research article new directions in x-ray...

June 2, 2011 11:47 Contemporary Physics draft9

Contemporary PhysicsVol. 00, No. 00, Month 200x, 1–27

RESEARCH ARTICLE

New Directions in X-ray Microscopy

Roger Falcone1,2, Chris Jacobsen3,4, Janos Kirz1, Stefano Marchesini1, David Shapiro5, and JohnSpence6

1Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA2Department of Physics, University of California, Berkeley, CA, USA

3Argonne National Laboratory,Argonne, IL, USA4Northwestern University,Evanston, IL, USA

5NSLS II, Brookhaven National Laboratory, Upton, NY, USA6Department of Physics, Arizona State University, Tempe, AZ, USA

(Received 00 Month 200x; final version received 00 Month 200x)

The development of high brightness X-ray sources and high resolution X-ray optics has led to rapid advances inX-ray microscopy. Scanning microscopes and full-field instruments are in operation at synchrotron light sourcesworldwide, and provide spatial resolution routinely in the 25 50 nm range using zone plate focusing elements.X-ray microscopes can provide elemental maps and/or chemical sensitivity in samples that are too thick forelectron microscopy. Lensless techniques, such as diffraction microscopy, holography and ptychography are alsobeing developed. In high resolution imaging of radiation-sensitive material the effects of radiation damage needsto be carefully considered. This article is designed to provide an introduction to the current state and futureprospects of X-ray microscopy for the non-expert.

Keywords: x-ray microscopy; x-ray diffraction, x-ray optics, phase-contrast

This is the June 2, 2011 version of the file draft9

ISSN: 0010-7514 print/ISSN 1366-5812 onlinec© 200x Taylor & FrancisDOI: 10.1080/0010-751YYxxxxxxxxhttp://www.informaworld.com


2 Falcone et al.

Acronyms Used

ALS Advanced Light Source. 1.9 GeV light source at Lawrence Berkeley Na-tional Laboratory, Berkeley, California, USA

APS Advanced Photon Source 7.0 GeV light source at Argonne National Lab-oratory, Argonne, Illinois, USA

ARPES Angel resolved photoemission. A technique to map electronic structureof solids and surfaces

BESSY II 1.7 GeV light source in Berlin, GermanyCAT Computerized Axial TomographyCCD Charge coupled deviceCLS Canadian Light Source 2.9 GeV light source in Saskatoon, Saskatchewan,

CanadaCRL Compound refractive lensCW Continuous waveCXDM Coherent X-ray diffraction microscopyDESY Deutsches Electronen-Synchrotron laboratory in Hamburg, GermanyELETTRA 2.0-2.4 GeV light source near Trieste, ItalyERL Energy recovery linacESRF European Synchrotron Radiation Facility 6.0 GeV light source in Greno-

ble, FranceFEL Free electron laserFLASH Soft X-ray free electron laser at DESY, Hamburg, GermanyLBNL Lawrence Berkeley National Laboratory, Berkeley, California, USALCLS Linac Coherent Light Source hard X-ray free electron laser at SLAC

National Accelerator Laboratory, Stanford, California, USAMAD Multiwavelength anomalous diffractionMLL Multilayer Laue lensNSLS National Synchrotron Light Source, Brookhaven National Laboratory,

Upton, Long Island, New York, USAPEEM Photoelectron emission microscopePETRA III 6 GeV lightsource at the DESY laboratory, Hamburg, GermanySAD Single wavelength anomalous diffractionSAXS Small angle X-ray scatteringSLS Swiss Light Source 2.4 GeV light source at the Paul Scherrer Institute

Villigen, SwitzerlandSPEM Scanning Photoemission microscopeSSRL Stanford Synchrotron Radiation Lightsource 3.0 GeV light source at

SLAC National Accelerator Laboratory, Stanford, California, USASTXM Scanning transmission X-ray microscopeTXM Transmission X-ray microscope (full field)WAXS Wide angle X-ray scatteringXFEL X-ray free electron laserXM1, XM2 Transmission X-ray microscopes at the Advanced Light SourceXMCD X-ray magnetic circular dichroismXMLD X-ray magnetic linear dichroism

1 Introduction: Why X-rays, why now?

Most of what we know about the micro-world was learned from microscopy. Until the 1930’smicroscopes used almost exclusively visible light to illuminate the specimen and to form theimage. It was well understood that the wavelength of visible light restricted the finest detail


Contemporary Physics 3

that could be resolved with these instruments to around a micrometer, or slightly less. A hugeamount of information was accumulated using these microscopes especially about biology andmedicine.

The microscopist is very often faced with the need to improve the resolution, to see more detailin the specimen. It was known since the early part of the 20th century that X-rays had aboutthree orders of magnitude shorter wavelength than visible light, hence in principle they shouldopen up the nano-world to inspection. In fact X-rays were widely used not only for radiology, butalso for imaging the arrangement of atoms in molecules when these molecules could be arrangedto form crystals. Clearly the “resolution” in crystallography was at the atomic scale, at a fractionof a nanometer. Yet it was also “well known” that lenses do not focus, and mirrors do not reflectX-rays, hence building X-ray microscopes was “well known” to be impossible.

Much has happened in the past 80 years. The first observations of individual atoms were madein Erwin Muller’s group using field-ion microscopy in the early nineteen fifties [1]. Albert Crewe,who died in late November 2009, was first to see a single atom using the electron microscopein 1970 [2]. Electron microscopes with sub-nanometer resolution quickly followed, and werewidely adopted. With further advances and aberration correction, today these instruments canattain sub-Angstrom resolution. However, these instruments primarily achieve this resolutionin images which show a projection through a thin slice of crystalline material. For the imagingof surface structure at high resolution, the more recent development of the scanning probemicroscopes in the early nineteen eighties has proven more powerful. Microscopes using visiblelight have also made remarkable progress, following Zernike’s development of the phase plate inthe nineteen thirties, for improving the contrast of images of thin biological samples [3, 4]. Lately,confocal microscopes, two-photon microscopes, and especially microscopes using fluorescent tagshave been used to beat the diffraction “limit” of visible light. Furthermore, a variety of super-resolution schemes have been developed to probe distances smaller than the wavelength of light.Today distances as small as 30 nm can be resolved with the most advanced instruments of thistype [5, 6].

Even in the face of these remarkable developments we believe there is a role for x-ray mi-croscopy. As we shall discuss in this article, the nature of the interaction of X-rays with matterprovides information and contrast that is not available using other techniques, and the methodoperates in a regime that may be inaccessible to other techniques [7]. Furthermore there havebeen important recent breakthroughs in X-ray optics, X-ray sources, imaging modalities anddetectors that have lead to the rapid development of X-ray microscopes [8–10].

As with any form of microscopy using ionizing radiation, one must always keep in mind thedamage the sample will suffer due to the beam. X-rays break chemical bonds, create free radicals,and the radiation dose required to form a statistically meaningful image increases rapidly withthe desired resolution. Hence, while it is possible to create movies of insect physiology at fewmicron resolution, the dose required to form a single image at 0.1 micron resolution will killeven the most radiation resistant living organism. As discussed in detail elsewhere, the radiationdamage effect is a strong function of resolution [11]. In order to record sufficient informationfrom the smaller volume element involved in imaging at higher resolution, the sample must beexposed by a radiation dose that increases as the inverse fourth power of the linear dimension.Morphological manifestations of radiation damage can be reduced by keeping the sample atliquid nitrogen temperature. Calculations indicate that this may allow even radiation sensitivebiological samples to be imaged to a resolution of 10 nm, and more robust samples to considerablyhigher resolution. Alternatively, if the image can be acquired in a single ultrafast flash exposure(on the order of 10 fs or faster), the morphology is captured before the sample has a chance todisintegrate [12].


4 Falcone et al.

1.1 Penetrating thick specimens

The penetrating power of X-rays and the contrast due to differing absorptivity of differentmaterials was noted by Rontgen in the first paper that announced his discovery of this “newtype of radiation.” It is the basis of all diagnostic radiology. A critically important feature of thisphenomenon is that by changing the X-ray wavelength one can adjust the penetrating power overan enormous range. Longer wavelengths are absorbed by a few tens of nanometers of material,while short wavelengths can be used to look for voids in metal castings, defects in welds, orfor broken bones in an elephant. The best contrast in absorption-based imaging is achieved byselecting a wavelength where different components in the sample absorb some, but not all of theradiation.

Simple absorptivity maps with the beam incident from one direction are often too complexto interpret for thick specimens. It was therefore a true breakthrough when Hounsfield andCormack developed a way to reconstruct a three dimensional representation of the sample (suchas part of the human body) by the technique of CAT scans, or tomography. This, combined withrapid increases in computing power, provided the incentive for dramatic advances in the nowlarge field of tomographic image processing, and the award of a Nobel prize [13].

1.2 Contrast mechanisms

1.2.1 Absorption contrast

The fraction of X-rays transmitted through matter follows the Lambert–Beer Law:

I = I0e−µt (1)

The linear absorption coefficient µ is proportional to the absorption cross section, and is shownfor a few materials in Figure 1. While the overall trend shows the steep increase with wavelengthnoted in the previous section, there are dramatic jumps at “absorption edges.” For X-rays (asfor all electromagnetic radiation) the relation between the wavelength and the energy of thecorresponding photon is:

E =hc

λ

The edge-jumps occur where the photon energy just exceeds the binding energy of some ofthe core electrons of the element in question, so it can liberate these via the photoelectriceffect. Closer inspection reveals that the absorption coefficient undergoes rapid and dramaticchanges near the absorption edge, and that these variations depend on the chemical state of theelement. These spectral features provide a way to identify both the elemental and the chemicalconstituents of a sample at the location probed by the X-ray beam [14].

If the atoms or molecules of the sample happen to be aligned or polarized in some way, addi-tional absorption effects can provide information about these phenomena. For ferromagnetic ma-terials illuminated with circularly polarized X-rays there is a several percent difference betweenthe absorptivity of the photons polarized along and opposite to the direction of magnetizationnear the L absorption edges. This X-ray Magnetic Circular Dichroism (XMCD) can be used tomap domains of ferromagnetic films. Even for antiferromagnets, where there is only a favoredalignment but no polarization direction, one can map the alignment with linearly polarized X-rays due to the difference in absorptivity near L absorption edges as a function of the anglebetween the X-ray polarization and the alignment in the material (XMLD, or X-ray MagneticLinear Dichroism). Similar differences in absorptivity have been demonstrated in polymers withaligned molecules near the carbon K absorption edge [15].



Figure 1. Linear absorption coefficients for gold, water, and protein with empirical formula H50C30N9O10S1 derived usingtabulated values for the indices of refraction [http://henke.lbl.gov/optical_constants/].

1.2.2 Fluorescence

X-ray absorption is dominated by the photoelectric effect. The hole created by the removal of acore electron is filled by an electron from a less strongly bound state. The extra energy is carriedaway either by a photon (fluorescence), or by a third electron (Auger process). The energy carriedby the fluorescence is characteristic of the element, so that the spectrum of fluorescence photonscan be used to identify the elemental constituents of the irradiated region of the specimen.

1.2.3 Diffraction

Some of the X-rays incident on the sample undergo elastic scattering. If there is some organizedpattern in the sample with a periodicity comparable to or larger than the wavelength, thescattering will be enhanced in a direction given by the Fourier transform of the periodic structure.This is the basis of crystallography and small angle scattering. If, on the other hand, the sampleis non-crystalline, i.e. it does not have an organized pattern, then the scattering pattern is muchweaker since it is not concentrated into specific directions. Rather, it is diffuse and continuousthough still measurable.

