X-ray microscopy
Chris Jacobsen
Department of Physics & Astronomy
Stony Brook University, NY, USA
Chris.Jacobsen@stonybrook.edu
Slides at http://tinyurl.com/ye9ldvb
1

Long Island, New York, USA

Stony
Brook
Brookhaven

NYC
JFK

Stony Brook University
National Synchrotron Light Source, Brookhaven National Laboratory2

X-ray microscopy group at Stony Brook
Jan Steinbrener,
Lisseth Gavilan,
Xiaojing Huang,
Christian Holzner,
Rachel Mak, Josh
Turner, Johanna
Nelson, Chris
Jacobsen, RobertTowers. Not
shown: Sue Wirick,Chris Peltzer.
Phase contrast andfluorescence
Spectromicroscopy
XDM/CXDI
Summer at Stony Brook: groups take turns sponsoring
the 4:30 pm Friday beer keg
3Wilhelm Röntgen
Universität Würzburg
Dec. 1895

Michael Pupin
Columbia University/New YorkFeb. 1896“This is of the hand of a gentleman resident in New York, who, while on a hunting trip inEngland a few months ago, was so unfortunate as to discharge his gun into his right hand, no lessthan forty shot lodging in the palm and fingers. The hand has since healed completely; but the
shot remain in it, the doctors being unable to remove them, because unable to determine their
exact location. The result is that the hand is almost useless, and often painful.” - Cleveland
Moffett, McClure’s Magazine, April 1896
4

The X-ray Microscope
It would be a big improvement on microscopes using
light or electrons, for X-rays combine shortwavelengths, giving fine resolution, and penetration.
The main problems standing in the way have now
been solved.

5useful complement toSome further problems were solved after 1949...
Grazing incidence mirror optics: Kirkpatrick and Baez, 1949; Wolter 1952
Zone plate optics: Baez 1960; Schmahl and Rudolph 1969; Ceglio 1980
Synchrotron radiation: Horowitz and Howell 1972; Aoki et al., 1972; Niemann,
Schmahl et al., 1976
Scanning: Horowitz and Howell 1972; Rarback, Kirz et al., 1980
Fluorescence: Horowitz and Howell 1972; Sparks 1980
Cryo: Schneider et al., 1995; Maser, Jacobsen et al., 1996
Tomography: Haddad et al., 1994; Schneider, Weiss et al. 1998
NEXAFS spectromicroscopy: Ade, Kirz et al., 1992
6

Historical comments• Following Röntgen: use visible light microscopes to examine
detail of x-ray micrographs on film.
• 1940’s & 1950’s: reflective optics (Kirkpatrick & Baez; Wolter)• 1960’s: point source projection (Cosslett, Nixon and others)• “modern” era with zone plates:– UV holography for fabrication, full-field imaging using synchrotron:
Schmahl et al., Göttingen [Optik 29, 577--585 (1969); Applied
Optics 15, 1883--1884 (1976)]– Electron beam lithography for zone plate fabrication: proposed by
Sayre [IBM technical report RC 3974 (#17965), 1972], and first
implemented by Ceglio et al., J. Vac. Sci. Tech. B 1, 1285 (1983) and
Kern et al., SPIE 447, 204 (1984).
– Scanning microscopy with zone plates: Kirz et al., Stony Brook[Scanned Image Microscopy, E.A. Ash, Editor. 1980: London. p. 449]

7

X raysElectrons• Absorption dominates• Inelastic scattering is weak
• No multiple scattering• Inelastic scattering dominates(energy filters)• Multiple scattering often present• High contrast from small things

8The refractive index• Damped, driven harmonic oscillator• Damping: scattering, absorption• Driving: incident electromagnetic wave
• Harmonic oscillator: electron quantum state withenergy9Damped, driven harmonic oscillator• Single resonance: absorption peak, phaseshift across resonance

10The preponderance of plasmons
Dividing line between low and high frequency
limits of refractive index

11Dispersion in glasses

12

Mysteries of the refractive index
Write refractive index as
Phase velocity is faster than light invacuum!

