RESEARCH ARTICLE New Directions in X

Transcription

June 2, 2011
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Contemporary Physics
draft9
Vol. 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 John
Spence6
1
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
2
Department of Physics, University of California, Berkeley, CA, USA
3
Argonne National Laboratory,Argonne, IL, USA
4
Northwestern University,Evanston, IL, USA
5
NSLS II, Brookhaven National Laboratory, Upton, NY, USA
6
Department 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 in
X-ray microscopy. Scanning microscopes and full-field instruments are in operation at synchrotron light sources
worldwide, 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 for
electron microscopy. Lensless techniques, such as diffraction microscopy, holography and ptychography are also
being developed. In high resolution imaging of radiation-sensitive material the effects of radiation damage needs
to be carefully considered. This article is designed to provide an introduction to the current state and future
prospects 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 online
c 200x Taylor & Francis
DOI: 10.1080/0010-751YYxxxxxxxx
http://www.informaworld.com
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Acronyms Used
ALS
APS
ARPES
BESSY II
CAT
CCD
CLS
CRL
CW
CXDM
DESY
ELETTRA
ERL
ESRF
FEL
FLASH
LBNL
LCLS
MAD
MLL
NSLS
PEEM
PETRA III
SAD
SAXS
SLS
SPEM
SSRL
STXM
TXM
WAXS
XFEL
XM1, XM2
XMCD
XMLD
1
Advanced Light Source. 1.9 GeV light source at Lawrence Berkeley National Laboratory, Berkeley, California, USA
Advanced Photon Source 7.0 GeV light source at Argonne National Laboratory, Argonne, Illinois, USA
Angel resolved photoemission. A technique to map electronic structure
of solids and surfaces
1.7 GeV light source in Berlin, Germany
Computerized Axial Tomography
Charge coupled device
Canadian Light Source 2.9 GeV light source in Saskatoon, Saskatchewan,
Canada
Compound refractive lens
Continuous wave
Coherent X-ray diffraction microscopy
Deutsches Electronen-Synchrotron laboratory in Hamburg, Germany
2.0-2.4 GeV light source near Trieste, Italy
Energy recovery linac
European Synchrotron Radiation Facility 6.0 GeV light source in Grenoble, France
Free electron laser
Soft X-ray free electron laser at DESY, Hamburg, Germany
Lawrence Berkeley National Laboratory, Berkeley, California, USA
Linac Coherent Light Source hard X-ray free electron laser at SLAC
National Accelerator Laboratory, Stanford, California, USA
Multiwavelength anomalous diffraction
Multilayer Laue lens
National Synchrotron Light Source, Brookhaven National Laboratory,
Upton, Long Island, New York, USA
Photoelectron emission microscope
6 GeV lightsource at the DESY laboratory, Hamburg, Germany
Single wavelength anomalous diffraction
Small angle X-ray scattering
Swiss Light Source 2.4 GeV light source at the Paul Scherrer Institute
Villigen, Switzerland
Scanning Photoemission microscope
Stanford Synchrotron Radiation Lightsource 3.0 GeV light source at
SLAC National Accelerator Laboratory, Stanford, California, USA
Scanning transmission X-ray microscope
Transmission X-ray microscope (full field)
Wide angle X-ray scattering
X-ray free electron laser
Transmission X-ray microscopes at the Advanced Light Source
X-ray magnetic circular dichroism
X-ray magnetic linear dichroism
Introduction: Why X-rays, why now?
Most of what we know about the micro-world was learned from microscopy. Until the 1930’s
microscopes used almost exclusively visible light to illuminate the specimen and to form the
image. It was well understood that the wavelength of visible light restricted the finest detail
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that could be resolved with these instruments to around a micrometer, or slightly less. A huge
amount of information was accumulated using these microscopes especially about biology and
medicine.
The microscopist is very often faced with the need to improve the resolution, to see more detail
in the specimen. It was known since the early part of the 20th century that X-rays had about
three orders of magnitude shorter wavelength than visible light, hence in principle they should
open up the nano-world to inspection. In fact X-rays were widely used not only for radiology, but
also for imaging the arrangement of atoms in molecules when these molecules could be arranged
to form crystals. Clearly the “resolution” in crystallography was at the atomic scale, at a fraction
of a nanometer. Yet it was also “well known” that lenses do not focus, and mirrors do not reflect
X-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 made
in 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 microscope
in 1970 [2]. Electron microscopes with sub-nanometer resolution quickly followed, and were
widely adopted. With further advances and aberration correction, today these instruments can
attain sub-Angstrom resolution. However, these instruments primarily achieve this resolution
in images which show a projection through a thin slice of crystalline material. For the imaging
of surface structure at high resolution, the more recent development of the scanning probe
microscopes in the early nineteen eighties has proven more powerful. Microscopes using visible
light have also made remarkable progress, following Zernike’s development of the phase plate in
the 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 tags
have been used to beat the diffraction “limit” of visible light. Furthermore, a variety of superresolution 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 this
type [5, 6].
Even in the face of these remarkable developments we believe there is a role for x-ray microscopy. As we shall discuss in this article, the nature of the interaction of X-rays with matter
provides information and contrast that is not available using other techniques, and the method
operates in a regime that may be inaccessible to other techniques [7]. Furthermore there have
been important recent breakthroughs in X-ray optics, X-ray sources, imaging modalities and
detectors 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 the
damage 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 with
the desired resolution. Hence, while it is possible to create movies of insect physiology at few
micron resolution, the dose required to form a single image at 0.1 micron resolution will kill
even the most radiation resistant living organism. As discussed in detail elsewhere, the radiation
damage effect is a strong function of resolution [11]. In order to record sufficient information
from the smaller volume element involved in imaging at higher resolution, the sample must be
exposed 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 at
liquid nitrogen temperature. Calculations indicate that this may allow even radiation sensitive
biological samples to be imaged to a resolution of 10 nm, and more robust samples to considerably
higher 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 to
disintegrate [12].