1.2.4 Phase contrast

Over the last decade we have seen dramatic advances in the use of phase-contrast in X-rayimaging. Fresnel fringes, the simplest evidence of this effect, were observed in the earliest days ofX-ray diffraction [16], but control of this useful effect has come only recently, motivated by therealization that the constrast due to interference between two waves can vary between zero andunity, yet result from very small changes in a material’s properties. While phase-constrast X-raymicroscopy has attempted to follow many of the ideas in optical phase contrast imaging [17], thepractical implementation has resulted in entirely different instruments, due (until very recently)to the very limited spatial coherence of X-ray sources. For an extended ideally incoherent X-raysource which subtends a semi-angle α at a sample, the transverse coherence at the sample isapproximately λ/α, or several microns for a typical undulator at a soft X-ray synchrotron. Thisdistance must span spacings in the sample for which coherent imaging effects are expected, just asit must span the pinholes in Young’s fringe experiment in order to produce strong interferencefringes. With the growing interest in sub-micron structures, phase-contrast X-ray imaging isbecoming increasingly powerful. The temporal coherence, measured in number of wavelengths,is approximately equal to the photon energy divided by the energy spread in the beam. Bothforms of coherence, together with the choice of detector pixel number and spacing, may limit


6 Falcone et al.

Figure 2. Zone plates are circular diffraction gratings where the line width decreases with increasing distance from theoptic axis. Figure courtesy of Xradia (www.xradia.com)

the resolution of phase-contrast images.It is useful to compare the strength of these various contrast mechanisms. In protein crystal-

lography, for example, over 95% of the incident X-rays do not interact at all with the sample,and are directed into a central beam dump. Of the remainder, over 90% are annihilated in theprocess of photoelectron production (or Compton scattering at higher beam energies), and someof which may contribute to absorption contrast in regions of the sample with a high concen-tration of atoms whose absorption edge coincides with the beam energy. The remaining smallfraction are available for elastic scattering and phase contrast effects.

1.3 X-ray Optics

1.3.1 Mirrors

It was Albert Einstein [18] who pointed out that X-rays should undergo total external reflectionat grazing angles. This idea was taken up by Kirkpatrick and Baez in the design of the focusingsystem that bears their names. Over the last few years the technology of shaping, polishing,mounting and aligning K-B mirrors has advanced to the point that focusing X-ray beams to lessthan 10 nm has been demonstrated [19]. Grazing incidence reflection is also used in polycapillaryconcentrators and monocapillary microscope condensers [20].

1.3.2 Lenses

Going beyond mirrors, it is also a consequence of Einstein’s analysis that ordinary refractivelenses can actually work, except that the focal lengths are extraordinarily long. The directionof refraction for X-rays is opposite to that for visible light, therefore focusing elements haveconcave surfaces rather than convex. In the last 14 years much work has been done to developcompound refractive lenses (CRL) [21], made of a series of concave lenses with nearly zeromaterial between them so as to minimize absorption, and maximize focusing. Cylindrical lensarrays can be fabricated lithographically, and point focusing is accomplished by a pair of crossedelements of this type. These find applications mostly with high energy X-rays, 15 KeV andabove.

Diffractive optical elements can also be used as lenses. Fresnel zone plates were inventedsome 120 years ago, but their use with X-rays is a more recent development [22]. These circulardiffraction gratings are fabricated in such a way that the spacing between adjacent zones providesconstructive interference in the direction of the primary focus. The resolution, as for all focusingelements, is given by

r =0.610λ

NA(2)

where NA, the numerical aperture is the sine of the maximum diffraction angle. For a grating



with period d, this angle in first order is just

θ =λ

2d

Thus, for a zone plate with a finest spacing of ∆Rn the resolution is just 1.22∆Rn [23]. Inother words, the resolution is essentially the width of the finest zone that can be fabricated.To get to nanometer-scale resolution, one needs the most modern nanofabrication techniques.What makes this particularly challenging is the requirement that the zones be thick enough tosignificantly affect the incident X-rays, and this leads to the need for very high aspect ratios.The highest resolution demonstrated to date is 12 nm in first order, [24] and 14 nm in using thehigher numerical aperture of a third order focus [25].

An alternate nanofabrication technique is to create a multilayer with appropriately arrangedlayer thicknesses, and then slice this device to the appropriate thickness. This method can easilylead to high aspect ratios, but has proven to be challenging in the circular geometry. Doingit on a planar substrate leads to linear zone plates that focus in one dimension. The resultingMultilayer Laue Lens (MLL) has been shown to focus 30 KeV X-rays to less than 20 nm in onedimension. Again, two such elements in crossed geometry can provide point focusing. In thiscase it is also possible to increase the efficiency (the fraction of incident X-rays that end up inthe first order focus) by tilting the multilayer to approximately fulfill the Bragg condition.

1.4 X-ray Sources

Today one can buy off the shelf a variety of X-ray microscopes that use conventional electron-bombardment X-ray sources. These can perform absorption-contrast and even phase contrasttomography with a resolution of 50 nm [26]. This is a new development that seemed impossiblea decade ago.

Higher resolution and faster image acquisition is possible at third generation synchrotron lightsources. These machines are electron storage rings designed to accommodate many undulatorswhich offer several orders of magnitude higher brightness than conventional sources, and theirnumber is rapidly growing around the world. Although the X-rays are emitted with a pulsedtime structure (typically 50-100 ps long pulses with a spacing of 2 ns or so), few microscopes takeadvantage of this feature. The X-ray energy is typically selectable based on a monochromatorwith a resolving power of between 1000 and 10000. The energy range rarely exceeds one orderof magnitude, so that some beamlines specialize in soft, while others provide hard X-ray beams.While most undulator-based sources provide beams with linear polarization, some have special-ized undulators where the polarization is freely selectable. These sources host the microscopesthat set the state of the art today.

New storage ring sources are being built (PETRA III, NSLS II) or planned that have evenhigher brightness, and are designed to produce beams that have coherence properties that ex-ceed those available at existing light sources. All storage ring sources produce beams that aremuch smaller in the vertical than in the horizontal plane. There is considerable interest in thedevelopment of a different type of facility, the Energy Recovery Linac (ERL), that, among othernovel properties provides beams that are small in both dimensions.

Other types of sources are also being developed, and will offer remarkable new capabilities: Asoft X-ray Free Electron Laser (FEL) has been in operation at the DESY laboratory in Hamburg.It produces ultrashort pulses (10 fs) of spatially coherent x-rays of exceedingly high peak powerat 10 Hz. The first hard X-ray FEL, the LCLS, started operation at Stanford in late 2009, whileother facilities are under construction. Unlike conventional and synchrotron based sources, FELsare most useful for single-shot flash-imaging [27].


8 Falcone et al.

Figure 3. Optical layout of a TXM. Reproduced from [28]

2 X-ray microscopes

Two distinct forms of microscope are common: the scanning transmission microscope (STXM),and the conventional full-field non-scanning instrument (TXM), which operates somewhat likea camera. The scanning instrument scans the sample across a focused beam and detects trans-mitted or scattered radiation, which is displayed using the same two-dimensional raster whichscans the sample.

2.1 Transmission X-ray Microscopes (TXM)

The Transmission X-ray Microscope operates on the same principle as the standard visible lightmicroscope. It involves a source of illumination, a condenser that shapes the illumination anddelivers it to the sample, an objective lens that is responsible for forming the magnified image,and a detector. In TXMs today the objective lens is a zone plate, the detector is a CCD, andthe condenser may be a second zone plate, a capillary, or some other optical element. For bestperformance the numerical aperture of the condenser should match the objective, but that isoften difficult to arrange. The typical TXM has a field of view of 15-25 micrometers and amagnification of 1000-2000. To assure uniform illumination of the field, the condenser is eitherwobbled, or moved in a spiral path. To image a larger area, images of neighboring fields are tiledtogether. The first modern TXM was built by the Gottingen group [29]. Microscopes of this typeare particularly well suited for tomographic imaging, and several of them are in routine operationwith soft X-rays at the ALS and BESSY, often in the range between the carbon and oxygenabsorption edges in the ”water window” where water is relatively transparent compared to othermaterials. Hard X-ray TXMs operate at the SSRL, the Taiwan Light Source and elsewhere,while others, using conventional X-ray sources, are available commercially.

In a TXM it is also possible to enhance the image contrast using Zernike phase-contrast.In 1935, Zernike showed that it is possible to convert phase information in the sample planeinto intensity modulations in the detector plane if the phase relationship between scattered andunscattered light in the microscope is adjusted. This can be accomplished in a TXM through theaddition of a phase ring into the back focal plane of the objective zone plate. If the geometry ofthe phase ring is such that it phase shifts only the x-rays which are not scattered by the samplethen the intensity contrast in the image plane can be enhanced. This technique was pioneeredfor soft x-rays but is also of high importance for hard x-rays where absorption contrast is veryweak [17].

2.2 Scanning Transmission X-ray Microscopes (STXM)

In a STXM a focused beam of X-rays is incident on the sample, and the fraction of X-raystransmitted is recorded. Either the beam or the sample is raster-scanned to form a map of the



Figure 4. Optical layout of a STXM. Reproduced from [28]

sample’s absorptivity. Typically a zone plate forms the focused beam [30]. There are no lossyoptical elements between the sample and the detector. The scan range and step size can be freelychosen. Coarse, large area exploratory scans can be followed by fine, high resolution imaging.These features are particularly advantageous when the sample is sensitive to radiation damage.By taking images at several energies close to an elemental absorption edge, maps of differentchemical constituents can be created. This form of “spectromicroscopy” is available at severallightsources, including the NSLS, ALS, SLS, CLS, APS, ESRF with more instruments coming online. These instruments operate with soft or medium energy X-rays, often in the water window.

A variation on the STXM theme is the hard X-ray nanoprobe. In the hard X-ray range absorp-tion contrast tends to be weak, hence other contrast mechanisms are commonly used. Detectionof fluorescent X-rays leads to high resolution trace element mapping, while the detection ofdiffracted X-rays from polycrystalline materials is a powerful tool in the study of microstruc-ture, and material response to stress and other insults.

2.3 Photoemission microscopes: PEEM, SPEM and nano-ARPES

When a sample is exposed to an X-ray beam, photoelectrons and Auger electrons are generated.Unless the X-ray was absorbed in the first few atomic layers of the surface, the electrons will losemost of their energy in collisions, and emerge as low energy secondary electrons. The higher theabsorptivity near the surface, the higher the yield of secondary electrons. By imaging the ”totalelectron yield”, the surface absorptivity can be mapped. The instrument designed to do thatis the PhotoEmission Electron Microscope (PEEM). The X-ray beam illuminates a few-micronarea of the sample, while an electron-optical column creates the magnified image of the surface.By varying the X-ray energy and/or the polarization, this instrument can provide excellentchemical or magnetic contrast. With aberration corrected instruments now becoming available,the spatial resolution can be better than 10 nm.

In a Scanning PhotoEmission Microscope (SPEM) a zone plate is used to focus the X-raybeam onto the sample, which is raster-scanned much as in the STXM. One can form the imagefrom the total electron yield or, in a scheme that is sensitive to just the top few atomic layersof the surface, analyze the emitted electron energy to form the image using either the Augerelectrons or the photoelectrons [31]. The former provide information on the atoms present, whilethe latter are also sensitive to the chemical state through the chemical shift in the photoelectronenergy. By recording not just the energy but also the direction of the photoelectron, the localband structure can be mapped in the instrument that is referred to as nano-ARPES.

2.4 x-ray holography

In Gabor’s original idea of a holographic microscope [32], coherent radiation is scattered froman object and interferes with unscattered photons that pass (or bypass, in the later improvedoff-axis geometry) the object undisturbed. The undisturbed radiation is the reference wave andthe interference results in a coherent scattering pattern known as a hologram. The diverging


10 Falcone et al.

photon beam from a point source creates a projection of the sample, thus magnifying the objectand providing an out-of-focus coherent shadow image. (Gabor’s reconstruction method providedan imperfect focus correction, marred by the so-called ”twin image”). If the detector is a phototransparency, the observer may look through the transparency in the direction of the (now ab-sent) object; if only the reference beam is shining on the detector, the interference pattern servesto ”un-scatter” (diffract) the wavefront and reconstruct the object’s image. Digital holographyaccomplishes numerical reconstruction by simulation of this optical wavefront propagation.