Prisms refract x rays the opposite
way from visible light!
Phase is advanced rather thanretarded! Total external reflection
with critical angle

But group velocity is OK:
13

X-ray refractive index
Refractive index: basedon a damped, driven
harmonic oscillator
model in the limit of highfrequency and low
damping:

where na gives atoms/
volume, re=2.82×10-15 m
is the classical radius of
the electron, and (f1+if2)
specify the atom’s
oscillator strength at agiven photon energy
14Phase velocity greater than group velocity

15

X rays in media

16

Electron interactions

These plots: Jacobsen, Medenwaldt, and Williams, in X-ray
Microscopy & Spectromicroscopy (Springer, 1998)
17

X rays and electrons

Consider penetration
distance: 1/e absorption
length for x rays,
scattering mean freepaths for electrons18Electrons: inelastic
energy deposition
Inelastic scattering: energy transfer
of 35-45 eV
At 100 keV, 1 e-/nm2

3.2x104 Gray

(1 Gray=1 J/kg)

19

X rays are better than electrons for thick specimens• λ=100-10 nm: minimum penetration in entire electromagnetic spectrum.
• No more than 1 high-resolution image of wet, soft samples unless frozen.
• At energies >3 keV, opportunities for thick specimens.

Phase contrast is important!
These plots: based on Jacobsen, Medenwaldt, and Williams, in X-ray Microscopy & Spectromicroscopy (Springer, 1998). See
also Sayre et al., Science 196, 1339 (1977).

20

3Detecting trace elements• Differential
absorption is greatfor soft x-ray
spectromicroscopy,
but at >1%
concentration.
• X-ray fluorescence:~1000x better
sensitivity thanelectrons for traceelemental mapping(ion concentrationsetc.). Parts per
billion!

4

Fluorescence: trace element concentrations
Proton (p), electron (e)stimulated fluorescence
X-ray differential absorption

X-ray fluorescence

J. Kirz, in Scanning Electron Microscopy 2,
1980, p. 239. EELS=electron energy loss
spectroscopy. Hard-to-find reprint:
http://tinyurl.com/2eu7q4
22

Total internal reflection• Snell’s law: n1sinθ1=n2sinθ2• When θ1=90°, we have sinθ2=n1/n2

Larsson, Siegbahn, and Waller, Naturwiss. (1924)

23

Reflective x-ray optics• Grazing incidence critical angle for mirror reflection:or• Use two orthogonal cylinders for 2D focusing: Kirkpatrick andBaez, J. Opt. Soc. Am. 38, 766 (1948)
Mimura, Yamauchi et al., Appl. Phys.
Lett. 90, 051903 (2007): 25 nm usingelastic emission machining.

Synthetic multilayer mirrors: work well at approx. λ≥10 nm
24Compound refractive lenses• Röntgen tried to make lenses, but
found no focusing.
• Focal length of one lens is long –so combine many lenses! Tomie;
Snigirev et al., Nature 384, 49(1996); Lengeler et al., J. Synch.
Rad. 9, 119 (2002).
• Resolution approaching 100 nm at
5-10 keV with parabolic beryllium
lensesCompoundrefractive lenses atUniversität Aachen

25X-ray focusing: Fresnel zone plates• Diffractive optics: radiallyvaried grating spacing

Diameter d, outermost zone width
drN, focal length f, wavelength λ:• Largest diffraction angle isgiven by outermost (finest)zone width drN as θ=λ/(2drN)• Rayleigh resolution is 0.61 λ/(θ)=1.22drN• Zones must be positioned to~1/3 width over diameter(10 nm in 100 µm, or 1:104)

Central stop and order sorting
aperture (OSA) to isolate firstorder focus
26

Fresnel zone plate images
R. W. Wood (1898): zone
plate figure drawn with a
pen and a compass!
Photographically reduced27

Zone plate efficiency and thickness
For binary zones, 1:1 mark:space ratio.
See Kirz, J. Opt. Soc. Am. 64, 301 (1974)

28

Zone plates by electron beam lithography• Electron beam lithography: produces the finest possible structures (otherthan what nature can be persuaded to make by itself)• M. Lu, A. Stein (PhD 2002; now BNL), S. Spector (PhD 1998; now
Lincoln Lab), C. Jacobsen (Stony Brook)• D. Tennant (Lucent/New Jersey Nanotech Consortium)• JEOL JBX-9300FS: 1 nA into 4 nm spot, 1.2 nm over 500 µm, 100 keV