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1.1
Penetrating thick specimens
The penetrating power of X-rays and the contrast due to differing absorptivity of different
materials was noted by Röntgen in the first paper that announced his discovery of this “new
type of radiation.” It is the basis of all diagnostic radiology. A critically important feature of this
phenomenon is that by changing the X-ray wavelength one can adjust the penetrating power over
an 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, or
for broken bones in an elephant. The best contrast in absorption-based imaging is achieved by
selecting a wavelength where different components in the sample absorb some, but not all of the
radiation.
Simple absorptivity maps with the beam incident from one direction are often too complex
to interpret for thick specimens. It was therefore a true breakthrough when Hounsfield and
Cormack developed a way to reconstruct a three dimensional representation of the sample (such
as part of the human body) by the technique of CAT scans, or tomography. This, combined with
rapid increases in computing power, provided the incentive for dramatic advances in the now
large field of tomographic image processing, and the award of a Nobel prize [13].
1.2
1.2.1
Contrast mechanisms
Absorption contrast
The fraction of X-rays transmitted through matter follows the Lambert–Beer Law:
I = I0 e−µt
(1)
The linear absorption coefficient µ is proportional to the absorption cross section, and is shown
for a few materials in Figure 1. While the overall trend shows the steep increase with wavelength
noted in the previous section, there are dramatic jumps at “absorption edges.” For X-rays (as
for all electromagnetic radiation) the relation between the wavelength and the energy of the
corresponding photon is:
E=
hc
λ
The edge-jumps occur where the photon energy just exceeds the binding energy of some of
the core electrons of the element in question, so it can liberate these via the photoelectric
effect. Closer inspection reveals that the absorption coefficient undergoes rapid and dramatic
changes near the absorption edge, and that these variations depend on the chemical state of the
element. These spectral features provide a way to identify both the elemental and the chemical
constituents 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, additional absorption effects can provide information about these phenomena. For ferromagnetic materials illuminated with circularly polarized X-rays there is a several percent difference between
the absorptivity of the photons polarized along and opposite to the direction of magnetization
near the L absorption edges. This X-ray Magnetic Circular Dichroism (XMCD) can be used to
map domains of ferromagnetic films. Even for antiferromagnets, where there is only a favored
alignment but no polarization direction, one can map the alignment with linearly polarized Xrays due to the difference in absorptivity near L absorption edges as a function of the angle
between the X-ray polarization and the alignment in the material (XMLD, or X-ray Magnetic
Linear Dichroism). Similar differences in absorptivity have been demonstrated in polymers with
aligned molecules near the carbon K absorption edge [15].
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Figure 1. Linear absorption coefficients for gold, water, and protein with empirical formula H50 C30 N9 O10 S1 derived using
tabulated 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 a
core electron is filled by an electron from a less strongly bound state. The extra energy is carried
away either by a photon (fluorescence), or by a third electron (Auger process). The energy carried
by the fluorescence is characteristic of the element, so that the spectrum of fluorescence photons
can 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 organized
pattern in the sample with a periodicity comparable to or larger than the wavelength, the
scattering 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 sample
is non-crystalline, i.e. it does not have an organized pattern, then the scattering pattern is much
weaker since it is not concentrated into specific directions. Rather, it is diffuse and continuous
though still measurable.
1.2.4
Phase contrast
Over the last decade we have seen dramatic advances in the use of phase-contrast in X-ray
imaging. Fresnel fringes, the simplest evidence of this effect, were observed in the earliest days of
X-ray diffraction [16], but control of this useful effect has come only recently, motivated by the
realization that the constrast due to interference between two waves can vary between zero and
unity, yet result from very small changes in a material’s properties. While phase-constrast X-ray
microscopy has attempted to follow many of the ideas in optical phase contrast imaging [17], the
practical 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-ray
source which subtends a semi-angle α at a sample, the transverse coherence at the sample is
approximately λ/α, or several microns for a typical undulator at a soft X-ray synchrotron. This
distance must span spacings in the sample for which coherent imaging effects are expected, just as
it must span the pinholes in Young’s fringe experiment in order to produce strong interference
fringes. With the growing interest in sub-micron structures, phase-contrast X-ray imaging is
becoming 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. Both
forms of coherence, together with the choice of detector pixel number and spacing, may limit
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Figure 2. Zone plates are circular diffraction gratings where the line width decreases with increasing distance from the
optic 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 crystallography, 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 the
process of photoelectron production (or Compton scattering at higher beam energies), and some
of which may contribute to absorption contrast in regions of the sample with a high concentration of atoms whose absorption edge coincides with the beam energy. The remaining small
fraction are available for elastic scattering and phase contrast effects.
1.3
1.3.1
X-ray Optics
Mirrors
It was Albert Einstein [18] who pointed out that X-rays should undergo total external reflection
at grazing angles. This idea was taken up by Kirkpatrick and Baez in the design of the focusing
system 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 less
than 10 nm has been demonstrated [19]. Grazing incidence reflection is also used in polycapillary
concentrators and monocapillary microscope condensers [20].
1.3.2
Lenses
Going beyond mirrors, it is also a consequence of Einstein’s analysis that ordinary refractive
lenses can actually work, except that the focal lengths are extraordinarily long. The direction
of refraction for X-rays is opposite to that for visible light, therefore focusing elements have
concave surfaces rather than convex. In the last 14 years much work has been done to develop
compound refractive lenses (CRL) [21], made of a series of concave lenses with nearly zero
material between them so as to minimize absorption, and maximize focusing. Cylindrical lens
arrays can be fabricated lithographically, and point focusing is accomplished by a pair of crossed
elements of this type. These find applications mostly with high energy X-rays, 15 KeV and
above.
Diffractive optical elements can also be used as lenses. Fresnel zone plates were invented
some 120 years ago, but their use with X-rays is a more recent development [22]. These circular
diffraction gratings are fabricated in such a way that the spacing between adjacent zones provides
constructive interference in the direction of the primary focus. The resolution, as for all focusing
elements, is given by
r=
0.610λ
NA
(2)
where NA, the numerical aperture is the sine of the maximum diffraction angle. For a grating
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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]. In
other 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 to
significantly 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 the
higher numerical aperture of a third order focus [25].