In holographic imaging the phase retrieval problem is transformed into a linear problem byadding a known modulating reference wave at the detector. The reference beam of known ampli-tude R and intensity IR = |R|2 interferes with light scattered from an unknown object wavefieldO according to:

I = |R+O|2

= IR +R∗O +O∗R+ |O|2. (3)

where the four terms on the right hand side are referred to as the reference term, the holographicterm, the twin holographic term, and the object term respectively. Signal reconstruction fromoff-axis holograms may be understood simply by solving for O in the linear equation,

R∗O = H (4)

Proper geometric arrangement of the object and reference ensure that the holographic term Hcan be extracted or that other terms can be neglected where the hologram H is measured, andR known.

Early demonstrations of X-ray holographic imaging [33–35] were limited by the detector (aphotographic film) resolution. Projection holograms from a point source provide magnification,but are limited in resolution by the size of the reference source. Although the measurement maytake place in the far field, the diffracted wave is related to the object via the Fresnel diffractionformalism so that one obtains a magnified version of an inline hologram [36, 37]. In this originalin-line geometry it is not possible to separate the hologram from its twin term, however thesimplicity of the Gabor geometry remains attractive and competitive [36, 38]. In special cases,holograms at resolutions as low as 0.5 A have been obtained using a fluorescing atom in a crystalas a point source [39].

A different geometry explored by McNulty et al. [40] (“Fourier Transform Holography” [41–43])does not suffer from this limitation. A point source located in the sample plane and translatedfrom the object provides the reference beam. Since the measurement is performed in Fourierspace, the resolution is determined by the numerical aperture of the detector and the maximumscattering angle illuminated by the reference wave (determined by the size of the reference waveemerging from the pinhole). The holographic term H is modulated by this oscillating phase term,and can be extracted from the measured intensity by Fourier filtering.

Fourier Transform holography may be the only geometry in which reconstruction can beachieved with a single Fourier Transform of the scattering distribution. It is therefore free of theconvergence issues which complicate iterative phasing schemes when using imperfect or noisydata. McNulty et al. relied on diffractive optical elements to generate the reference wave, and thiscaused significant distortions in the resulting image. With renewed interest in diffractive imagingit became apparent that the presence of small object nearby a specimen could yield a holographicimage that would aid the phase retrieval problem [45]. But it was not until the work of Eisebittet al. [44] that Fourier transform x-ray holography became a practical method for imaging. Inthis implementation the sample is placed behind a lithographically manufactured mask with amicrometer sized sample aperture and a nanometer sized hole that defines a reference beam(Fig. 5).

One limitation of this approach is that the reference wave is normally much weaker than the



Figure 5. Imaging of magnetic domains in a Co/Pt multilayer film using Fourier transform holography. In this implemen-tation the sample is placed behind a lithographically manufactured mask with a micrometer sized sample aperture and ananometer sized hole that defines a reference beam (lower inset) Coherent X-rays are incident on a mask-sample structureand a CCD detector measures the diffracted X-rays. Magnetic contrast is obtained by using circularly polarized X-raystuned to the resonant wavelength of Co L3 absorption (Reproduced from [44]).

Figure 6. Fourier transform holography of a fabricated nanostructure. In this implementation the reference beam is gener-ated by a multitude of reference scatterers placed in a uniformly redundant array. [50]).

object. When the reference wave is the dominant term, the signal to noise ratio is constant.However, when using a mask to select a reference wave, the latter is generated by a pinhole thatis much smaller than the object, and the resulting intensity is weaker.

Complicated references [46], multiple pinhole references [47], or edge-like structures [48, 49]have been suggested to increase the relative amplitude of the reference beam. A reference struc-ture that is optimal for imaging because it contains all the relevant frequencies has been employedto achieve increased brightness and resolution at the Advanced Light Source and the FLASHfree electron laser facility [50]. In this geometry, the reference structure is a uniformly redundantarray (Fig. 6). Deconvolution of the coded aperture is accomplished by a convolution with abinary function, minimizing noise propagation.

As both amplitude and phase are recorded up to a maximum angle given by the numericalaperture (NA) of the detection system, partial three-dimensional information is present in ahologram. By numerically propagating the wavefront through different planes it is possible toreconstruct an entire stack of image planes. Resolution is reduced in the depth direction, es-pecially at shorter wavelengths for which scattering at large angles is unlikely. Unlike confocalmicroscopy light scattered from different planes contributes to coherent “speckle” noise to thefinal image. However, since holographic data procesing is a linear problem, holography is wellsuited to take advantage of recent progress in the field of “compressive sensing” [51, 52] which


12 Falcone et al.

can, under certain conditions, increase the dimensionality of the image from 2D to 3D [53].

2.5 Diffraction microscopy

Diffraction microscopy is based on the elastically scattered (diffracted) X-rays. If the incident X-ray beam is spatially and temporally coherent, the scattered radiation forms speckles. If one couldrecord the complex amplitude of these speckles, the specimen could be reconstructed by simpleinverse Fourier transformation. Detectors, unfortunately, record only the intensity of the speck-les; the phase is lost. With sufficient additional information about the specimen the phase can berecovered, and the specimen reconstructed. Over the past decade, since the first demonstrationby Miao et al [54] there have been several demonstrations of this ”diffractive” or lensless imagingmethod, in which a computer is used in place of a lens to solve the phase problem. Resolution isthen limited only by the size of the detector and the wavelength, together with experimental fac-tors such as background noise. The image is free of the lens aberrations which otherwise preventfaithful imaging. A considerable literature exists on this ”non-crystallographic phase problem”,building on early work by Sayre [55], Gerchberg and Saxton [56] and Fienup [57]. In summary,it is found from computational trials that for a weakly scattering object, whose boundary isappoximately known, the phases of the scattered radiation can be found if that scattering is suf-ficiently finely sampled in the angular domain. (The sampling must satisfy Shannon’s theoremin the Fourier domain for the autocorrelation of the object, which imposes a finite ”bandpass”domain on the diffracted intensity). The most common reconstruction algorithms iterate be-tween imposing the measured scattering intensities in the scattering domain and imposing theadditional constraints (such as the spatial extent of an isolated sample, known as finite supportin real space. Reviews of the relevant theory which summarise the many developments can befound in Spence [58] and Marschesini [59]. Of these developments, the ”shrinkwrap” algorithmhas become perhaps the most popular [60]. For two-dimensional image reconstruction from aphased far-field diffraction pattern, the question arises as to which plane across the optic axisnear the sample is reconstructed, and what is the depth of focus. The depth of focus is that ofan equivalent lens whose numerical aperture is that fixed by the detector in the diffractive imag-ing experiment. Experimental and theoretical studies using a three-dimensional object whoseextension along the optic axis is greater than this depth of focus shows that the method recon-structs a local projection on that plane (normal to the optic axis in the object space) for whicha compact support is provided [61]. It is shown here also that, since the complex object wave-field is recovered, this may be propagated to other nearby planes along the optic axis, allowingvirtual focusing. A recent application of the method to three-dimensional imaging of inorganicstructures at 10nm resolution, with full details of the method, can be found in Chapman et al[62]. It will be seen that some of the most exciting applications of this lensless imaging methodarise from its use with X-ray free-electron lasers, where it has already demonstrated the abilityto reconstruct a sequence of ”movie” frames from ten-femtosecond X-ray pulses [63].

The most important difficulties with these iterative phasing methods are i) The need to pre-pare isolated samples, so that it is known a-priori that no material outside the defined sampleboundary (the ”support”) contributes to the diffraction pattern. Inversion is usually only pos-sible with a very precisely defined support. ii) Stagnation of the algorithm when using poorquality or noisy data.iii) The need for a beamstop, which usually results in a loss of low spatialfrequencies. These issues are resolved to varying degrees by alternative methods such as X-rayholography and Ptychography.

2.6 Ptychography

Ptychography (from the greek ”to fold”) is a form of diffractive imaging in which a coherentfocused beam is scanned across a sample, and diffraction patterns are recorded at overlappingpositions of the probe. Real-space images of the sample may be reconstructed from this data



Figure 7. Time-resolved sequence of images with magnetic dichroism contrast of a Permalloy disk sample from the XM1microscope. Images obtained at various delay times from t = 0 ns up to t = 9 ns show the translational motion of the corecenter. Black (white) contrast indicates that the direction of the magnetization is to the left (right). Reproduced from [68]

with super-resolution beyond the diffraction limit imposed by the probe-forming lens. The ad-vantages of Ptychography are that it solves both the beam-stop problem (loss of low spatialfrequency information in the vicinity of the unscattered beam) and the isolated sample problemof diffractive imaging, that the inversion algorithms are much less prone to stagnation, and thatthe scanning probe geometry may be very readily combined with spectroscopy. It does, however,have the important disadvantage that, since the patterns are a real and reciprocal space hybrid,the resolution depends on the mechanical stability of the instrument. They are hybrid in thesense that, for a periodic sample, the fringes at the interference between overlapping orders areactually a magnified coherent shadow image (or in-line hologram) of the sample, and so aresenstive to movements of the defocused probe (the point of projection) relative to the sample.The optimum geometry for collection of three-dimensional data also requires careful thought.The method was first proposed by Hoppe in the late nineteen sixties for electron microscopy[64]. Much of the modern work is the result of research by Rodenburg and co-workers in elec-tron microscopy, and is well reviewed in [65]. Rodenburg shows that if a particular plane in thefour-dimensional (q, R) space is Fourier Transformed, then the result is an image with twice thenormal resolution. The first attempt using X-rays by Chapman [66] used the method of Wignerdeconvolution, in which the phase-retrieval problem is reduced to a linear problem. When usingpatterns from a few, overlapping coherent probe positions it becomes the Ptychography methodof Rodenburg, which solves the resulting non-linear but convex problem. The inversion becomeslinear in the limit where the probe positions differ by one pixel, in which case one has exactly themethod of scanning transmission lattice imaging. Ptychography is convex if the probes overlapby at least 50%. Recent X-ray Ptychography results are reported in Thibault et al [67], where ahighly efficient new algorithm is described.

In summary, apart from the challenge of mechanical stability, Ptychography appears to bethe most important and promising development in X-ray imaging, because it offers the prospectof super-resolution, phasing with a robust algorithm and integration with spatially resolvedspectroscopy, while able to accommodate a wider range of samples and avoiding the use of abeamstop.

2.7 State of the art, and applications

2.7.1 Transmission X-ray microscopes

Full field transmission X-ray microscopes (TXMs) using soft X-rays are in operation at severallaboratories. At the Advanced Lightsource in Berkeley the microscope XM1 has been used for thedevelopment of high resolution imaging capabilities [24], and to study magnetisation dynamics.

The newly commissioned microscope at the National Center for X-ray Tomography emphasizesthe 3D imaging of biological samples at cryogenic temperatures. It also includes a cryo microscopeusing visible light for correlative studies.

These two instruments use bending magnet sources and condenser zone plates to illuminate the


14 Falcone et al.

Figure 8. Soft X-ray tomographic reconstruction of phenotypically distinct C. albicans cells from the XM2 microscope atthe National Center for X-ray Tomography. A representative orthoslice from each tomographic reconstruction is shown fora yeast-like (A), germ-tube (C) and hyphal (E) cell. Volume rendered views of the same cells are shown in (B, D, and F)respectively showing selected organelles that have been segmented and color-coded for identification. Blue, nucleus; orange,nucleolus; gray, mitochondria; yellow, vacuole; green, lipid bodies. (Scale bar for A-D, 0.5 µm, for E and F, 2.0 µm.).Reproduced from [69]

sample. The TXM at BESSY uses an undulator, grating monochromator and capillary condenserfor high spectral resolution.

Figure 9. High spatial and spectral resolution is demonstrated by the BESSY TXM. Left: Image of a multilayer teststructure. Bottom: spectrum from TiO2 nanoparticles, with images at the three wavelengths above. Data acquired using thethird diffraction order of the objective zone plate. The use of a monochromator and capillary condenser allows for energytunability with a bandwidth of ∼ 0.01% Reproduced from [70]

The instrument at the Stockholm Institute of Technology uses a droplet stream interceptedby a powerful laser as the source of soft X-rays. A multilayer mirror forms the condenser, andselects the wavelength from among the spectral features of the laser-plasma. The main advantageis that no synchrotron radiation source is used; however the image acquisition time is very muchlonger.