A. Stein and JBX-9300FS
29

Fresnel Zone Plates in nickel

Diameter: 160 μm or about 3x
diameter of one hair (A. Stein)

Finest linewidth: 0.030 μm or 30 nm,
or about 150 atoms across (M. Lu)

30

Fabrication of zone plates

15.1 nm half-pitch multilayer
slice imaged with a 15 nm
outermost zone width zone
plate. Chao et al., Nature 435,
1210 (2005). But efficiency
only ~3%. Other results: 9.2%
at 20 nm: Peuker, Appl. Phys.
Lett. 78, 2208 (2001)

Gold zone plates, Xradia, Inc.: 70 nm outermost
zones, 1 µm thick

Test structures
showing fabrication
challenges (M. Lu)

31

Zone plate fabrication examples

PSI, 20 nm wide, 170 nm tall Ir, 100 μm diameter:
Jefimovs et al., Phys. Rev. Lett. 99, 264801 (2007).

CXRO/LBL, 15 nm wide, 80 nm tall Au, 30 μm diameter:
Chao et al., Nature 435, 1210 (2005).

Stony Brook, 18 nm wide, 60 nm tall Ni, 80 μm diameter:
Spector et al., J. Vac. Sci. Tech. B 15, 2872 (1997).

Xradia, 24 nm wide, 300 nm tall Au, 133 μm diameter:
Feng et al., J. Vac. Sci. Tech. B 25, 2004 (2007).
32

Multilayer Laue lenses• Forget top-down circles, and go sideways! Start by depositing thinnest
zones first on a flat substrate, and work your way up to thicker zones. Cross
two 1D lenses for 2D focusing. Maser et al., SPIE 5539, 185 (2004)• For thick optics, you want to tilt to be on the Bragg condition anyway[Maser, PhD thesis; Maser and Schmahl, Opt. Comm. 89, 355 (1992)]

Maser et al., SPIE 5539, 185 (2004)

16 nm 1D focus: Kang et al.,Appl. Phys. Lett. 92, 21114 (2008)33

X-ray optics: best published resolution

Best resolution (nm)1000

Zone plate >1 keV
100

10

1
1970

Zone plate <1 keV
MLL (1D)

1980

1990

Year

2000

2010

2020
34

Zone plate microscopes
TXM• Incoherent illumination; works
well with a bending magnet,
with fast imaging• More pixels (e.g., 20482)• Moderate spectral resolution inmost cases - but new
instrument at BESSY, Berlin!

STXM• Coherent illumination; works bestwith an undulator• Less dose to sample (~10% efficient
ZP)• Better suited to conventional grating
monochromator [high E/(ΔE)]• Microprobes: fluorescence etc.

35

Scanning and full-field• General property of lenses:
preserve size•angle product(Liouville’s Theorem), so

Scanning• Microprobe/STXM: wantso that diffraction limit of optic
rather than geometrical imageof source dominates spot size
• Rayleigh resolution ofthus gives phase space of• Full-field: each pixel in object isdiffraction limit of optic, but
can have many pixels
simultaneously!

Full-field
36

Controlling spatial coherence• Coherent flux: phasespace area of λ in eachdimension. Coherent
flux is B•λ2. Green,
BNL-50522 (1976);
Kondratenko andSkrinsky, Opt. Spectr. 42,
189 (1977).
• Spatial filter: pinhole atthe focus of a lens.
Passes only the spatiallycoherent fraction of anincident beam.

Diagram, photofrom Newport
catalog37

Effects of spatial incoherence on STXM
How close must p=hθ be to λ?

Effect on modulation transfer function MTF(50% central stop)

Effect on point spread function PSF(50% central stop)

Jacobsen et al., Ultramicroscopy 47, 55 (1992); Winn et al., J. Synch. Rad. 7, 395 (2000).
38

2D imaging with Stony Brook STXMs
Scanning zone plate microscopes
U15 and X17t (1983-1987): Kirz
(Stony Brook) and Rarback(NSLS).
X1A (since 1989): Kirz andJacobsen (Stony Brook)
2D imaging is moderately
useful but...
• Cannot track fluroescentlylabeled proteins in living cells• Resolution is inferior tocryoEM, though do not needto section• Best utility may lie beyond
simple 2D imaging

Human sperm(unfixed): Wirick,
Fleckenstein,
Sheynkin et al.