An alternate nanofabrication technique is to create a multilayer with appropriately arranged
layer thicknesses, and then slice this device to the appropriate thickness. This method can easily
lead to high aspect ratios, but has proven to be challenging in the circular geometry. Doing
it on a planar substrate leads to linear zone plates that focus in one dimension. The resulting
Multilayer Laue Lens (MLL) has been shown to focus 30 KeV X-rays to less than 20 nm in one
dimension. Again, two such elements in crossed geometry can provide point focusing. In this
case it is also possible to increase the efficiency (the fraction of incident X-rays that end up in
the 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 electronbombardment X-ray sources. These can perform absorption-contrast and even phase contrast
tomography with a resolution of 50 nm [26]. This is a new development that seemed impossible
a decade ago.
Higher resolution and faster image acquisition is possible at third generation synchrotron light
sources. These machines are electron storage rings designed to accommodate many undulators
which offer several orders of magnitude higher brightness than conventional sources, and their
number is rapidly growing around the world. Although the X-rays are emitted with a pulsed
time structure (typically 50-100 ps long pulses with a spacing of 2 ns or so), few microscopes take
advantage of this feature. The X-ray energy is typically selectable based on a monochromator
with a resolving power of between 1000 and 10000. The energy range rarely exceeds one order
of 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 specialized undulators where the polarization is freely selectable. These sources host the microscopes
that set the state of the art today.
New storage ring sources are being built (PETRA III, NSLS II) or planned that have even
higher brightness, and are designed to produce beams that have coherence properties that exceed those available at existing light sources. All storage ring sources produce beams that are
much smaller in the vertical than in the horizontal plane. There is considerable interest in the
development of a different type of facility, the Energy Recovery Linac (ERL), that, among other
novel properties provides beams that are small in both dimensions.
Other types of sources are also being developed, and will offer remarkable new capabilities: A
soft 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 power
at 10 Hz. The first hard X-ray FEL, the LCLS, started operation at Stanford in late 2009, while
other facilities are under construction. Unlike conventional and synchrotron based sources, FELs
are most useful for single-shot flash-imaging [27].
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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 like
a camera. The scanning instrument scans the sample across a focused beam and detects transmitted or scattered radiation, which is displayed using the same two-dimensional raster which
scans the sample.
2.1
Transmission X-ray Microscopes (TXM)
The Transmission X-ray Microscope operates on the same principle as the standard visible light
microscope. It involves a source of illumination, a condenser that shapes the illumination and
delivers 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, and
the condenser may be a second zone plate, a capillary, or some other optical element. For best
performance the numerical aperture of the condenser should match the objective, but that is
often difficult to arrange. The typical TXM has a field of view of 15-25 micrometers and a
magnification of 1000-2000. To assure uniform illumination of the field, the condenser is either
wobbled, or moved in a spiral path. To image a larger area, images of neighboring fields are tiled
together. The first modern TXM was built by the Göttingen group [29]. Microscopes of this type
are particularly well suited for tomographic imaging, and several of them are in routine operation
with soft X-rays at the ALS and BESSY, often in the range between the carbon and oxygen
absorption edges in the ”water window” where water is relatively transparent compared to other
materials. 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 plane
into intensity modulations in the detector plane if the phase relationship between scattered and
unscattered light in the microscope is adjusted. This can be accomplished in a TXM through the
addition of a phase ring into the back focal plane of the objective zone plate. If the geometry of
the phase ring is such that it phase shifts only the x-rays which are not scattered by the sample
then the intensity contrast in the image plane can be enhanced. This technique was pioneered
for soft x-rays but is also of high importance for hard x-rays where absorption contrast is very
weak [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-rays
transmitted is recorded. Either the beam or the sample is raster-scanned to form a map of the
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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 lossy
optical elements between the sample and the detector. The scan range and step size can be freely
chosen. 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 different
chemical constituents can be created. This form of “spectromicroscopy” is available at several
lightsources, including the NSLS, ALS, SLS, CLS, APS, ESRF with more instruments coming on
line. 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 absorption contrast tends to be weak, hence other contrast mechanisms are commonly used. Detection
of fluorescent X-rays leads to high resolution trace element mapping, while the detection of
diffracted X-rays from polycrystalline materials is a powerful tool in the study of microstructure, 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 lose
most of their energy in collisions, and emerge as low energy secondary electrons. The higher the
absorptivity near the surface, the higher the yield of secondary electrons. By imaging the ”total
electron yield”, the surface absorptivity can be mapped. The instrument designed to do that
is the PhotoEmission Electron Microscope (PEEM). The X-ray beam illuminates a few-micron
area 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 excellent
chemical 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-ray
beam onto the sample, which is raster-scanned much as in the STXM. One can form the image
from the total electron yield or, in a scheme that is sensitive to just the top few atomic layers
of the surface, analyze the emitted electron energy to form the image using either the Auger
electrons or the photoelectrons [31]. The former provide information on the atoms present, while
the latter are also sensitive to the chemical state through the chemical shift in the photoelectron
energy. By recording not just the energy but also the direction of the photoelectron, the local
band 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 from
an object and interferes with unscattered photons that pass (or bypass, in the later improved
off-axis geometry) the object undisturbed. The undisturbed radiation is the reference wave and
the interference results in a coherent scattering pattern known as a hologram. The diverging
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photon beam from a point source creates a projection of the sample, thus magnifying the object
and providing an out-of-focus coherent shadow image. (Gabor’s reconstruction method provided
an imperfect focus correction, marred by the so-called ”twin image”). If the detector is a photo
transparency, the observer may look through the transparency in the direction of the (now absent) object; if only the reference beam is shining on the detector, the interference pattern serves
to ”un-scatter” (diffract) the wavefront and reconstruct the object’s image. Digital holography
accomplishes numerical reconstruction by simulation of this optical wavefront propagation.
In holographic imaging the phase retrieval problem is transformed into a linear problem by
adding a known modulating reference wave at the detector. The reference beam of known amplitude R and intensity IR = |R|2 interferes with light scattered from an unknown object wavefield
O 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 holographic
term, the twin holographic term, and the object term respectively. Signal reconstruction from
off-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 H
can be extracted or that other terms can be neglected where the hologram H is measured, and
R known.