Multi-KeV TXM’s are available commercially from Xradia. They use capillary condensersand zone plates optimized for high X-ray energies. Several of these instruments are installedat synchrotron light sources, including SSRL, the APS, NSLS, the Taiwanese Light Source, theShanghai Light Source, etc. They have demonstrated ∼ 30 nm resolution. They are also availablewith conventional rotating anode X-ray sources and are ideally suited to form tomographicimages, since the depth of focus at a given resolution is inversely proportional to the wavelength.



Figure 10. The Stockholm table-top TXM utilizing a laser-plasma x-ray source and multilayer condenser lens [71].

For lower resolution applications no objective lens is needed. Simple projection microscopesoperating at high X-ray energy can be used for time resolved imaging of live insect physiology, orfor tomographic imaging of bone, porous rock samples and many other objects that are opaquein visible light. Such microscopes operate at the APS, at the ALS, and other lightsources. Phasecontrast techniques are used especially at the instruments operating at the ESRF in Grenobleand at the Swiss Light Source. Commercial instruments of this type are also available for non-synchrotron use, with a rather slower data acquisition rate.

2.7.2 Scanning X-ray microscopes (STXM)

Scanning x-ray microscopes using zone plate optics are in great demand for nanoscale elementaland chemical mapping. At soft x-ray energies of less than about 2 keV, a number of synchrotronlight sources host scanning transmission x-ray microscopes (STXMs) with 20–30 nm resolutionzone plates and image acquisition times of tens of seconds to minutes. At hard x-ray energiesof about 5–20 keV, phase contrast provides the best transmission images [73, 74], but mostexperiments use either Kirkpatrick-Baez mirrors to produce a 100–1000 nm focus or Frenselzone plates to produce a 30–100 nm focus and an energy dispersive detector to record x-rayfluorescence emitted by trace elements. A smaller number of experiments use an area detectorto collect the microdiffracted beam for applications such as imaging the strain in crystallinematerials [75].

In soft x-ray STXMs, one can acquire images above and below an absorption edge for elementalmapping, or at energies near a particular element’s absorption edge to image different chemicalbonding states of that element. This is especially useful for looking at organic materials at thecarbon K edge at about 290 ev [76], including polymers, biomaterials, environmental and soilspecimens [77], and astrobiological materials [78] (see Fig. 12). One can work with wet specimensat “water window” energies and above using various small sealed chambers, or with heatingchambers for applications such as the imaging of small catalysts at work [79]. The STXMs at theAdvanced Light Source are good examples of this instrument type; they use laser interferometerstages for precision scan fields [80], and they are frequently used in a spectromicroscopy “stack”mode where a series of images are acquired to yield spectrum-per-pixel data [81]. For complex,heterogeneous materials, one can apply multivariate statistical analysis and pattern recognitionmethods to obtain a set of signature spectra and their representative weighting within thespecimen [82]. Finally, x-ray fluorescence detection for light elements is beginning to be realizedas an alternative mode [10].

Hard x-ray microprobe applications center on the mapping of trace elements [83], where onecan obtain a sensitivity that is about a thousand times better than with electron microprobes,into the parts per billion range. This is accomplished by detecting the emission of characteristicX rays using either an energy dispersive detector such as a silicon drift diode, or a wavelengthdispersive system using a crystal spectrometer and array detector. These trace element mappingcapabilities allow one to study the role of copper in the development of the blood vessels thatsupply cancerous tumors [84], or the role of zinc in the develoment of fertilized oocytes of mam-malian egg cells [85]. Elemental mapping also plays an important role in environmental science,


16 Falcone et al.

Figure 11. Full-field 2-D projection images created using phase-contrast synchrotron x-rays at the APS. Images werechosen to highlight the highest quality imagery currently obtainable (a, b) and corresponding stills from live video (c-l).(a) Carabid beetle (Pterostichus stygicus) in dorsoventral view with legs removed and sacrificed prior to imaging. Image isa high-resolution composite of multiple images. The air-filled tubes of the tracheal system can be prominently seen. Thedark spots on the left side, mid-body are soil particles on the outer surface of the elytra. (b) Close-in view of one sectionof the prothorax, showing the branching pattern of tracheae. (c, d) One half-cycle of rhythmic tracheal collapse in a livecarabid beetle (Platynus decentis) in dorsoventral view. Images are frame grabs from a video recording; time interval is 0.5s. Total time of collapse and reinflation of the tubes is 1.0 s. (e-l) Visualization of internal food movement using labeledmarkers. (e) Schematic of the head and thorax of a butterfly (Pieris rapae) in lateral view. The foregut is shown in red; thesquare highlights the region of video stills in (f-h), and black arrow indicates the direction of food movement. (f-h) Videostills of passage of a food bolus posteriorly through the esophagus, moving through the frame from upper right to lowerleft. Red arrows indicate the leading (f) and trailing (h) edges of the bolus. Interval between frames is 0.5 s. Food is sugarwater/iodine mixture. X-ray energy (33.2 keV) was tuned to just above the K-edge absorption band for iodine. (i) Schematicof a carabid beetle (Pterostichus stygicus) in dorsoventral view (legs removed). Circular structures in mid-body representcoxae; the gut is represented in gray and red. Square highlights video in (j-l), visualization of cadmium-laced food in theforegut. Video stills (j-l) show movement of gut including anterior-posterior translation and squeezing of the crop (cr) andtranslation and rotation of the proventriculus (pr). The proventriculus is a valve that leads to the midgut [41]; here, it isclosed. Note that only parts of the gut with contrast agent can be seen. Interval between frames: j-k, 2 s; k-l, 6 s. X-rayenergy, 25 keV. Scale bars: a,b, 1 mm; c,d, 200 µm; f-h, 200 µm; j-l, 1 mm. Reproduced from [72]

and in the earth and planetary sciences [86]. Up until now work has been done primarily on roomtemperature specimens, but cryo systems are now becoming available at the ESRF in Grenobleand the APS in Chicago for studies of soft, hydrated materials with minimal preparation ar-tifacts and sample damage. An additional capability has been the development of fluorescencetomography to map elemental distributions in three dimensions, for example to study the roleof iron in the growth of marine protists [87] (Fig. 13).

2.7.3 X-ray microscopes with near-surface sensitivity

Photoelectron emission microscopes (PEEM) are also available commercially, but custom-made versions are operating at BESSY and the ALS. State-of-the-art instruments offer aberrationcorrection, and correspondingly high resolution. They find applications to map the orientation ofsurface domains in magnetic materials, multiferroics, biominerals and polymers, among others.

Scanning photoelectron microscopes (SPEM) were first developed at the NSLS, but currentlyinstruments of this type are operating at ELETTRA and at the Taiwanese light source. They



Figure 12. STXM image of organic matter (red) and an intriguing hollow organic spherule in an ultra-thin section of acarbonaceous chondritic meteorite. The image is composed of six images above and below the C(red), Ca (green), and Fe(blue) X-ray absorption edges. Such studies of extraterrestrial organic solids in meteorites and comets shed light onto thechemical history of the early Solar System. The image width is 5 microns. The hollow nano spherule is 840 nm wide andthe thickness of the nanospherule wall is on the order of 240 nm. Reproduced from [78]

Figure 13. 3D renderings of elemental distributions in the marine protist Cyclotella meneghiniana obtained by x-rayfluorescence tomography [87]. Isosurface concentrations used for the display are indicated in mmol/L. Clear correspondencesbetween P, K, and Ca are observed in the organelles, with a small amount of Mn apparent. The Si frustules and the Fe andMn rings are striking; and the cytoplasmic pillar (running along the axis of the diatom) contains mainly Cl, Cu, Zn, and S.As with the concentration thresholds shown here, total elemental content spans three orders of magnitude, ranging from 8µg for Si to 2 ng for Mn.

map the oxidation state of surface atoms and of atoms adsorbed on the surface.Angle resolved photoemission spectroscopy (ARPES) has been a powerful tool for mapping

band structure at or near surfaces, where samples with reasonably uniform surfaces over mil-limeter areas have been available. To extend the technique to inhomogeneous surfaces and tonanostructures, a new instrument is being constructed at the ALS that combines zone platefocusing with angle resolved photoelectron analysis, with 50 nm spatial resolution as the goal.

2.7.4 Diffraction microscopy

At several existing third generation synchrotron facilities there exist beamlines optimized forcoherent x-ray diffraction microscopy. These beamlines are capable of delivering a high coherentflux (109-1010 photons/s) with high spectral resolving power (E/dE ∼ 103 − 104) in a beamfootprint a few tens of micrometers wide. Using commercially available CCD detectors, these


18 Falcone et al.

Figure 14. Experimental and simulated data on nacre ordering. (A) Polarization dependent imaging contrast map of carbonobtained by the ratio of π∗ and σ∗ images acquired with PEEM-3 at the ALS in a region at the nacre-prismatic boundary,separating nacre (top) and the prismatic layer (bottom), from a H. rufescens cross section. In this pattern of contrast stacksof tablets with the same gray level have the same crystal orientation, and the decrease in overall contrast moving awayfrom the nacre-prismatic boundary indicates that tablet /c/ axis orientations become closer to perpendicular to the organicmatrix layers. In this image the polarization vector formed an angle of approximately 45◦ with the vertical nacre growthdirection. (B) Simulation results for a model in which each layer grows to completion before the next layer is nucleated,all nucleation sites are randomly distributed with x and y coordinates each constrained to be within a distance η froma nucleation site in the layer below, and each tablet adopts the orientation of the tablet below its nucleation site withprobability 1− ε. The growth rates (= gray levels) of the tablets in the first layer as well as those not co-oriented with thetablet below are chosen uniformly and randomly in the range [1 − δ/2, 1 + δ/2]. Parameter values are ε = 0.015, δ = 0.25,and η = 1.5µm. A two-dimensional vertical slice through the three-dimensional simulation is shown. Gray levels denote thegrowth rates of the tablets (light represents higher growth rate). The ordering moving away from the boundary, includingdecreasing tablet contrast, tablet size, and stacking direction, are in qualitative agreement with the experimental data.Reproduced from [88]

Figure 15. Chemical state mapping of near-surface structures using the SPEM instrument at ELETTRA. (a) 20× 20 and5 × 8 µm2 Ni 3p maps and intensity profiles, corresponding to the round, 1, and elongated, 2, islands, respectively. (b)Si 2p and valence band (VB) spectra of round (top), elongated (middle) 3D islands and the 2D phase (bottom). In thedeconvoluted Si 2p spectra the grey-filled component corresponds to the non-reacted Si cap on top of the islands or bulk Sifor the 2D phase. Reproduced from [89]

beamlines can produce x-ray diffraction data from single micrometer-sized particles with 10-20nm resolution in a few minutes of x-ray exposure. These capabilities have enabled the three-dimensional visualization of microscopic structures at resolutions that are not available by anyother technique. Of particular interest at these length scales are engineered nano-materials andsingle biological cells or their organelles. Several key demonstrations have shown the flexibilityof diffraction microscopy with respect to illuminating wavelength and experimental geometry.Among the first to generate a three-dimensional image by x-ray diffraction, Miao et al, show oneof the principal advantages of using hard x-rays with their tomographic reconstruction of a GaNquantum dot [90]. The short wavelength, 2.48 A, ensures that each two dimensional diffractionpattern recorded, each from a different angular orientation of the object, provides a true pro-jection image of the sample. These projections can then be tomographically combined into thethree-dimensional object volume. Alternatively, the full three dimensional diffraction volumemay be assembled from the two-dimensional diffraction views and a single three-dimensionalreconstruction performed [62]. Barty et al, have provided the highest resolution of a complexstructure to date with the reconstruction of an ultra-low density aerogel foam (Figure 16) [91]. At15 nm resolution, the reconstructed volume clearly shows the node-beam structure of the aero-gel network and, when included in computer models, suggests a way of increasing the materialstrength through thinning of the nodes.