NIL 8 fibroblast (wet, fixed):
Oehler et al.

Fibroblast (frozen hydrated): Maser et al., J. Micros. 197, 68 (2000)

39

Absorption edges
Lambert-Beer law: linear absorption
coefficient µThis coefficient makes a jump at specificelemental absorption edges!
This example: 0.1 µm protein, silica

40

X-ray microscopy of colloids• U. Neuhäusler (Stony Brook/Göttingen), S. Abend (Kiel), G. Lagaly (Kiel),
C. Jacobsen (Stony Brook), Colloid and Polymer Science 277, 719 (1999)• Emulsion: water, oil droplets, clay, and layered double hydroxides (LDH)• “Caged” part of oil droplet remains fixed; “uncaged” part can disperse

346 eV: calcium
weakly absorbing.
Clays and LDHs
absorb equally352.3 eV: calcium
strongly absorbing.
Calcium-rich LDHs
are highlighted.

290 eV: carbon
strongly absorbing

284 eV: carbon(oil drop) weakly
absorbing41

Near-edge absorption fine structure (NEXAFS) or
X-ray absorption near-edge structure (XANES)• Fine-tuning of the x-ray energy near an atom’s edge gives sensitivity to
the chemical bonding state of atoms of that type
• First exploitation for chemical state transmission imaging: Ade, Zhang
et al., Science 258, 972 (1992) – Stony Brook/X1A

Compared with UV “tickling” of molecular orbitals, corelevel electrons come from a single, well-defined state!

42

Near-edge spectroscopy: ELNES and XANESELNES (electron Energy Loss)• Plural inelastic scattering• Many elements at once - but plasmon
modes are always excited (damage)• ΔE was ~0.6 eV, but now <0.1 eV insome cases

XANES (X-ray Absorption)• No plural scattering• One element at a time slow but less damage• ΔE of 0.05-0.1 eV iscommonElectrons ~1000x
more damaging:•Isaacson andUtlaut, Optik 50,
213 (1978)•Rightor et al., J.
Phys. Chem. B
101, 1950 (1997).

43

C-XANES spectral bands

44

C-XANES of amino acids• K. Kaznacheyev et al., J. Phys. Chem. A 106, 3153 (2002)• Experiment: K. Kaznacheyev et al., Stony Brook (now CLS)
• Theory: O. Plashkevych, H. Ågren et al., KTH Stockholm; A.
Hitchcock, McMaster

Polymers: see e.g., Dhez, Ade, and Urquhart, JESRP 128, 85 (2003)

45

Spectromicroscopy from image sequences

Lu in hematite (T. Schäfer)Aligned spectral image sequences:
Jacobsen et al., J. Microscopy 197,
173 (2000)

104-105 spectra! Too many to analyze “by hand.”Complex mixtures etc.; life is not made up of
uniform thin films.
How to deal with the complexity?
1. PCA for noise reduction, orthogonalization.
2. Cluster analysis to find patterns.
3. Non-negative matrix factorization for final
analysis.
46

We measure the optical density D=μt from I=I0exp[-μt], which gives
us a matrix over n=1..N energies and p=1..P pixels of the data:

What we haveSpectromicroscopy analysis

We would also have a matrix of their thicknesses

What we wish we had

We wish we could interpret this in terms of a set of s=1..S
components. We would then have a matrix of their spectra47

Doing the math• We measure the data but want to interpret it as spectra times thicknesses:or• If we know all S components and their spectra
thickness maps:, we can obtainof all spectra can be inverted using singular matrix• Matrix
decomposition (SVD). See e.g., Zhang et al., J. Struct. Biol. 116, 335(1996); Koprinarov et al., J. Phys. Chem. B 106, 5358 (2002).

48

What if we don’t know the components ortheir spectra?
• “Natural” specimens, such as in biology orenvironmental science• Reactive phases, rather than simple mixing• Complexity! 300x300 pixel image contains 105
spectra!
• Let’s reduce the complexity using principal
component analysis or PCA
PCA in spectromicroscopy: King et al., J. Vac. Sci. Tech. A 7, 3301 (1989); A.
Osanna & C. Jacobsen, XRM99 proceedings; Bonnet et al., Ultramicroscopy 77,
97 (1999).