Early demonstrations of X-ray holographic imaging [33–35] were limited by the detector (a
photographic 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 may
take place in the far field, the diffracted wave is related to the object via the Fresnel diffraction
formalism so that one obtains a magnified version of an inline hologram [36, 37]. In this original
in-line geometry it is not possible to separate the hologram from its twin term, however the
simplicity 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 crystal
as 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 translated
from the object provides the reference beam. Since the measurement is performed in Fourier
space, the resolution is determined by the numerical aperture of the detector and the maximum
scattering angle illuminated by the reference wave (determined by the size of the reference wave
emerging 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 be
achieved with a single Fourier Transform of the scattering distribution. It is therefore free of the
convergence issues which complicate iterative phasing schemes when using imperfect or noisy
data. McNulty et al. relied on diffractive optical elements to generate the reference wave, and this
caused significant distortions in the resulting image. With renewed interest in diffractive imaging
it became apparent that the presence of small object nearby a specimen could yield a holographic
image that would aid the phase retrieval problem [45]. But it was not until the work of Eisebitt
et al. [44] that Fourier transform x-ray holography became a practical method for imaging. In
this implementation the sample is placed behind a lithographically manufactured mask with a
micrometer 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
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Figure 5. Imaging of magnetic domains in a Co/Pt multilayer film using Fourier transform holography. In this implementation the sample is placed behind a lithographically manufactured mask with a micrometer sized sample aperture and a
nanometer sized hole that defines a reference beam (lower inset) Coherent X-rays are incident on a mask-sample structure
and a CCD detector measures the diffracted X-rays. Magnetic contrast is obtained by using circularly polarized X-rays
tuned 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 generated 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 that
is 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 structure that is optimal for imaging because it contains all the relevant frequencies has been employed
to achieve increased brightness and resolution at the Advanced Light Source and the FLASH
free electron laser facility [50]. In this geometry, the reference structure is a uniformly redundant
array (Fig. 6). Deconvolution of the coded aperture is accomplished by a convolution with a
binary function, minimizing noise propagation.
As both amplitude and phase are recorded up to a maximum angle given by the numerical
aperture (NA) of the detection system, partial three-dimensional information is present in a
hologram. By numerically propagating the wavefront through different planes it is possible to
reconstruct an entire stack of image planes. Resolution is reduced in the depth direction, especially at shorter wavelengths for which scattering at large angles is unlikely. Unlike confocal
microscopy light scattered from different planes contributes to coherent “speckle” noise to the
final image. However, since holographic data procesing is a linear problem, holography is well
suited to take advantage of recent progress in the field of “compressive sensing” [51, 52] which
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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 Xray beam is spatially and temporally coherent, the scattered radiation forms speckles. If one could
record the complex amplitude of these speckles, the specimen could be reconstructed by simple
inverse Fourier transformation. Detectors, unfortunately, record only the intensity of the speckles; the phase is lost. With sufficient additional information about the specimen the phase can be
recovered, and the specimen reconstructed. Over the past decade, since the first demonstration
by Miao et al [54] there have been several demonstrations of this ”diffractive” or lensless imaging
method, in which a computer is used in place of a lens to solve the phase problem. Resolution is
then limited only by the size of the detector and the wavelength, together with experimental factors such as background noise. The image is free of the lens aberrations which otherwise prevent
faithful 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 is
appoximately known, the phases of the scattered radiation can be found if that scattering is sufficiently finely sampled in the angular domain. (The sampling must satisfy Shannon’s theorem
in 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 between imposing the measured scattering intensities in the scattering domain and imposing the
additional constraints (such as the spatial extent of an isolated sample, known as finite support
in real space. Reviews of the relevant theory which summarise the many developments can be
found in Spence [58] and Marschesini [59]. Of these developments, the ”shrinkwrap” algorithm
has become perhaps the most popular [60]. For two-dimensional image reconstruction from a
phased far-field diffraction pattern, the question arises as to which plane across the optic axis
near the sample is reconstructed, and what is the depth of focus. The depth of focus is that of
an equivalent lens whose numerical aperture is that fixed by the detector in the diffractive imaging experiment. Experimental and theoretical studies using a three-dimensional object whose
extension along the optic axis is greater than this depth of focus shows that the method reconstructs a local projection on that plane (normal to the optic axis in the object space) for which
a compact support is provided [61]. It is shown here also that, since the complex object wavefield is recovered, this may be propagated to other nearby planes along the optic axis, allowing
virtual focusing. A recent application of the method to three-dimensional imaging of inorganic
structures 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 method
arise from its use with X-ray free-electron lasers, where it has already demonstrated the ability
to 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 prepare isolated samples, so that it is known a-priori that no material outside the defined sample
boundary (the ”support”) contributes to the diffraction pattern. Inversion is usually only possible with a very precisely defined support. ii) Stagnation of the algorithm when using poor
quality or noisy data.iii) The need for a beamstop, which usually results in a loss of low spatial
frequencies. These issues are resolved to varying degrees by alternative methods such as X-ray
holography and Ptychography.
2.6
Ptychography
Ptychography (from the greek ”to fold”) is a form of diffractive imaging in which a coherent
focused beam is scanned across a sample, and diffraction patterns are recorded at overlapping
positions of the probe. Real-space images of the sample may be reconstructed from this data
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Figure 7. Time-resolved sequence of images with magnetic dichroism contrast of a Permalloy disk sample from the XM1
microscope. Images obtained at various delay times from t = 0 ns up to t = 9 ns show the translational motion of the core
center. 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 advantages of Ptychography are that it solves both the beam-stop problem (loss of low spatial
frequency information in the vicinity of the unscattered beam) and the isolated sample problem
of diffractive imaging, that the inversion algorithms are much less prone to stagnation, and that
the 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 the
sense that, for a periodic sample, the fringes at the interference between overlapping orders are
actually a magnified coherent shadow image (or in-line hologram) of the sample, and so are
senstive 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 electron microscopy, and is well reviewed in [65]. Rodenburg shows that if a particular plane in the
four-dimensional (q, R) space is Fourier Transformed, then the result is an image with twice the
normal resolution. The first attempt using X-rays by Chapman [66] used the method of Wigner
deconvolution, in which the phase-retrieval problem is reduced to a linear problem. When using
patterns from a few, overlapping coherent probe positions it becomes the Ptychography method
of Rodenburg, which solves the resulting non-linear but convex problem. The inversion becomes
linear in the limit where the probe positions differ by one pixel, in which case one has exactly the
method of scanning transmission lattice imaging. Ptychography is convex if the probes overlap
by at least 50%. Recent X-ray Ptychography results are reported in Thibault et al [67], where a
highly efficient new algorithm is described.