The Bragg geometry can also be utilized for small crystalline samples where one is interestedin imaging deformations or imperfections in the crystal lattice. Strain fields in the crystal latticeresult in an effectively complex electron density that produces asymmetry in the diffuse x-



Figure 16. Diffraction microscope image of a Ta2O5 aerogel foam obtained at the ALS. Section and isosurface renderingof a 500 nm cube from the interior of the 3D volume. The foam structure shows globular nodes that are interconnected bythin beamlike struts. Approximately 85% of the total mass is associated with the nodes. Reproduced from [91].

ray diffraction pattern surrounding reciprocal lattice points [92]. The diffraction pattern of acrystal which is fully coherently illuminated is the convolution of the reciprocal lattice with thediffraction pattern of the overall crystal density. Therefore the diffuse Bragg spots may be phasedusing the CXDM technique in order to image the strain field within the crystal, projected alongthat particular momentum transfer. Pfeifer et al have produced three-dimensional images of suchdeformation fields within a sub-micron crystal of lead [93]. This sort of study of crystal strainon the nanoscale will ultimately help lead to an understanding of how their properties changewith respect to the bulk state and how to control such properties for the sake of engineeringnano-devices.

The efficiency of CXDM, due to its lack of optical elements downstream of the sample andthe use of a high quantum efficiency detector, make it desirable for high-resolution imaging ofradiation sensitive materials like biological cells. Several demonstrations have so far been madeof the two-dimensional visualization of the internal structure of whole biological cells by thistechnique. The natural x-ray contrast has been imaged in both the dry [94] and frozen hydratedstates [95, 96] while contrast enhancement has been shown for stained samples using hard x-rays[97] and a specifically labeled cell using soft x-rays [98]. The latter technique by Nelson et alachieve the highest recorded resolution of 13 nm. Such resolution cannot be extended into threedimensions without the use of cryo-protection to avoid radiation induced structural changes.However, the three-dimensional visualization of a dry human chromosome has been achievedat a moderate resolution of 120 nm [99]. This resolution is adequate to resolve internal densitygradients not apparent in projection imaging and is among the highest resolutions achieved forx-ray phase-contrast tomography.

3 The future

New synchrotron light sources with unprecedented brightness and high coherent flux are comingon line (PETRA III at DESY) or are under construction (NSLS II at Brookhaven NationalLaboratory). According to the design documents NSLS-II, under construction at BrookhavenNational Laboratory, will provide currently un-achievable spatial resolution, spectral resolutionand data acquisition times. The medium energy and very low emittance storage ring, 3 GeVelectron energy with 0.008 nm-rad emittance in the vertical and 0.55 nm-rad in the horizontal,and small source sizes, σh = 28µm and σv = 2.6µm, will enable scientific experiments thatrequire a high degree of coherence and high brightness, i.e. those requiring a small spot size andhigh spectral resolution. An aggressive research and development project is underway to developthe optics needed to provide a 1 nm spot size for a hard x-ray nano-probe and 0.1 meV energyresolution for an inelastic x-ray scattering instrument. The techniques of choice to obtain these


20 Falcone et al.

revolutionary capabilities are multi-layer Laue lenses for focusing to ultra-small spot sizes and amonochromator based on asymmetric backscattering for high energy resolution. These techniqueswill be applied to a range of scientific problems such as the study of the structure and functionof single nanoparticles and the study of structural phase transitions driven by phonon modesoftening. The facility will also provide other instruments requiring a high coherent photon fluxsuch as coherent x-ray diffraction microscopy of nanomaterials at near-atomic resolution, x-rayphoton correlation spectroscopy of membrane and polymer dynamics with sub-microsecond timeresolution, and resonant soft x-ray scattering from orbitally ordered materials.

3.1 Plans for LCLS

3.1.1 Diffractive imaging of Viruses and Cells.

The Linac Coherence Light Source (Figure 17), the world’s first hard-X-ray laser user facility,began operation in late 2009. With 70 fs and even shorter pulses delivered at 30-120 Hz at ener-gies between 2kV and 8 kV, the machine promises a revolutionary impact on ultrafast science andimaging. Diffraction patterns can be read out after each pulse, and we are especially interestedin the ”diffract-and-destroy” mode established at Flash. Here it was shown that a sufficientlyshort pulse of radiation may terminate before radiation damage commences, yet contain enoughphotons to provide a useful diffraction pattern. The limits of spatial resolution of this methodhave been explored in a number of publications (with estimates of about 1nm based on simula-tions). The most recent experimental results from single-shot imaging of a single Mimi virus atthe LCLS give a resolution of about 20nm in two-dimensional images reconstructed from phaseddiffraction patterns recorded at 1.8 kV [100]. This was achieved using a 3 micron diameter X-raybeam containing about 1013 photons per pulse. The merging of many of these diffraction pat-terns from identical particles in random orientations in order to from a three-dimensional imagedepends on the development of methods to determine their relative orientations, an analysiswhich can be combined with phasing [101]. The collection of a sufficient quantity of good datafor this purpose has proven challenging, since it requires a very high ”hit rate” from the particleinjection device, and identical particles free of conformational variation. Thus the destructivereadout nature of this method requires a means for injecting a continuous supply of identicalparticles into the beam. Two types of injectors have been developed for bioparticles, whichrequire hydration under the vacuum conditions commonly used. Either a gas-phase stream ofparticles [102] or a liquid phase stream [103] (with gas focusing to prevent clogging) may be used,similar to an ink-jet printer. The micron-sized column of liquid (containing bioparticles) breaksup into a stream of droplets, which freeze in the vacuum environment as they cross the pulsedX-ray beam. The droplets may be synchronized with the XFEL pulses, so that one X-ray pulsehits one droplet containing, on average (by choice of concentration) one particle, producing onediffraction pattern which is read out before the sequence is repeated. The data collection ratemay thus be limited by either source, injector or detector read-out rate. By reducing the X-raybeam diameter to submicron dimensions the intensity of high-angle scattering may be increased,and, using injectors with a higher hit rate, it is therefore expected to greatly improve resolutionin the near future, and to collect sufficient data to form three-dimensional images. The optimumchoice of beam energy has yet to be determined - the improved contrast in the water-windowmay yet favor soft X-ray snap-shot imaging for single-particles , despite the resulting limits onresolution.

3.1.2 Femtosecond protein nanocrystallography

Many proteins form showers of submicron microcrystals too small for study by conventionalprotein crystallography. This includes the important class of membrane proteins, important fordelivery of small drug molecules through the cell membrane. Over the past few years at ASU aprotein nanocrystal injector system (”aerojet”) has been developed, capable of firing a single-filestream of submicron droplets across the LCLS pulsed laser beam. This instrument has been



Figure 17. The Linac Coherent Light Source (LCLS) shoots carefully tailored buches of electrons accelerated using onekilometer of the Stanford Linear Accelerator through the 100 meter long array of undulators shown here to produce powerfulultrashort pulses of X-rays 120 time a second.

tested using nanocrystals of Photosystem 1 at the ALS [104]. This will allow the collection ofdiffraction patterns from individual protein nanocrystals (one in each droplet), with the lat-eral coherence width spanning the entire crystallite. Associated with each Bragg peak is then a”shape transform” distribution of intensity, given by a section of the Fourier Transform of thecrystallite shape.(Diffraction patterns from individual crystallites are readout after each laserpulse). Because the patterns can be indexed by standard crystallographic methods, the orienta-tion of each crystallite can be found, and so the two-dimensional data sets can be assembled inthree dimensions. By adding together all Bragg spots from different snap-shots with the sameMiller indices, a Monte-Carlo integration over angle around the Bragg condition can be per-formed. Theory then tells us that the structure factor modulus we seek is proprotional to thisvolume integral. A ”Monte-Carlo” approach to analyzing this new kind of crystallographic datafrom nanocrystals of varying size is described by Kirian et al [105], who show that the sumover crystal size converges to the required structure factors. This method of femtosecond pro-tein nanodiffraction has now been demonstrated experimentally at the LCLS for nanocrystals ofPhotosystem I, using 1.8 kV X-ray pulses of 70 fs duration (each containing about 1013 photons),for which millions of snap-shot patterns were recorded in the ”diffract-before-destroy” mode ofdestructive read-out crystallography [106]. The resolution of 8 Angstroms achieved was limitedby the X-ray wavelength. Some of these diffraction patterns, from nanocrystals containing asfew as 20 unit cells on a side, show strong interference fringes running between Bragg reflections.These can provide the oversampling needed to solve for the phases of the structure factors, bytaking advantage of the fact that whereas the ”shape transforms” around each lattice point aredifferent for nanocrystals of different sizes, the molecular transforms are independent of crystalsize. A method of achieving this phasing for nanocrystals of varying size, using all the data, hasnow been described [107]. In practical terms, the advantages of this new form of femtosecondprotein nanocrystallography appear to be i). The ability to circumvent the radiation damagelimit to resolution, for sufficiently brief pulses. ii) The ability to work with crystals in solutionat room temperature, without the need for cooling, to avoid radiation damage. This is allowingthe development of ”snap-shot” chemistry, as chemical reactions occur along a liquid jet stream.iii) The ability to analyze proteins which fail to produce large crystals. iv) Convenient inte-gration with pump-probe time-resolved protein crystallography, for which the XFELs providevery high time resolution, allowing study of the early stages of bond breaking and formation inchemical processes. Preliminary experiments in mid-2011 using a pump-laser fitted to the liquidinjector [108] were successful in showing changes in the structure factors of membrane proteinnanocrystals with the time delay between pump laser and X-ray snapshot .

3.1.3 Correlation methods and femtosecond WAXS.

In 1977, it was pointed out by Z. Kam that it may be possible to extract an image of one particle(in a gas or solution) by using the much stronger scattering from many identical particles, lying


22 Falcone et al.

in random orientations [109]. This is essentially the problem which Wide Angle X-ray Scattering(WAXS) attempts to solve. In conventional WAXS or SAXS solution scattering, one attemptsto reconstruct a three-dimensional real-space density map of a molecule using one-dimensionaldata together with much a-priori information (such as allowable chemical bond lengths). How-ever for particles frozen in either space or time, this one-dimensional scattering pattern developsfluctuations, and so becomes two-dimensional. Reconstruction of a three-dimensional distribu-tion from data projected onto two dimensions then becomes more favorable. With the limitedcomputing facilities and X-ray intensities available at that time, Kam’s approach achieved littlesuccess, however it has recently been further developed, and may be useful when applied tofemtosecond X-ray diffraction data. For particles frozen in time, the recording time must be lessthan the rotational diffusion time of the molecules. The essential idea can be understood if weconsider the much simpler problem of, for example, a set of identical nanorods lying on theirside on a transparent substrate. They differ only by random rotations about the normal to thesubstrate, which runs along the X-ray beam. Then rotation of one rod rotates its diffractionpattern about this axis. We consider many diffraction patterns, each obtained from a few tensof rods, and therefore showing fluctuations about their isotropic SAXS background. Interferencebetween scattering from different particles is washed out in the analysis, or produces interfer-ence fringes finer than one detector pixel. Kam pointed out that if the angular autocorrelationfunctions taken around rings in these two-dimensional patterns are added together (rather thanthe individual diffraction patterns), then the resulting sum will eventually converge to the au-tocorrelation function for a single (aligned) rod. It then remains to reconstruct the real-spacedensity of the molecule from the autocorrelation function of its diffracted intensity. This requiresthe phase problem to be solved twice - first to recover the diffracted intensity from its autocor-relation function, and secondly to retrieve the real-space density from the diffracted intensity.This may be done by modern iterative or optimization phasing methods. (For rods, the phaseproblem becomes a sign problem). Recently Saldin et al. have demonstrated this convergence insimulations for a 2D array of membrane proteins [110], and, experimentally, for gold nanorods ona substrate [111, 112]. Here the image of one rod was indeed reconstructed using the soft X-rayscattering from many, randomly oriented, identical rods, a-priori, without the use of SAXS-typemodeling. If the expansion of the sample density is made for a general three- dimensional ob-ject in spherical harmonics instead of the simple 2D polar harmonics used for the rods, thenthe method may be extended to three dimensions. The double phase problem is then greatlysimplied for molecules which possess some known symmetry, however the reconstruction of athree-dimensional model from two-dimensional data is very much more difficult [113]. Indeed,it has been shown that if the number of photons scattered per particle per pixel is less thanunity, then the signal to noise ratio in this method is less than unity, and falls off with scatteringangle [114]. This method might be applied to a beam of droplets, each of which contains manyidentical macromolecules. Because these molecules may be analyzed in their natural hydratedstate, without any crystallographic constraints, this approach could have an important impacton structural biology. If successful, it would open the way to dynamic experiments where, forexample, data is collected from proteins during the unfolding process (or enzymes completing acatalytic cycle) under the action of chemical agents, using snap-shot diffraction patterns recordedat different times during chemical reactions along a liquid jet stream.