49

Principal component analysis (PCA)
Can we find new
orthogonal
coordinates that
better represent
the data?
Scatterplot: pixels plotted basedon signal at two different photon
energies50

Principal component analysis (PCA)
Can we find new
orthogonal
coordinates that
better represent
the data?
1. Find the axis along which there is
the greatest variance51

Principal component analysis (PCA)
Can we find new
orthogonal
coordinates that
better represent
the data?
1. Find the axis along which there is
the greatest variance
2. Find an orthogonal axis of next
greatest variance52

Principal component analysis (PCA)
Can we find new
orthogonal
coordinates that
better represent
the data?
1. Find the axis along which there is
the greatest variance
2. Find an orthogonal axis of next
greatest variance
3. Gives a new coordinate system

53

Principal component analysis (PCA)
Can we find new
orthogonal
coordinates that
better represent
the data?
1. Find the axis along which there is
the greatest variance
2. Find an orthogonal axis of next
greatest variance
3. Gives a new coordinate system
4. Rotate onto new, orthogonal
coordinate system

54

PCA and factor compression
For an abstract component: contribution is singular value times
singular spectrum

Find reduced number ofsignificant components

55

PCA and factor compression
For an abstract component: contribution is singular value times
singular spectrum

Find reduced number ofsignificant components

56

PCA and factor compression
For an abstract component: contribution is singular value times
singular spectrum

Find reduced number ofsignificant components

57

PCA and factor compression
For an abstract component: contribution is singular value times
singular spectrum

Find reduced number ofsignificant components

58Eigenimages
1

3

4

6

59

PCA gets us something…
• Principal component analysis lets you reduce andorthogonalize the data set!
• Reduction: filter out spectral variations that are poorly
correlated throughout the dataset (smells like photon
noise!). We went from N=140 energies to=4components• Orthogonality might have nice consequences
But we have a problem…
• Eigenspectra > 1 are abstract. They have negative
optical densities, so they are not readily interpretable.
• “Rotating” eigenspectra to make them positive is notalways sufficient; can have more distinct mixtures thaneigenspectra.
60

A well-known problem
We chose to follow an approach which is wellknown in the literature:“You can’t always get what you want; but if you
try sometimes, well you just might find you getwhat you need”
M. Jagger, K. Richards et al., Let it Bleed 1, 1 (1969)

61

Cluster analysis:
Euclidian distance learning algorithm• Kohonen, Proc. IEEE 78,
1464 (1990)• Pixels are scatteredaccording to weighting ofeach component

Start from PCA

62

Cluster analysis:
Euclidian distance learning algorithm• Kohonen, Proc. IEEE 78,
1464 (1990)• Pixels are scatteredaccording to weighting ofeach component• Put down cluster centers at
random positions.

63Cluster analysis:
Euclidian distance learning algorithm• Kohonen, Proc. IEEE 78,
1464 (1990)• Pixels are scatteredaccording to weighting ofeach component• Put down cluster centers at
random positions.
• Iterate through all pixels,
several times:– Calculate distances fromone pixel to all cluster
centers.

64

Cluster analysis:
Euclidian distance learning algorithm• Kohonen, Proc. IEEE 78,
1464 (1990)• Pixels are scatteredaccording to weighting ofeach component• Put down cluster centers at
random positions.
• Iterate through all pixels,
several times:– Calculate distances fromone pixel to all cluster
centers.
– Pick shortest distance.
– Move cluster center partway
to pixel.

65

Cluster analysis:
Euclidian distance learning algorithm• Kohonen, Proc. IEEE 78,
1464 (1990)• Pixels are scatteredaccording to weighting ofeach component• Put down cluster centers at
random positions.
• Iterate through all pixels,
several times:– Calculate distances fromone pixel to all cluster
centers.
– Pick shortest distance.
– Move cluster center partway
to pixel.