In summary, apart from the challenge of mechanical stability, Ptychography appears to be
the most important and promising development in X-ray imaging, because it offers the prospect
of super-resolution, phasing with a robust algorithm and integration with spatially resolved
spectroscopy, while able to accommodate a wider range of samples and avoiding the use of a
beamstop.
2.7
2.7.1
State of the art, and applications
Transmission X-ray microscopes
Full field transmission X-ray microscopes (TXMs) using soft X-rays are in operation at several
laboratories. At the Advanced Lightsource in Berkeley the microscope XM1 has been used for the
development of high resolution imaging capabilities [24], and to study magnetisation dynamics.
The newly commissioned microscope at the National Center for X-ray Tomography emphasizes
the 3D imaging of biological samples at cryogenic temperatures. It also includes a cryo microscope
using visible light for correlative studies.
These two instruments use bending magnet sources and condenser zone plates to illuminate the
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Figure 8. Soft X-ray tomographic reconstruction of phenotypically distinct C. albicans cells from the XM2 microscope at
the National Center for X-ray Tomography. A representative orthoslice from each tomographic reconstruction is shown for
a 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 condenser
for high spectral resolution.
Figure 9. High spatial and spectral resolution is demonstrated by the BESSY TXM. Left: Image of a multilayer test
structure. Bottom: spectrum from TiO2 nanoparticles, with images at the three wavelengths above. Data acquired using the
third diffraction order of the objective zone plate. The use of a monochromator and capillary condenser allows for energy
tunability with a bandwidth of ∼ 0.01% Reproduced from [70]
The instrument at the Stockholm Institute of Technology uses a droplet stream intercepted
by a powerful laser as the source of soft X-rays. A multilayer mirror forms the condenser, and
selects the wavelength from among the spectral features of the laser-plasma. The main advantage
is that no synchrotron radiation source is used; however the image acquisition time is very much
longer.
Multi-KeV TXM’s are available commercially from Xradia. They use capillary condensers
and zone plates optimized for high X-ray energies. Several of these instruments are installed
at synchrotron light sources, including SSRL, the APS, NSLS, the Taiwanese Light Source, the
Shanghai Light Source, etc. They have demonstrated ∼ 30 nm resolution. They are also available
with conventional rotating anode X-ray sources and are ideally suited to form tomographic
images, since the depth of focus at a given resolution is inversely proportional to the wavelength.
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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 microscopes
operating at high X-ray energy can be used for time resolved imaging of live insect physiology, or
for tomographic imaging of bone, porous rock samples and many other objects that are opaque
in visible light. Such microscopes operate at the APS, at the ALS, and other lightsources. Phase
contrast techniques are used especially at the instruments operating at the ESRF in Grenoble
and at the Swiss Light Source. Commercial instruments of this type are also available for nonsynchrotron 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 elemental
and chemical mapping. At soft x-ray energies of less than about 2 keV, a number of synchrotron
light sources host scanning transmission x-ray microscopes (STXMs) with 20–30 nm resolution
zone plates and image acquisition times of tens of seconds to minutes. At hard x-ray energies
of about 5–20 keV, phase contrast provides the best transmission images [73, 74], but most
experiments use either Kirkpatrick-Baez mirrors to produce a 100–1000 nm focus or Frensel
zone plates to produce a 30–100 nm focus and an energy dispersive detector to record x-ray
fluorescence emitted by trace elements. A smaller number of experiments use an area detector
to collect the microdiffracted beam for applications such as imaging the strain in crystalline
materials [75].
In soft x-ray STXMs, one can acquire images above and below an absorption edge for elemental
mapping, or at energies near a particular element’s absorption edge to image different chemical
bonding states of that element. This is especially useful for looking at organic materials at the
carbon K edge at about 290 ev [76], including polymers, biomaterials, environmental and soil
specimens [77], and astrobiological materials [78] (see Fig. 12). One can work with wet specimens
at “water window” energies and above using various small sealed chambers, or with heating
chambers for applications such as the imaging of small catalysts at work [79]. The STXMs at the
Advanced Light Source are good examples of this instrument type; they use laser interferometer
stages 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 recognition
methods to obtain a set of signature spectra and their representative weighting within the
specimen [82]. Finally, x-ray fluorescence detection for light elements is beginning to be realized
as an alternative mode [10].