3.1.4 X-ray microscopy with future soft X-ray FEL’s

The coherence properties and flash imaging capabilities of free electron lasers are very at-tractive for microscopy in the soft X-ray range. Just as with synchrotron radiation sources, wehave here the powerful inherent contrast mechanisms due to spectral signatures near absorptionedges, the water window for aqueous samples, and magnetic dichroism to study domain struc-tures. The coherent nature of the beam makes either diffraction microscopy or Fourier transformholography particularly suitable for image acquisition. The longer wavelength compared to X-ray FEL’s provides stronger signals, since both the scattering and absorption cross sections aremuch higher for these lower photon energies. According to Bergh et al., it is in the sub-kV energy


REFERENCES 23

range that one can record the highest resolution single-shot images using diffraction microscopy[115].

A particularly attractive prospect is to pursue pump-image experiments. In cases where iden-tical samples are available, samples can be supplied by the injection devices described above,which have been fitted with pump laser facilities [108]. The high time resolution of the XFELthen allows study of the earliest stages of electron transfer reactions, bond breaking and forma-tion, in addition to the much longer microsecond time scale of protein docking and folding. Ithas been shown that sufficiently low liquid jet speeds can be obtained so that a particle struckby the FEL pulse will, at an earlier time, have fallen within a pump laser focus centered on theXFEL optic axis and target region. Where identical samples are not available, one would usepulses with fewer photons so as to stay within the single-shot damage limit.

A number of laboratories are proposing to build soft X-ray FEL’s. The facility proposed bythe LBNL team is designed to serve a large user community with several independently tunableFEL’s served by a high repetition rate CW superconducting linac.

4 Summary

X-ray microscopes have found a broad range of applications, especially in the study of samplestoo thick for electron microscopy. The resolution obtained is typically 25-50 nm, although higherresolution has been demonstrated in some experiments. By combining imaging with spectroscopyor the detection of fluorescent X-rays the samples chemical or elemental constituents can bemapped. To mitigate the effects of radiation damage in high resolution imaging, samples maybe examined at cryogenic temperature.

Scanning X-ray microscopes as well as full-field instruments are installed at most synchrotronlight sources, and full-field instruments are also commercially available for home-laboratory use.The majority of X-ray microscopes use zone plates as the high- resolution optical element.

Diffraction microscopes, holographic imaging and ptychography require coherent illumination,but do not depend on high-resolution optics. Image reconstruction is performed by computa-tion. The required illumination is derived from high brightness synchrotron light sources, X-raylasers, or from free electron lasers (FELs). Ultrashort pulse FELs make it possible to performpump-probe experiments and flash-imaging on time scales short enough to outrun the effects ofradiation damage.

Acknowledgements

The Advanced Light Source is supported by the Director, Office of Science, Office of Basic En-ergy Sciences, of the US Department of Energy under Contract DE-AC02-05CH11231. Supportof this work at the National Synchrotron Light Source and NSLS-II, Brookhaven National Labo-ratory, was provided by the U.S. Department of Energy, Office of Science, Office of Basic EnergySciences, under Contract No. DE-AC02-98CH10886. The Advanced Photon source is supportedby the Director, Office of Science, Office of Basic Energy Sciences, of the US Department ofEnergy under contract DE-AC02-06CH11357. We (CJ, JK) also wish to thank the Division ofMaterials Research, Department of Energy for support under contract DE-FG0204-ER46128 andthe National Institutes for Health for support under grant 5R01GM064846-07. RF also receivedpartial support at UC Berkeley under the DOE SSAA Program, Contract DE-FG52-06NA26212.JS is supported by the Human Frontiers Science Program 20110.

References

[1] E W Muller and K Bahadur. Field ionization of gases at a metal surface and the resolution of the field ion microscope.Phys Rev, 102(3):624–631, 1956.


24 REFERENCES

[2] A V Crewe, J Wall, and J Langmore. Visibility of single atoms. Science, 168(3937):1338–40, 1970.[3] F Zernike. Phase contrast, a new method for the microsopic observation of transparent objects. Physica, 9:686–698,

1942.[4] F Zernike. Phase contrast, a new method for the microscopic observation of transparent objects part ii. Physica,

9:974–986, 1942.[5] R Heintzmann, T M Jovin, and C Cremer. Saturated patterned excitation microscopy—a concept for optical resolution

improvement. J. Opt. Soc. Am. A, 19(8):1599–1609, 2002.[6] M G L Gustafsson. Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy.

J Microsc, 198:82–87, 2000.[7] C.J.Jacobsen M.R.Howells J.Kirz. Soft x-ray microscopes and their biological applications. Q.Rev.Biophys., 28:33–130,

1995.[8] Henry N. Chapman and Keith A. Nugent. Coherent lensless x-ray imaging. Nat Photon, 4(12):833–839, 2010.

10.1038/nphoton.2010.240.[9] Anne Sakdinawat and David Attwood. Nanoscale x-ray imaging. Nat Photon, 4(12):840–848, 2010. 10.1038/npho-

ton.2010.267.[10] Burkhard Kaulich, Pierre Thibault, Alessandra Gianoncelli, and Maya Kiskinova. Transmission and emission x-

ray microscopy: operation modes, contrast mechanisms and applications. Journal of Physics: Condensed Matter,23(8):083002, 2011.

[11] Malcolm R Howells, Tobias Beetz, Henry N Chapman, C Cui, J. M Holton, Chris Jacobsen, J Kirz, Enju Lima,Stefano Marchesini, Huijie Miao, David Sayre, David A Shapiro, John C. H Spence, and D Starodub. An assessmentof the resolution limitation due to radiation-damage in x-ray diffraction microscopy. J. Electron Spectrosc. Relat.Phenom., 170(1-3):4–12, 2009.

[12] Henry N Chapman. X-ray imaging beyond the limits. Nat Mater, 8(4):299–301, 2009.[13] G N Hounsfield. Computerized transverse axial scanning (tomography). 1. description of system. Br J Radiol,

46(552):1016–22, 1973.[14] X. Zhang, H. Ade, C. Jacobsen, J. Kirz, S. Lindaas, S. Williams, and S. Wirick. Micro-XANES: Chemical contrast in

the scanning transmission X-ray microscope. Nuclear Instruments and Methods in Physics Research A, 347:431–435,August 1994.

[15] H. Ade and B. Hsiao. X-ray linear dichroism microscopy. Science, 262:1427–1429, 1993.[16] Arthur H. Compton and Samuel K. Allison. X-rays in theory and experiment. MacMillan, London, 1935.[17] G Schmahl, D Rudolph, G Schneider, P Guttmann, and B Niemann. Phase-contrast x-ray microscopy studies. Optik,

97(4):181–182, 1994.[18] Albert Einstein. Lassen sich brechungsexponenten der korper fur rontgenstrahlen experimentell ermitteln? Deutsche

Physikalische Gesellschaft, 20:86, 1918.[19] Hidekazu Mimura, Soichiro Handa, Takashi Kimura, Hirokatsu Yumoto, Daisuke Yamakawa, Hikaru Yokoyama,

Satoshi Matsuyama, Kouji Inagaki, Kazuya Yamamura, Yasuhisa Sano, Kenji Tamasaku, Yoshinori Nishino, MakinaYabashi, Tetsuya Ishikawa, and Kazuto Yamauchi. Breaking the 10 nm barrier in hard-x-ray focusing. Nature Physics,6(2):122–125, 2010.

[20] D H Bilderback, D J Thiel, R PAHL, and K E Brister. X-ray applications with glass-capillary optics. J SynchrotronRadiat, 1:37–42, 1994.

[21] A Snigirev, V Kohn, I Snigireva, and B Lengeler. A compound refractive lens for focusing high-energy x-rays. Nature,384:49, 1996.

[22] Albert V. Baez. Fresnel zone plate for optical image formation using extreme ultraviolet and soft x radiation. J. Opt.Soc. Am., 51(4):405–412, Apr 1961.

[23] C. Jacobsen, J. Kirz, and S. Williams. Resolution in soft x-ray microscopes. Ultramicroscopy, 47(1-3):55–79, 1992.[24] Weilun Chao, Jihoon Kim, Senajith Rekawa, Peter Fischer, and Erik H Anderson. Demonstration of 12 nm resolution

fresnel zone plate lens based soft x-ray microscopy. Optics Expr, 17(20):17669–17677, 2009.[25] S Rehbein, S Heim, P Guttmann, S Werner, and G Schneider. Ultrahigh-resolution soft-x-ray microscopy with zone

plates in high orders of diffraction. Phys Rev Lett, 103:110801, 2009.[26] Andrei Tkachuk, Fred Duewer, Hongtao Cui, Michael Feser, Steve Wang, and Wenbing Yun. X-ray computed tomog-

raphy in zernike phase contrast mode at 8 kev with 50-nm resolution using cu rotating anode x-ray source. Zeitschriftfur Kristallographie, 222(11):650–655, 2007. doi: 10.1524/zkri.2007.222.11.650.

[27] K. J. Gaffney and H. N. Chapman. Imaging atomic structure and dynamics with ultrafast x-ray scattering. Science,316(5830):1444–1448, 2007.

[28] Tobias Beetz. Soft x-ray diffraction imaging with and without lenses and radiation damage studies. Ph. D. Disser-tation, Stony Brook University, 2004.

[29] G Schmahl, D Rudolph, B Niemann, and O. Christ. Zone-plate x-ray microscopy. Quarterly Reviews of Biophysics,13(3):297–315, 1980.

[30] J.M. Kenney, J. Kirz, H. Rarback, M.R. Howells, P. Chang, P.J. Coane, R. Feder, P.J. Houzego, D.P. Kern, andD. Sayre. Soft x-ray microscopy at the nsls. Nuclear Instruments and Methods in Physics Research, 222(1-2):37–40,IN1–IN3, 41, 1984.

[31] Harald Ade, Janos Kirz, Steve Hulbert, Erik Johnson, Erik Anderson, and Dieter Kern. Scanning photoelectronmicroscope with a zone plate generated microprobe. Nuclear Instruments and Methods in Physics Research SectionA: Accelerators, Spectrometers, Detectors and Associated Equipment, 291(1-2):126–131, 1990.

[32] D Gabor. Microscopy by reconstructed wave-fronts. Proc R Soc Lon Ser-A, 197(1051):454–&, 1949.[33] Malcolm R Howells, C Jacobsen, J Kirz, R Feder, K McQuaid, and S Rothman. X-ray holograms at improved

resolution: a study of zymogen granules. Science, 238(4826):514, 1987.[34] J E Trebes, S B Brown, J Campbell, D L Matthews, D G Nilson, G F Stone, and D A Whelan. Demonstration of

x-ray holography with an x-ray laser. Science, 238(4826):517–9, 1987.[35] Sadao Aoki, Yutaka Ichihara, and Seishi Kikuta. X-ray hologram obtained by using synchrotron radiation. Japanese

Journal of Applied Physics, 11(12):1857–1857, 1972.[36] G. J Williams, H. M Quiney, B. B Dhal, C. Q Tran, Keith A Nugent, A. G Peele, D Paterson, and M. D de Jonge.