• Cluster pixels with theirnearest cluster center66

Cluster analysis: Lu in hæmatite•Lu as a stand-in for Am innuclear wastes; hæmatite can bea groundwater colloid that
increases transport rate 1000x•Oxygen XANES shows two
different incorporation phases of
Lu in hæmatite (clusters 2 and 5)•Lerotic, Jacobsen, Schäfer, Vogt,
Ultramic. 100, 35 (2004)

cluster 3

cluster 1cluster 2cluster 4cluster 5

Red spots: negative values, because cluster
spectra are not guaranteed to “span the set”

67

Cluster analysis: simplifying complexity• Ethanol from lignocellulose materials is promising: large fraction of total biomass,easier cultivation.
• But there are great challenges in economically separating cellulose from lignin!
• Soft x-ray spectromicroscopy can map cellulose and lignin so that one can see theeffects of various enzymes.
Lignin and cellulose
in 400 million year
old chert: Boyce etal., Proc. Nat. Acad.
Sci. 101, 17555(2004), withsubsequent patternrecognition analysis
by Lerotic et al.,Ultramicroscopy
100, 35 (2004).
68

Cluster analysis: human sperm
Biochemical organization of sperm revealed directly from data: enzymerich region, DNA+histones, mitochondria and flagellar motor, lipid
H. Fleckenstein, M. Lerotic, Y.
Sheynkin et al., Stony Brook.
Human sperm, air-dried.

Red spots: negative values, because cluster
spectra are not guaranteed to “span the set”

69Spectromicroscopy can be damaging!

• Study: polyacrilimide-induced flocculation of clays(irrigation of loamy soils)• Mass loss is visible after acquiring spectra with focused
beam (wet sample at room temperature)• U. Neuhaeusler, PhD Thesis (Stony Brook/Göttingen)70Calculating dose
• SI units for ionizing radiation: 1 Gray=1 J/kg=100 rad• Lambert-Beer law with inverse absorption length µ(=1.3mm for protein at 8.98 keV):• Energy per thickness:• Energy per mass:

71

Dose numbers• G factor: number of bonds broken per 100 eV. G~5for many organic molecules (room temp.)• Break 1 bond per atom:• Representative dose in crystallography:• X-ray microscopy: doses of 106-108 Gray arecommon, depending on resolution72

X-ray absorption: the aftermath

Primary electrons
undergo multiple
inelastic collisions
Continuous slowing
down approximation(CSDA): range overwhich majority ofenergy is deposited73

Radiation damage on(initially) living cells• X-rays are ionizing
radiation. The dose perhigh resolution image isabout 100,000 times
what is required to kill a
person• Makes it hard to view
living cells!

Experiment by V.
Oehler, J. Fu, S.
Williams, and C.
Jacobsen, Stony Brook
using specimen holder
developed by Jerry
Pine and John Gilbert,
CalTech74

Wet, fixed samples: one image is OK• Chromosomes are among
the most sensitive
specimens.
• V. faba chromosomes
fixed in 2%
glutaraldehyde. S.
Williams et al., J.
Microscopy 170, 155(1993)• Repeated imaging of one
chromosome shows massloss, shrinkage

75

Frozen hydrated specimens
Grids with live cells are• Taken from culture medium andblotted• Plunged into liquid ethane(cooled by liquid nitrogen)
Maser et al., J. Micros. 197,
68 (2000)

76

100 nm

1 μm

500 nm• Human blood
platelets• 1 MeV transmission
electron microscope(JEOL-1000)• O’Toole, Wray,
Kremer, andMcIntosh, J. Struct.
Bio. 110, 55 (1993)

2% glutaraldehyde fix
1% OsO4 postfix
critical-point dry

1 μm

Frozen hydrated

100 nm77

Electrons: frozen hydrated
Polymer spheres inamorphous ice viewed
with low dose rate at
100 keV
Smaller spheres:
PMMA
Larger spheres: PS
Doses are in Gray
From Y. Talmon, in
Steinrecht and Zierold,
Cryotechniques in
Biological Electron
Microscopy (Springer, “Bubbling” dose in cryo electron microscopy:
2 or about 3x107 Gray. Bubbles:
~1000
e-/nm
1987)
hydrogen gas [Leapman, Ultramic. 59, 71(1995); Sun et al., J. Mic. 177, 18 (1995)]
78

Radiation damage resistance incryo
Left: frozen
hydrated image
after exposing
several regions
to ~1010 Gray

Maser et al., J.
Microscopy 197,
Maser
et al., J. Micros.
68 (2000)
197, 68 (2000)

Right: after
warmup in
microscope(eventually
freeze-dried):holes indicate
irradiatedregions!
79

Hints of damage?