Hard x-ray microprobe applications center on the mapping of trace elements [83], where one
can 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 characteristic
X rays using either an energy dispersive detector such as a silicon drift diode, or a wavelength
dispersive system using a crystal spectrometer and array detector. These trace element mapping
capabilities allow one to study the role of copper in the development of the blood vessels that
supply cancerous tumors [84], or the role of zinc in the develoment of fertilized oocytes of mammalian egg cells [85]. Elemental mapping also plays an important role in environmental science,
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Figure 11. Full-field 2-D projection images created using phase-contrast synchrotron x-rays at the APS. Images were
chosen 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 is
a high-resolution composite of multiple images. The air-filled tubes of the tracheal system can be prominently seen. The
dark spots on the left side, mid-body are soil particles on the outer surface of the elytra. (b) Close-in view of one section
of the prothorax, showing the branching pattern of tracheae. (c, d) One half-cycle of rhythmic tracheal collapse in a live
carabid beetle (Platynus decentis) in dorsoventral view. Images are frame grabs from a video recording; time interval is 0.5
s. Total time of collapse and reinflation of the tubes is 1.0 s. (e-l) Visualization of internal food movement using labeled
markers. (e) Schematic of the head and thorax of a butterfly (Pieris rapae) in lateral view. The foregut is shown in red; the
square highlights the region of video stills in (f-h), and black arrow indicates the direction of food movement. (f-h) Video
stills of passage of a food bolus posteriorly through the esophagus, moving through the frame from upper right to lower
left. Red arrows indicate the leading (f) and trailing (h) edges of the bolus. Interval between frames is 0.5 s. Food is sugar
water/iodine mixture. X-ray energy (33.2 keV) was tuned to just above the K-edge absorption band for iodine. (i) Schematic
of a carabid beetle (Pterostichus stygicus) in dorsoventral view (legs removed). Circular structures in mid-body represent
coxae; the gut is represented in gray and red. Square highlights video in (j-l), visualization of cadmium-laced food in the
foregut. Video stills (j-l) show movement of gut including anterior-posterior translation and squeezing of the crop (cr) and
translation and rotation of the proventriculus (pr). The proventriculus is a valve that leads to the midgut [41]; here, it is
closed. 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-ray
energy, 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 room
temperature specimens, but cryo systems are now becoming available at the ESRF in Grenoble
and the APS in Chicago for studies of soft, hydrated materials with minimal preparation artifacts and sample damage. An additional capability has been the development of fluorescence
tomography to map elemental distributions in three dimensions, for example to study the role
of 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 custommade versions are operating at BESSY and the ALS. State-of-the-art instruments offer aberration
correction, and correspondingly high resolution. They find applications to map the orientation of
surface domains in magnetic materials, multiferroics, biominerals and polymers, among others.
Scanning photoelectron microscopes (SPEM) were first developed at the NSLS, but currently
instruments of this type are operating at ELETTRA and at the Taiwanese light source. They
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Figure 12. STXM image of organic matter (red) and an intriguing hollow organic spherule in an ultra-thin section of a
carbonaceous 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 the
chemical history of the early Solar System. The image width is 5 microns. The hollow nano spherule is 840 nm wide and
the 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-ray
fluorescence tomography [87]. Isosurface concentrations used for the display are indicated in mmol/L. Clear correspondences
between P, K, and Ca are observed in the organelles, with a small amount of Mn apparent. The Si frustules and the Fe and
Mn 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 8
µg 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 millimeter areas have been available. To extend the technique to inhomogeneous surfaces and to
nanostructures, a new instrument is being constructed at the ALS that combines zone plate
focusing 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 for
coherent x-ray diffraction microscopy. These beamlines are capable of delivering a high coherent
flux (109 -1010 photons/s) with high spectral resolving power (E/dE ∼ 103 − 104 ) in a beam
footprint a few tens of micrometers wide. Using commercially available CCD detectors, these
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Figure 14. Experimental and simulated data on nacre ordering. (A) Polarization dependent imaging contrast map of carbon
obtained 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 stacks
of tablets with the same gray level have the same crystal orientation, and the decrease in overall contrast moving away
from the nacre-prismatic boundary indicates that tablet /c/ axis orientations become closer to perpendicular to the organic
matrix layers. In this image the polarization vector formed an angle of approximately 45◦ with the vertical nacre growth
direction. (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 from
a nucleation site in the layer below, and each tablet adopts the orientation of the tablet below its nucleation site with
probability 1 − . The growth rates (= gray levels) of the tablets in the first layer as well as those not co-oriented with the
tablet below are chosen uniformly and randomly in the range [1 − δ/2, 1 + δ/2]. Parameter values are = 0.015, δ = 0.25,
and η = 1.5µm. A two-dimensional vertical slice through the three-dimensional simulation is shown. Gray levels denote the
growth rates of the tablets (light represents higher growth rate). The ordering moving away from the boundary, including
decreasing 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 and
5 × 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 the
deconvoluted Si 2p spectra the grey-filled component corresponds to the non-reacted Si cap on top of the islands or bulk Si
for the 2D phase. Reproduced from [89]
beamlines can produce x-ray diffraction data from single micrometer-sized particles with 10-20
nm resolution in a few minutes of x-ray exposure. These capabilities have enabled the threedimensional visualization of microscopic structures at resolutions that are not available by any
other technique. Of particular interest at these length scales are engineered nano-materials and
single biological cells or their organelles. Several key demonstrations have shown the flexibility
of 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 one
of the principal advantages of using hard x-rays with their tomographic reconstruction of a GaN
quantum dot [90]. The short wavelength, 2.48 Å, ensures that each two dimensional diffraction
pattern recorded, each from a different angular orientation of the object, provides a true projection image of the sample. These projections can then be tomographically combined into the
three-dimensional object volume. Alternatively, the full three dimensional diffraction volume
may be assembled from the two-dimensional diffraction views and a single three-dimensional
reconstruction performed [62]. Barty et al, have provided the highest resolution of a complex
structure to date with the reconstruction of an ultra-low density aerogel foam (Figure 16) [91]. At
15 nm resolution, the reconstructed volume clearly shows the node-beam structure of the aerogel network and, when included in computer models, suggests a way of increasing the material
strength through thinning of the nodes.
The Bragg geometry can also be utilized for small crystalline samples where one is interested
in imaging deformations or imperfections in the crystal lattice. Strain fields in the crystal lattice
result in an effectively complex electron density that produces asymmetry in the diffuse x-
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Figure 16. Diffraction microscope image of a Ta2 O5 aerogel foam obtained at the ALS. Section and isosurface rendering
of a 500 nm cube from the interior of the 3D volume. The foam structure shows globular nodes that are interconnected by
thin 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 a
crystal which is fully coherently illuminated is the convolution of the reciprocal lattice with the
diffraction pattern of the overall crystal density. Therefore the diffuse Bragg spots may be phased
using the CXDM technique in order to image the strain field within the crystal, projected along
that particular momentum transfer. Pfeifer et al have produced three-dimensional images of such
deformation fields within a sub-micron crystal of lead [93]. This sort of study of crystal strain
on the nanoscale will ultimately help lead to an understanding of how their properties change
with respect to the bulk state and how to control such properties for the sake of engineering
nano-devices.