Fresnel coherent diffractive imaging. Phys Rev Lett, 97:25506, 2006.[37] Brian Abbey, Keith A Nugent, Garth J Williams, Jesse N Clark, Andrew G Peele, Mark A Pfeifer, Martin de Jonge,

and Ian McNulty. Keyhole coherent diffractive imaging. Nature Physics, 4:394, 2008.


REFERENCES 25

[38] Axel Rosenhahn, Florian Staier, Thomas Nisius, David Schaefer, Ruth Barth, Christof Christophis, Lorenz-M Stadler,Simone Streit-Nierobisch, Christian Gutt, Adrian Mancuso, Andreas Schropp, Johannes Gulden, Bernd Reime, JosefFeldhaus, Edgar Weckert, Bastian Pfau, Christian M Guenther, Rene Koennecke, Stefan Eisebitt, Michael Martins,Bart Faatz, Natalia Guerassimova, Katja Honkavaara, Rolf Treusch, Evgueni Saldin, Siegfried Schreiber, Evgeny ASchneidmiller, Mikhail V Yurkov, Ivan Vartanyants, Gerhard Gruebel, Michael Grunze, and Thomas Wilhein. Digitalin-line holography with femtosecond vuv radiation provided by the free-electron laser flash. Optics Expr, 17(10):8220–8228, 2009.

[39] Miklos Tegze, G Faigel, and Stefano Marchesini. Three dimensional imaging of atoms with isotropic 0.5 a resolution.Phys Rev Lett, 1999.

[40] I McNulty, J Kirz, C Jacobsen, Erik H Anderson, Malcolm R Howells, and D P Kern. High-resolution imaging byfourier-transform x-ray holography. Science, 256(5059):1009–1012, 1992.

[41] George W Stroke. An introduction to coherent optics and holography 2nd edition. An Introduction to CoherentOptics and Holography 2nd edition by George W. Stroke New York, 1969.

[42] R J Collier, Christoph B. Burckhardt, and Lawrence H. Lin. Optical holography. page 605, 1971.[43] B Reuter and H Mahr. Experiments with fourier transform holograms using 4.48 nm x-rays. Journal of Physics E:

Scientific Instruments, 9(9):746, 1976.[44] S Eisebitt, J Luning, W F Schlotter, M Lorgen, O Hellwig, W Eberhardt, and J Stohr. Lensless imaging of magnetic

nanostructures by x-ray spectro-holography. Nature, 432(7019):885–888, 2004.[45] H He, Stefano Marchesini, Malcolm R Howells, U Weierstall, G Hembree, and John C. H Spence. Experimental

lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering. Acta Cryst A, 59(2):143–152, 2003.[46] Abraham Szoke. Holographic microscopy with a complicated reference. J Imaging Sci Techn, 41(4):332–341, 1997.[47] W. F Schlotter, R Rick, K Chen, A Scherz, J Stoehr, J Luening, S Eisebitt, Ch Guenther, W Eberhardt, O Hellwig, and

I McNulty. Multiple reference fourier transform holography with soft x rays. Applied Physics Letters, 89(16):163112,2006.

[48] S. G Podorov, K. M Pavlov, and D. M Paganin. A non-iterative reconstruction method for direct and unambiguouscoherent diffractive imaging. Optics Expr, 15(16):9954–9962, 2007.

[49] Manuel Guizar-Sicairos and James R Fienup. Holography with extended reference by autocorrelation linear differentialoperation. Optics Expr, 15(26):17592–17612, 2007.

[50] Stefano Marchesini, Sebastien Boutet, Anne E Sakdinawat, Michael J Bogan, Sasa Bajt, Anton Barty, Henry NChapman, Matthias Frank, Stefan P Hau-Riege, Abraham Szoke, Congwu Cui, David A Shapiro, Malcolm R Howells,John C. H Spence, Joshua W Shaevitz, Joanna Y Lee, Janos Hajdu, and Marvin M Seibert. Massively parallel x-rayholography. Nat Photon, 2, 2008.

[51] EJ Candes, J Romberg, and T Tao. Robust uncertainty principles: Exact signal reconstruction from highly incompletefrequency information. Information Theory, IEEE Transactions on, 52(2):489–509, 2006.

[52] DL Donoho. Compressed sensing. Ieee T Inform Theory, 52(4):1289–1306, 2006.[53] David J Brady, Kerkil Choi, Daniel L Marks, Ryoichi Horisaki, and Sehoon Lim. Compressive holography. Optics

Expr, 17(15):13040–13049, 2009.[54] Jianwei W Miao, P Charalambous, J Kirz, and David Sayre. Extending the methodology of x-ray crystallography to

allow imaging of micrometre-sized non-crystalline specimens. Nature, 400(6742):342–344, 1999.[55] David Sayre. Some implications of a theorem due to shannon. Acta Crystallographica, 5(6):843–843, 1952.[56] R W Gerchberg and W O Saxton. A practical algorithm for the determination of phase from image and diffraction

plane pictures. Optik, 35:237–246, 1972.[57] J R Fienup. Phase retrieval algorithms - a comparison. Appl. Opt, 21(15):2758–2769, 1982.[58] P W. Hawkes and John C. H Spence. Science of microscopy, volume 1. page 1318, 2007.[59] Stefano Marchesini. A unified evaluation of iterative projection algorithms for phase retrieval. Review of Scientific

Instruments, 78:1301, 2007.[60] Stefano Marchesini, H He, Henry N Chapman, Stefan P Hau-Riege, A Noy, Malcolm R Howells, U Weierstall, and

John C. H Spence. X-ray image reconstruction from a diffraction pattern alone. Physical Review B, 68(14):140101,2003.

[61] J C H Spence, U Weierstall, and M Howells. Phase recovery and lensless imaging by iterative methods in optical,x-ray and electron diffraction. Philos Transact A Math Phys Eng Sci, 360(1794):875–895, 2002.

[62] Henry N Chapman, Anton Barty, Stefano Marchesini, A Noy, Stefan P Hau-Riege, C Cui, Malcolm R Howells, R Rosen,H He, John C. H Spence, U Weierstall, Tobias Beetz, Chris Jacobsen, and David A Shapiro. High-resolution ab initiothree-dimensional x-ray diffraction microscopy. J. Opt. Soc. Am. A, 23(5):1179–1200, 2006.

[63] Anton Barty, Sebastien Boutet, Michael J Bogan, Stefan P Hau-Riege, Stefano Marchesini, Klaus Sokolowski-Tinten,Nikola Stojanovic, Ra’anan Tobey, Henri Ehrke, Andrea Cavalleri, Stefan Dusterer, Matthias Frank, Sasa Bajt,Bruce W Woods, M Seibert, Janos Hajdu, Rolf Treusch, and Henry N Chapman. Ultrafast single-shot diffractionimaging of nanoscale dynamics. Nat Photon, 2(7):415–419, 2008.

[64] W. Hoppe and R. Hegerl. Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneousprimary wave field. Berichte Bunsen-Gesellschaft Physikalische Chemie, 74:1148, 1970.

[65] JM Rodenburg. Ptychography and related diffractive imaging methods. Advances in Imaging and Electron Physics,150:87–184, 2008.

[66] HN Chapman. Phase-retrieval x-ray microscopy by wigner-distribution deconvolution. Ultramicroscopy, 66(3-4):153–172, 1996.

[67] Pierre Thibault, Martin Dierolf, Andreas Menzel, Oliver Bunk, Christian David, and Franz Pfeiffer. High-resolutionscanning x-ray diffraction microscopy. Science, 321(5887):379–382, 2008.

[68] Shinya Kasai, Peter Fischer, Mi-Young Im, Keisuke Yamada, Yoshinobu Nakatani, Kensuke Kobayashi, Hiroshi Kohno,and Teruo Ono. Probing the spin polarization of current by soft x-ray imaging of current-induced magnetic vortexdynamics. Phys Rev Lett, 101(23):237203, 2008.

[69] Maho Uchida, Gerry McDermott, Modi Wetzler, Mark A Le Gros, Markko Myllys, Christian Knoechel, Annelise EBarron, and Carolyn A Larabell. Soft x-ray tomography of phenotypic switching and the cellular response to antifungalpeptoids in candida albicans. P Natl Acad Sci Usa, 106(46):19375–19380, 2009.

[70] S Heim, P Guttmann, and S Rehbein ldots. Energy-tunable full-field x-ray microscopy: Cryo-tomography and nano-spectroscopy with the new bessy txm. Journal of Physics: Conference Series, 186:012041, 2009.

[71] P. A. C. Takman, H. Stollberg, G. A. Johannson, A. Holmberg, M. Lindblom, and H. M. Hertz. High-resolution


26 REFERENCES

compact x-ray microscopy. Journal of Microscopy, 226(2):175–181, 2007.[72] John J Socha, Mark W Westneat, Jon F Harrison, James S Waters, and Wah-Keat Lee. Real-time phase-contrast

x-ray imaging: a new technique for the study of animal form and function. Bmc Biol, 5:6, 2007.[73] B. Hornberger, M. D. de Jonge, M. Feser, P. Holl, C. Holzner, C. Jacobsen, D. Legnini, D. Paterson, P. Rehak,

L. Struder, and S. Vogt. Differential phase contrast with a segmented detector in a scanning x-ray microprobe.Journal of Synchrotron Radiation, 15(4):355–362, Jul 2008.

[74] C. Holzner, M. Feser, S. Vogt, B. Hornberger, S. B. Baines, and C. Jacobsen. Zernike phase contrast in scanningmicroscopy with x-rays. Nature Physics, 6:883–887, 2010.

[75] C.E. Murray, Z. Ren, A. Ying, S.M. Polvino, I.C. Noyan, and Z. Cai. Strain measured in a silicon-on-insulator,complementary metal-oxide-semiconductor device channel induced by embedded silicon-carbon source/drain regions.Applied Physics Letters, 94:063502, 2009.

[76] H. Ade, X. Zhang, S. Cameron, C. Costello, J. Kirz, and S. Williams. Chemical contrast in x-ray microscopy andspatially resolved XANES spectroscopy of organic specimens. Science, 258:972–975, 1992.

[77] J. Lehmann, D. Solomon, J. Kinyangi, L. Dathe, S. Wirick, and C. Jacobsen. Spatial complexity of soil organic matterforms at nanometre scales. Nature Geoscience, 1:238–242, April 2008.

[78] G.D. Cody, E. Heying, C.M.O. Alexander, L.R. Nittler, A.L.D. Kilcoyne, S.A. Sandford, and R.M. Stroud. Establishinga molecular relationship between chondritic and cometary organic solids. Proceeings of the National Academy ofSciences of the USA, 108:1–6, 2011.

[79] E. de Smit, I. Swart, J.F. Creemer, G.H. Hoevling, M.K. Gilles, T. Tyliszczak, P.J. Kooyman, H.W. Zandbergen,C. Morin, B.M. Weckhuysen, and F.M.F de Groot. Nanoscale chemical imaging of a working catalyst by scanningtransmission x-ray microscopy. Nature, 456:222–225, 2008.

[80] A. L. D. Kilcoyne, T. Tyliszczak, W. F. Steele, S. Fakra, P. Hitchcock, K. Franck, E. Anderson, B. Harteneck, E. G.Rightor, G. E. Mitchell, A. P. Hitchcock, L. Yang, T. Warwick, and H. Ade. Interferometer-controlled scanningtransmission X-ray microscopes at the Advanced Light Source. Journal of Synchrotron Radiation, 10(2):125–136,Mar 2003.

[81] C. Jacobsen, G. Flynn, S. Wirick, and C. Zimba. Soft x-ray spectroscopy from image sequences with sub-100 nmspatial resolution. Journal of Microscopy, 197(2):173–184, 2000.