Maser et al., J. Micros. 197, 68 (2000)
Note: we have never seen “bubbling” with soft x-rays. Lower relative dose inwater, plus lower dose rate to allow for gas diffusion?

80

X-ray irradiation: poly(methyl methacrylate) (PMMA)• PMMA: poly methyl methacrylate (plexiglass!) which isespecially radiation sensitive – it’s used as a resist for electron
beam lithography• X. Zhang et al., J. Vac. Sci. Tech. B 13, 1477 (1995)• Fine step size, high flux image for dose
• Slightly defocused beam for low dose
image off XANES peaks• At end, AFM for thickness• Defocused beam for spectrum• Gaussian fit to measure peak strengths
at XANES resonances81

Mass loss: small pieces fly away
X. Zhang, C. Jacobsen, S. Lindaas, S. Williams, J. Vac. Sci. Tech. B 13, 1477
(1995)•Chain scission: C=0 peak decrease•Crosslinking: C=C peak increase• Mass loss: optical density, AFM verification

Mass spectroscopy of fragments: see Tinone et al., J. Vac.
Sci. Tech. A 13, 1885 (1995)

82

PMMA at room, LN2 temperature• Beetz and Jacobsen, J. Synchrotron Radiation 10, 280 (2003)• Repeated sequence: dose (small step size, long dwell time), spectrum(defocused beam)• Images: dose region (small square) at end of sequenceRoomtemperature:mass loss
immediately
visibleLN2 temperature: nomass loss
immediately visible

After warm-up: massloss becomes visible

83

PMMA at LN2, room temperature:
XANES spectra• Peak at 531.4 eV: C=0 bond
• Plateau at 540 eV: total mass (plus some emphasis on oxygen σ* bonds)• Beetz and Jacobsen, J. Synchrotron Radiation 10, 280 (2003)

84

Results from fitting spectra
LN2 temp: protection against mass loss, but not against breaking bonds(at least C=0 bond in dry PMMA)

Plateau at
540 eV:
total mass
Peak at531.4 eV:
C=0 bond

Beetz and Jacobsen, J. Synchrotron Radiation 10, 280 (2003)

85

Tomography: projections in a microscope
Projections of a frozen hydrated 3T3 fibroblast. Y.
Wang et al., J. Microscopy 197, 80 (2000)

Text

Maser et al., J. Micros. 197, 68 (2000)
86Fibroblast reconstruction: Z slices
Y. Wang et al., J.
Microscopy 197, 80(2000)

87

3D imaging with lenses
1000
DO

F=1
m

m

Transverse resolution (nm)∆rNλTransverse:
=
∆t ⇒
4θ
2
∆rN
λ
Longitudinal: ∆! ⇒= 4∆rN
2
θ
λ

100

100

10 +

+m

m

1 +m

10
0.1

+m

10 n
m

1
0.2

1

10

20

Energy (keV)

20 nm resolution at 520 eV: depth of field ~1 µm

Through-focus deconvolution with lenses:• Confocal: fully incoherent (fluorescence)• EM: phase only, coherent• TXM: partially coherent, equal absorption andphase contrast, need for experimental CTF
88

Soft x-ray tomography of algae shock-frozen in liquid ethane:
Slices through a tomographic reconstruction

VacuoleNuclearmembrane
Nucleolus
Flagellar
roots andneuromotor
Cell wall
Flagella

Weiss, Schneider et al., Ultramicroscopy 84, 185 (2000).
See also Larabell and Le Gros, Molecular Biology of the Cell 115, 957 (2004)89

National Center for X-ray
Tomography

DoE/BER and NIH funded center at Advanced Light Source in Berkeley;sophisticated TXM for cryo tomography; Larabell, LeGros et al.
Parkinson et al., J. Struct. Bio. 162, 380(2008): fission yeast
Schizosaccharomyces pombe.
Nuclei, mitochondria, vacuoles…

6.7 μm long13

Radiation damage sets the ultimate resolution limit• For many specimens, radiation damage sets the ultimate limit onachievable resolution.
• Lenses phase the signal, but lose the signal. Example: 20 nm zone platewith 10% efficiency, 50% window transmission, 20% modulationtransfer function (MTF) for 15 nm half-period:
net transfer of 1% for high spatial frequencies• Can we avoid this ~100x signal loss, and also go beyond numericalaperture limit of available optics?