The efficiency of CXDM, due to its lack of optical elements downstream of the sample and
the use of a high quantum efficiency detector, make it desirable for high-resolution imaging of
radiation sensitive materials like biological cells. Several demonstrations have so far been made
of the two-dimensional visualization of the internal structure of whole biological cells by this
technique. The natural x-ray contrast has been imaged in both the dry [94] and frozen hydrated
states [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 al
achieve the highest recorded resolution of 13 nm. Such resolution cannot be extended into three
dimensions without the use of cryo-protection to avoid radiation induced structural changes.
However, the three-dimensional visualization of a dry human chromosome has been achieved
at a moderate resolution of 120 nm [99]. This resolution is adequate to resolve internal density
gradients not apparent in projection imaging and is among the highest resolutions achieved for
x-ray phase-contrast tomography.
3
The future
New synchrotron light sources with unprecedented brightness and high coherent flux are coming
on line (PETRA III at DESY) or are under construction (NSLS II at Brookhaven National
Laboratory). According to the design documents NSLS-II, under construction at Brookhaven
National Laboratory, will provide currently un-achievable spatial resolution, spectral resolution
and data acquisition times. The medium energy and very low emittance storage ring, 3 GeV
electron 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 that
require a high degree of coherence and high brightness, i.e. those requiring a small spot size and
high spectral resolution. An aggressive research and development project is underway to develop
the optics needed to provide a 1 nm spot size for a hard x-ray nano-probe and 0.1 meV energy
resolution for an inelastic x-ray scattering instrument. The techniques of choice to obtain these
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revolutionary capabilities are multi-layer Laue lenses for focusing to ultra-small spot sizes and a
monochromator based on asymmetric backscattering for high energy resolution. These techniques
will be applied to a range of scientific problems such as the study of the structure and function
of single nanoparticles and the study of structural phase transitions driven by phonon mode
softening. The facility will also provide other instruments requiring a high coherent photon flux
such as coherent x-ray diffraction microscopy of nanomaterials at near-atomic resolution, x-ray
photon correlation spectroscopy of membrane and polymer dynamics with sub-microsecond time
resolution, and resonant soft x-ray scattering from orbitally ordered materials.
3.1
3.1.1
Plans for LCLS
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 energies between 2kV and 8 kV, the machine promises a revolutionary impact on ultrafast science and
imaging. Diffraction patterns can be read out after each pulse, and we are especially interested
in the ”diffract-and-destroy” mode established at Flash. Here it was shown that a sufficiently
short pulse of radiation may terminate before radiation damage commences, yet contain enough
photons to provide a useful diffraction pattern. The limits of spatial resolution of this method
have been explored in a number of publications (with estimates of about 1nm based on simulations). The most recent experimental results from single-shot imaging of a single Mimi virus at
the LCLS give a resolution of about 20nm in two-dimensional images reconstructed from phased
diffraction patterns recorded at 1.8 kV [100]. This was achieved using a 3 micron diameter X-ray
beam containing about 1013 photons per pulse. The merging of many of these diffraction patterns from identical particles in random orientations in order to from a three-dimensional image
depends on the development of methods to determine their relative orientations, an analysis
which can be combined with phasing [101]. The collection of a sufficient quantity of good data
for this purpose has proven challenging, since it requires a very high ”hit rate” from the particle
injection device, and identical particles free of conformational variation. Thus the destructive
readout nature of this method requires a means for injecting a continuous supply of identical
particles into the beam. Two types of injectors have been developed for bioparticles, which
require hydration under the vacuum conditions commonly used. Either a gas-phase stream of
particles [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) breaks
up into a stream of droplets, which freeze in the vacuum environment as they cross the pulsed
X-ray beam. The droplets may be synchronized with the XFEL pulses, so that one X-ray pulse
hits one droplet containing, on average (by choice of concentration) one particle, producing one
diffraction pattern which is read out before the sequence is repeated. The data collection rate
may thus be limited by either source, injector or detector read-out rate. By reducing the X-ray
beam 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 resolution
in the near future, and to collect sufficient data to form three-dimensional images. The optimum
choice of beam energy has yet to be determined - the improved contrast in the water-window
may yet favor soft X-ray snap-shot imaging for single-particles , despite the resulting limits on
resolution.
3.1.2
Femtosecond protein nanocrystallography
Many proteins form showers of submicron microcrystals too small for study by conventional
protein crystallography. This includes the important class of membrane proteins, important for
delivery of small drug molecules through the cell membrane. Over the past few years at ASU a
protein nanocrystal injector system (”aerojet”) has been developed, capable of firing a single-file
stream of submicron droplets across the LCLS pulsed laser beam. This instrument has been
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Figure 17. The Linac Coherent Light Source (LCLS) shoots carefully tailored buches of electrons accelerated using one
kilometer of the Stanford Linear Accelerator through the 100 meter long array of undulators shown here to produce powerful
ultrashort pulses of X-rays 120 time a second.
