the coincidence probability as a function of energy bandwidth [5]. The method will provide an essential information for ultrafast synchrotron sources which are currently developed. [1] R. Hanbury-Brown and R. Q. Twiss, Nature (London), 177, 27 (1956). [2] E. Ikonen, Phys. Rev. Lett., 68, 2759 (1992); Y. Kunimune et al., J. Syn. Rad., 4, 199 (1997). [3] M. Yabashi, K. Tamasaku, S. Kikuta, and T. Ishikawa, Rev. Sci. Instrum., 72, 4080 (2001). [4] M. Yabashi, K. Tamasaku, and T. Ishikawa, Phys. Rev. Lett., 87, 140801 (2001). [5] M. Yabashi, K. Tamasaku, and T. Ishikawa, Phys. Rev. Lett., 88, 244801 (2002).
SUNY at Stony Brook, NY 11794 For many years crystallographers have been performing high-resolution lensless imaging of the unit cells of crystals by x-ray diffraction. With the arrival of more powerful x-ray sources it now appears probable that the technique can be successfully extended to general small structures. Assuming that this is so, a result will be a large increase in the consumption of photons, as well as in the range of structures which can be imaged. The subject, including imaging resolution issues, will be briefly reviewed. Diffraction Imaging with Coherent X-rays John Miao (SSRL) When a coherent diffraction pattern of a finite sample is sampled at a spacing finer than the Nyquist frequency (i.e. the inverse of the sample size), the phase information is embedded inside the diffraction pattern itself and can be directly retrieved by using an iterative process. In combination of this oversampling phasing method with coherent X-rays, a new imaging methodology (i.e. coherent imaging) has recently been developed to determine the electron density of nano-crystals, non-crystalline materials and biological samples. In this talk, I will discuss the principle of the oversampling method and present some recent experimental results. 3D X-ray microscopy by phasing diffraction patterns: prospects and limitations M. R. Howells1, H. Chapman2, R. M. Glaeser1, S. Hau-Riege2, H. He1, J. Kirz1,3, S. Marchesini1, H. A. Padmore1, J. C. H. Spence4,1, U. Weierstall4. 1Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
Corresponding author: mrhowells@lbl.gov This presentation addresses the questions of what performance can we expect from a 3D diffraction microscope and what will set the limits. In particular we make a quantitative calculation of the dose required for imaging at any given resolution and statistical accuracy with a model sample consisting of protein against a background of water. We derive the dose Invited Abstracts: Saturday Afternoon needed for 3D imaging by use of the dose-fractionation theorem of Hergel and Hoppe and determine that for 3D imaging, the dose scales inversely as the fourth power of the resolution. Thus far the calculation has made no reference to the amount of dose that the sample can tolerate. The critical dose for destruction of features of a given size in a protein sample has been fairly widely investigated by various interested communities (spot-fading experiments etc) and we have assembled a body of information from the literature of both x-ray and electron imaging. When the dose required for imaging a feature according to the Rose criterion and the critical dose for destruction of features is displayed on a common plot of the dose against feature-size, one can see that imaging life science samples with a resolution of about 10 nm should be possible. For the more radiation-resistant samples investigated in material science research, significantly better resolution of about 2-4 nm is expected. Another requirement for these experiments to be useful is that the exposure time should be not more than a few hours for a complete tilt series. We address this question in a similar way to the dose and find that (a) the required coherent flux also scales with the inverse fourth power of the resolution and (b) the exposure times are reasonable even for present-day synchrotron sources provided that optimally chosen undulators and optical systems achieving their design performance are used. Acknowledgements This work was supported by the Director, Office of Energy Research, Office of Basics Energy Sciences, Material Sciences Division of the U. S. Department of Energy, under Contract No. DE-AC03-76SF00098. Hydrodynamic Model of X-Ray Irradiated Biological Molecules Stefan P. Hau-Riege, Richard A. London, and Abraham Szöke Lawrence Livermore National Laboratory, Livermore, CA 94550, USA X-ray free electron laser (XFEL) synchrotron radiation sources can produce extremely short and intense X-ray pulses that potentially allow the three-dimensional structure determination through single-molecule diffraction imaging. One of the critical issues is the deterioration of a molecule induced by X-ray irradiation. Recently, molecular-dynamics calculations of the damage dynamics of biological molecules have been presented by Neutze et al. (Nature 406, 752 (2000)). In contrast, we have developed a simpler hydrodynamic model, but added several physical effects that strongly affect the dynamics. Most important is the effect of trapped electrons that have been stripped from the atoms but that are trapped by the electrostatic field of the molecule. In this paper, we will present a simple dynamics model that includes an approximate description of the dominant physical effects. We used this model to survey a wide range of parameters to obtain the image resolution as a function of molecule size, particle composition, and beam parameters. Classification of individual diffraction images according to the molecule orientation constrains the beam parameters further (G. Huldt et al., to be submitted). We determined the optimum resolution as a function of beam and molecule parameters considering both radiation damage and image classification.
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