91

Phase matters
Image→ Fourier transform→ zero magnitude or phase→
inverse Fourier transform

Malcolm Howells
at La Clusaz

Image using only
Fourier magnitudes

Image using only
Fourier phases

92

1 unit cell93

2x2 unit cells

See e.g., D. Sayre, “Some implications of a theorem due toShannon,” Acta Cryst. 5, 843 (1952)

94

3x3 unit cells

See e.g., D. Sayre, “Some implications of a theorem due toShannon,” Acta Cryst. 5, 843 (1952)95

4x4 unit cells

See e.g., D. Sayre, “Some implications of a theorem due toShannon,” Acta Cryst. 5, 843 (1952)

96

5x5 unit cells

See e.g., D. Sayre, “Some implications of a theorem due toShannon,” Acta Cryst. 5, 843 (1952)

97

1 unit cellSee e.g., D. Sayre, “Some implications of a theorem due toShannon,” Acta Cryst. 5, 843 (1952)

98

Who else might be interested?

Laser beam

Fienup, Opt. Lett. 3, 27 (1978); Appl.
Opt. 21, 2758 (1978); J. Opt. Soc.
Am. A 4, 118 (1987); and otherpapers. Introduces the use of a “finite
support”.

Detectors

Turbulent atmospheredegrades phase

Detectors

Cartoon based on presentations by Fienup from ERIM (Environmental
Research Institute of Michigan). Fienup is now at U. Rochester99

Imaging without lenses• Avoid losses of lens efficiency and transfer function• Must phase the diffraction intensities
Real space: finite support(or other constraints)←FT→

Fourier space: magnitudes
known, but phases arenotPhasing algorithms: Feinup, Opt. Lett. 3, 27(1978); Elser, JOSA A 20, 40 (2003); andothers. First x-ray demonstration: Miao et al.,100
Nature 400, 342 (1999).

Iterative phasing: simple example• High harmonic generation of XUV radiation fromfemtosecond lasers, illuminating two pinholes.
– R. Bartels, A. Paul, H. Green, H.C. Kapteyn, M.M. Murnane, S.
Backus, I.P. Christov, Y. Liu, D. Attwood, C. Jacobsen, Science 297,376 (2002)

Data

Support constraint(very loose)

Reconstruction error
101

The reconstruction
Real space

Real space

Magnitude

Phase

Far field

Far field

Magnitude

Phase

102

Fluctuating solutions• Ideally, there would be a single point of best
agreement between various constraints.
• Noise and incomplete constraints only
provide a neighborhood of acceptable
solutions.
• Choosing one iterate from one random
starting phase as “the” solution is
unwarranted!

Two individual iterates
103

Iterate averaging• If the solution fluctuates, let’s take many samples and averagethem!
• Non-reproducible phases get washed out; reproducible
phases get reinforced• Thibault, Elser, Jacobsen, Shapiro, and Sayre, Acta
Crystallographica A 62, 248 (2006)• Other approaches: compare results from several different
starting random phases (e.g., Miao, Robinson)

Example: save an iterate every
50 steps, and then average 100of them104Different starting random phases

Two separate runs of algorithm with different random starting phases. In bothcases, 125 iterates spaced 40 iterations apart were averaged (E. Lima).

105

Gold-labeled yeast

1.8 nm gold, silver-enhanced, dehydrated: J. Nelson et al., Stony Brook/ALS

106

Crystallinity, and strain within nanocrystals
Domain boundaries inpolycrystalline materials: Liu et al.,Ultramicroscopy 103, 199 (2005).

Coherent diffraction
about a Bragg peak
reveals the shape of andstrain within ananocrystalline domain
at 40 nm resolution.
Pfeiffer et al., Nature 442,
63 (2006).

Ptychography

Rodenburg et al., Phys. Rev. Lett. 98, 034801 (2007)14