tested using nanocrystals of Photosystem 1 at the ALS [104]. This will allow the collection of
diffraction patterns from individual protein nanocrystals (one in each droplet), with the lateral 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 the
crystallite shape.(Diffraction patterns from individual crystallites are readout after each laser
pulse). Because the patterns can be indexed by standard crystallographic methods, the orientation of each crystallite can be found, and so the two-dimensional data sets can be assembled in
three dimensions. By adding together all Bragg spots from different snap-shots with the same
Miller indices, a Monte-Carlo integration over angle around the Bragg condition can be performed. Theory then tells us that the structure factor modulus we seek is proprotional to this
volume integral. A ”Monte-Carlo” approach to analyzing this new kind of crystallographic data
from nanocrystals of varying size is described by Kirian et al [105], who show that the sum
over crystal size converges to the required structure factors. This method of femtosecond protein nanodiffraction has now been demonstrated experimentally at the LCLS for nanocrystals of
Photosystem 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 of
destructive read-out crystallography [106]. The resolution of 8 Angstroms achieved was limited
by the X-ray wavelength. Some of these diffraction patterns, from nanocrystals containing as
few 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, by
taking advantage of the fact that whereas the ”shape transforms” around each lattice point are
different for nanocrystals of different sizes, the molecular transforms are independent of crystal
size. A method of achieving this phasing for nanocrystals of varying size, using all the data, has
now been described [107]. In practical terms, the advantages of this new form of femtosecond
protein nanocrystallography appear to be i). The ability to circumvent the radiation damage
limit to resolution, for sufficiently brief pulses. ii) The ability to work with crystals in solution
at room temperature, without the need for cooling, to avoid radiation damage. This is allowing
the 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 integration with pump-probe time-resolved protein crystallography, for which the XFELs provide
very high time resolution, allowing study of the early stages of bond breaking and formation in
chemical processes. Preliminary experiments in mid-2011 using a pump-laser fitted to the liquid
injector [108] were successful in showing changes in the structure factors of membrane protein
nanocrystals 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
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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 attempts
to reconstruct a three-dimensional real-space density map of a molecule using one-dimensional
data together with much a-priori information (such as allowable chemical bond lengths). However for particles frozen in either space or time, this one-dimensional scattering pattern develops
fluctuations, and so becomes two-dimensional. Reconstruction of a three-dimensional distribution from data projected onto two dimensions then becomes more favorable. With the limited
computing facilities and X-ray intensities available at that time, Kam’s approach achieved little
success, however it has recently been further developed, and may be useful when applied to
femtosecond X-ray diffraction data. For particles frozen in time, the recording time must be less
than the rotational diffusion time of the molecules. The essential idea can be understood if we
consider the much simpler problem of, for example, a set of identical nanorods lying on their
side on a transparent substrate. They differ only by random rotations about the normal to the
substrate, which runs along the X-ray beam. Then rotation of one rod rotates its diffraction
pattern about this axis. We consider many diffraction patterns, each obtained from a few tens
of rods, and therefore showing fluctuations about their isotropic SAXS background. Interference
between scattering from different particles is washed out in the analysis, or produces interference fringes finer than one detector pixel. Kam pointed out that if the angular autocorrelation
functions taken around rings in these two-dimensional patterns are added together (rather than
the individual diffraction patterns), then the resulting sum will eventually converge to the autocorrelation function for a single (aligned) rod. It then remains to reconstruct the real-space
density of the molecule from the autocorrelation function of its diffracted intensity. This requires
the phase problem to be solved twice - first to recover the diffracted intensity from its autocorrelation 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 phase
problem becomes a sign problem). Recently Saldin et al. have demonstrated this convergence in
simulations for a 2D array of membrane proteins [110], and, experimentally, for gold nanorods on
a substrate [111, 112]. Here the image of one rod was indeed reconstructed using the soft X-ray
scattering from many, randomly oriented, identical rods, a-priori, without the use of SAXS-type
modeling. If the expansion of the sample density is made for a general three- dimensional object in spherical harmonics instead of the simple 2D polar harmonics used for the rods, then
the method may be extended to three dimensions. The double phase problem is then greatly
simplied for molecules which possess some known symmetry, however the reconstruction of a
three-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 than
unity, then the signal to noise ratio in this method is less than unity, and falls off with scattering
angle [114]. This method might be applied to a beam of droplets, each of which contains many
identical macromolecules. Because these molecules may be analyzed in their natural hydrated
state, without any crystallographic constraints, this approach could have an important impact
on structural biology. If successful, it would open the way to dynamic experiments where, for
example, data is collected from proteins during the unfolding process (or enzymes completing a
catalytic cycle) under the action of chemical agents, using snap-shot diffraction patterns recorded
at 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 attractive for microscopy in the soft X-ray range. Just as with synchrotron radiation sources, we
have here the powerful inherent contrast mechanisms due to spectral signatures near absorption
edges, the water window for aqueous samples, and magnetic dichroism to study domain structures. The coherent nature of the beam makes either diffraction microscopy or Fourier transform
holography particularly suitable for image acquisition. The longer wavelength compared to Xray FEL’s provides stronger signals, since both the scattering and absorption cross sections are
much higher for these lower photon energies. According to Bergh et al., it is in the sub-kV energy
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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 identical 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 XFEL
then allows study of the earliest stages of electron transfer reactions, bond breaking and formation, in addition to the much longer microsecond time scale of protein docking and folding. It
has been shown that sufficiently low liquid jet speeds can be obtained so that a particle struck
by the FEL pulse will, at an earlier time, have fallen within a pump laser focus centered on the
XFEL optic axis and target region. Where identical samples are not available, one would use
pulses 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 by
the LBNL team is designed to serve a large user community with several independently tunable
FEL’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 samples
too thick for electron microscopy. The resolution obtained is typically 25-50 nm, although higher
resolution has been demonstrated in some experiments. By combining imaging with spectroscopy
or the detection of fluorescent X-rays the samples chemical or elemental constituents can be
mapped. To mitigate the effects of radiation damage in high resolution imaging, samples may
be examined at cryogenic temperature.
Scanning X-ray microscopes as well as full-field instruments are installed at most synchrotron
light 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 computation. The required illumination is derived from high brightness synchrotron light sources, X-ray
lasers, or from free electron lasers (FELs). Ultrashort pulse FELs make it possible to perform
pump-probe experiments and flash-imaging on time scales short enough to outrun the effects of
radiation damage.
Acknowledgements
The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract DE-AC02-05CH11231. Support
of this work at the National Synchrotron Light Source and NSLS-II, Brookhaven National Laboratory, was provided by the U.S. Department of Energy, Office of Science, Office of Basic Energy
Sciences, under Contract No. DE-AC02-98CH10886. The Advanced Photon source is supported
by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of
Energy under contract DE-AC02-06CH11357. We (CJ, JK) also wish to thank the Division of
Materials Research, Department of Energy for support under contract DE-FG0204-ER46128 and
the National Institutes for Health for support under grant 5R01GM064846-07. RF also received
partial support at UC Berkeley under the DOE SSAA Program, Contract DE-FG52-06NA26212.
JS is supported by the Human Frontiers Science Program 20110.
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RESEARCH ARTICLE New Directions in X

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