[82] M. Lerotic, C. Jacobsen, T. Schafer, and S. Vogt. Cluster analysis of soft x-ray spectromicroscopy data. Ultrami-croscopy, 100(1–2):35–57, 2004.

[83] Jr. C. J. Sparks. X-ray fluorescence microprobe for chemical analysis. In H. Winick and S. Doniach, editors, Syn-chrotron Radiation Research, pages 459–512, New York, 1980. Plenum Press.

[84] L. Finney, S. Mandava, L. Ursos, W. Zhang, D. Rodi, S. Vogt, D. Legnini, J. Maser, F. Ikpatt, O. I. Olopade, andD. Glesne. X-ray fluorescence microscopy reveals large-scale relocalization and extracellular translocation of cellularcopper during angiogenesis. Proceedings of the National Academy of Sciences, 104(7):2247–2252, February 2007.

[85] Alison M. Kim, Stefan Vogt, Thomas V. O’Halloran, and Teresa K. Woodruff. Zinc availability regulates exit frommeiosis in maturing mammalian oocytes. Nature Chemical Biology, 6(9):674–681, SEP 2010.

[86] Pierre Bleuet, Alexandre Simionovici, Laurence Lemelle, Tristan Ferroir, Peter Cloetens, Remi Tucoulou, and JeanSusini. Hard x-rays nanoscale fluorescence imaging of earth and planetary science samples. Applied Physics Letters,92(21):213111, 2008.

[87] M. D. de Jonge, C. Holzner, S. B. Baines, B. S. Twining, K. Ignatyev, J. Diaz, D. L. Howard, D. Legnini, A. Miceli,I. McNulty, C. Jacobsen, and S. Vogt. Quantitative 3D elemental microtomography of cyclotella meneghiniana at400-nm resolutions. Proceedings of the National Academy of Sciences, 107(36):15676–15680, 2010.

[88] P. U. P. A Gilbert, Rebecca A Metzler, Dong Zhou, Andreas Scholl, Andrew Doran, Anthony Young, MartinKunz, Nobumichi Tamura, and Susan N Coppersmith. Gradual ordering in red abalone nacre. J Am Chem Soc,130(51):17519–17527, 2008.

[89] Alexei Barinov, Pavel Dudin, Luca Gregoratti, Andrea Locatelli, Tevfik Onur Mentes, Miquel Angel Nino, and MayaKiskinova. Synchrotron-based photoelectron microscopy. Nucl Instrum Meth A, 601(1-2):195–202, 2009.

[90] Jianwei W Miao, Chien-Chun Chen, Changyong Song, Yoshinori Nishino, Yoshiki Kohmura, Tetsuya Ishikawa, DamienRamunno-Johnson, Ting-Kuo Lee, and Subhash H Risbud. Three-dimensional GaN-Ga2O3 core shell structure re-vealed by x-ray diffraction microscopy. Phys Rev Lett, 97:215503, 2006.

[91] Anton Barty, Stefano Marchesini, Henry N Chapman, and C Cui. Three-dimensional coherent x-ray diffractionimaging of a ceramic nanofoam: determination of structural deformation mechanisms. Phys Rev Lett, 2008.

[92] Ian K Robinson, Ivan A Vartanyants, G. J Williams, M. A Pfeifer, and J. A Pitney. Reconstruction of the shapes ofgold nanocrystals using coherent x-ray diffraction. Phys Rev Lett, 87:195505, 2001.

[93] Mark A Pfeifer, Garth J Williams, Ivan A Vartanyants, Ross Harder, and Ian K Robinson. Three-dimensional mappingof a deformation field inside a nanocrystal. Nature, 442:63, 2006.

[94] David A Shapiro, Pierre Thibault, Tobias Beetz, Veit Elser, Malcolm R Howells, Chris Jacobsen, Janos Kirz, EnjuLima, Huijie Miao, Aaron M Neiman, and David Sayre. Biological imaging by soft x-ray diffraction microscopy. PNatl Acad Sci Usa, 102:15343, 2005.

[95] X Huang, J Nelson, J Kirz, Enju Lima, Stefano Marchesini, Huijie Miao, Aaron M Neiman, David A Shapiro, J Stein-brener, and A Stewart. Soft x-ray diffraction microscopy of a frozen hydrated yeast cell. Phys Rev Lett, 103(19):198101,2009.

[96] Enju Lima, Lutz Wiegart, Petra Pernot, Malcolm R Howells, Joanna Timmins, Federico Zontone, and Anders Madsen.Cryogenic x-ray diffraction microscopy for biological samples. Phys Rev Lett, 103:198102, 2009.

[97] Jianwei W Miao, Keith O Hodgson, Tetsuya Ishikawa, Carolyn A Larabell, Mark A Le Gros, and Yoshinori Nishino.Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction. P Natl Acad Sci Usa, 100:110, 2002.

[98] J Nelson, X Huang, J Steinbrener, David A Shapiro, J Kirz, Stefano Marchesini, Aaron M Neiman, J. J Turner, andChris Jacobsen. High-resolution x-ray diffraction microscopy of specifically labeled yeast cells. P Natl Acad Sci Usa,107:7235, 2010.

[99] Yoshinori Nishino, Yukio Takahashi, Naoko Imamoto, Tetsuya Ishikawa, and Kazuhiro Maeshima. Three-dimensionalvisualization of a human chromosome using coherent x-ray diffraction. Phys Rev Lett, 102:18101, 2009.

[100] Marvin Siebert et al. Single mimivirus particles intercepted and imaged with an x-ray laser. Nature, 470(5):78–81,2011 Feb 3.

[101] N. D. Loh, M. J. Bogan, V. Elser, A. Barty, S. Boutet, S. Bajt, J. Hajdu, T. Ekeberg, F. R. N. C. Maia, J. Schulz,M. M. Seibert, B. Iwan, N. Timneanu, S. Marchesini, I. Schlichting, R. L. Shoeman, L. Lomb, M. Frank, M. Liang,


REFERENCES 27

and H. N. Chapman. Cryptotomography: Reconstructing 3d fourier intensities from randomly oriented single-shotdiffraction patterns. Phys. Rev. Lett., 104(22):225501, Jun 2010.

[102] Michael J Bogan, W Henry Benner, Sebastien Boutet, Urs Rohner, Matthias Frank, Anton Barty, M Marvin Seibert,Filipe Maia, Stefano Marchesini, Sasa Bajt, Bruce Woods, Vincent Riot, Stefan P Hau-Riege, Martin Svenda, ErikMarklund, Eberhard Spiller, Janos Hajdu, and Henry N Chapman. Single particle x-ray diffractive imaging. NanoLett, 8(1):310–316, 2008.

[103] D DePonte, U Weierstall, K Schmidt, J. Warner, D Starodub, J C H Spence, and R. B Doak. Gas dynamic virtualnozzle for generation of microscopic droplet streams. J. Phys. D: Appl. Phys, 41:195505, 2008.

[104] David A Shapiro, Henry N Chapman, D DePonte, R. B Doak, P Fromme, G Hembree, M Hunter, Stefano Marchesini,K. E Schmidt, John C. H Spence, D Starodub, and U Weierstall. Powder diffraction from a continuous microjet ofsubmicrometer protein crystals. Journal of Synchrotron Radiation, 15:593–599, 2008.

[105] Richard A. Kirian, Xiaoyu Wang, Uwe Weierstall, Kevin E. Schmidt, John C. H. Spence, Mark Hunter, Petra Fromme,Thomas White, Henry N. Chapman, and James Holton. Femtosecond protein nanocrystallography—data analysismethods. Opt. Express, 18(6):5713–5723, Mar 2010.

[106] Henry N. Chapman, Petra Fromme, Anton Barty, Thomas A. White, Richard A. Kirian, Andrew Aquila, Mark S.Hunter, Joachim Schulz, Daniel P. DePonte, Uwe Weierstall, R. Bruce Doak, Filipe R. N. C. Maia, Andrew V. Martin,Ilme Schlichting, Lukas Lomb, Nicola Coppola, Robert L. Shoeman, Sascha W. Epp, Robert Hartmann, Daniel Rolles,Artem Rudenko, Lutz Foucar, Nils Kimmel, Georg Weidenspointner, Peter Holl, Mengning Liang, Miriam Barthelmess,Carl Caleman, Sebastien Boutet, Michael J. Bogan, Jacek Krzywinski, Christoph Bostedt, Sasa Bajt, Lars Gumprecht,Benedikt Rudek, Benjamin Erk, Carlo Schmidt, Andre Homke, Christian Reich, Daniel Pietschner, Lothar Struder,Gunter Hauser, Hubert Gorke, Joachim Ullrich, Sven Herrmann, Gerhard Schaller, Florian Schopper, Heike Soltau,Kai-Uwe Kuhnel, Marc Messerschmidt, John D. Bozek, Stefan P. Hau-Riege, Matthias Frank, Christina Y. Hampton,Raymond G. Sierra, Dmitri Starodub, Garth J. Williams, Janos Hajdu, Nicusor Timneanu, M. Marvin Seibert, JakobAndreasson, Andrea Rocker, Olof Jonsson, Martin Svenda, Stephan Stern, Karol Nass, Robert Andritschke, Claus-Dieter Schroter, Faton Krasniqi, Mario Bott, Kevin E. Schmidt, Xiaoyu Wang, Ingo Grotjohann, James M. Holton,Thomas R. M. Barends, Richard Neutze, Stefano Marchesini, Raimund Fromme, Sebastian Schorb, Daniela Rupp,Marcus Adolph, Tais Gorkhover, Inger Andersson, Helmut Hirsemann, Guillaume Potdevin, Heinz Graafsma, BjornNilsson, and John C. H. Spence. Femtosecond x-ray protein nanocrystallography. Nature, 470(7332):73–77, 2011.10.1038/nature09750.

[107] John C. H. Spence, Richard A. Kirian, Xiaoyu Wang, Uwe Weierstall, Kevin E. Schmidt, Thomas White, AntonBarty, Henry N. Chapman, Stefano Marchesini, and James Holton. Phasing of coherent femtosecond x-ray diffractionfrom size-varying nanocrystals. Opt. Express, 19(4):2866–2873, Feb 2011.

[108] U. Weierstall, R. B Doak, and J.C.H. Spence. A pump-probe xfel particle injector for hydrated samples.http://arxiv.org/abs/1105.2104.

[109] Z Kam. Determination of macromolecular structure in solution by spatial correlation of scattering fluctuations.Macromolecules, 10(5):927–934, 1977.

[110] D K Saldin, V L Shneerson, R Fung, and A Ourmazd. Structure of isolated biomolecules obtained from ultrashortx-ray pulses: exploiting the symmetry of random orientations. Journal of Physics: Condensed Matter, 21:134014,2009.

[111] D K Saldin, V L Shneerson, Malcolm R Howells, Stefano Marchesini, Henry N Chapman, Michael J Bogan, David AShapiro, R. A Kirian, U Weierstall, K. E Schmidt, and John C. H Spence. Structure of a single particle from scatteringby many particles randomly oriented about an axis: toward structure solution without crystallization? New J. Phys,12:5014, 2010.

[112] D. K. Saldin, H. C. Poon, M. J. Bogan, S. Marchesini, D. A. Shapiro, R. A. Kirian, U. Weierstall, and J. C. H. Spence.New light on disordered ensembles: Ab initio structure determination of one particle from scattering fluctuations ofmany copies. Phys. Rev. Lett., 106(11):115501, Mar 2011.

[113] Veit Elser. Strategies for processing diffraction data from randomly oriented particles. Ultramicroscopy, page (ac-cepted), 2011.

[114] R. A Kirian, K Schmidt, and J.C.H. Spence. Signal, noise and resolution in correlated fluctuations from snapshotsaxs. Phys. Rev. E, submitted.

[115] M. Bergh, G. Huldt, N. Timneanu, F.R.N.C Maia, and Janos Hajdu. Feasibility of imaging feasibility of imaging livingcells at subnanometer resolutions by ultrafast x-ray diffraction. Quarterly Reviews of Biophysics, 41(3/4):181–204,2008.

research article new directions in x-ray...

Documents