Transcript Slide 1

Imaging without lenses
S. Marchesini, H.N. Chapman, S.P. Hau-Riege, A. Noy
H. He, M. R. Howells,
U. Weierstall, J.C.H. Spence
Current x-ray diffractive imaging methods require prior knowledge of the
shape of the object, usually provided by a low-resolution “secondary”
image, which also provides the low spatial-frequencies unavoidably lost in
experiments. Diffractive imaging has thus previously been used to increase
the resolution of images obtained by other means. We demonstrate
experimentally here a new inversion method, which reconstructs the image
of the object without the need for prior knowledge or “secondary images”.
This new form of microscopy allows three-dimensional aberration-free
imaging of dynamical systems which cannot provide a secondary low
resolution image. UCRL-JC-153571
This work was performed under the auspices of the U.S. Department of Energy by the
Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48 and the
Director, Office of Energy Research, Office of Basics Energy Sciences, Materials Sciences
Division of the U. S. Department of Energy, under Contract No. DE-AC03-76SF00098. SM
acknowledges funding from the National Science Foundation. The Center for
Biophotonics, an NSF Science and Technology Center, is managed by the University of
California, Davis, under Cooperative Agreement No. PHY0120999.
Experiment
Layout of the diffraction chamber used for this experiment
at BL 9.0.1 at Advanced Light Source, LBL
Long WD External
Optical Microsocope
Phosphor
Mirror 1
Removable
Photodiode 1,
Absorption filter.
Undulator
Sample Gold
balls on SiN.
Mirror 2
and PT 2
Sample
Sample: 50 nm gold balls
randomly distributed on SiN
window (~100nm thickness and
22 m2)
Au 50nm SiN 100nm
Beam
stops
80 mm.
Zone plate
monchromator
25 mm
Energy dispersion Field limiting aperture.
slit . 25 microns
5 microns
Si substrate Side view of sample
105 mm
=2.1nm (588 eV)
Detector: 1024  1024 Princeton
back-illuminated CCD
Phase retrieval with blind support
F (k )  I (k ) known, j unknown
b=0.9 feedback
s=2 gaussian width (pixels)
s support estimated from Patterson
function
p(r)  FFT (I(k ))
j  random
support
Amplitude
constraint
Missing low frequency
components are treated
as free parameters.
t=0.2 threshold
Every 20 iterations
Hybrid Input Output
Every 20 iterations we
convolve the reconstructed
image (the absolute value
of
the
reconstructed
wavefield) with a Gaussian
to find the new support
mask. The mask is then
obtained by applying a
threshold at 20% of its
maximum.
new support
image reconstruction with shrink-wrapping support
Measured x-ray
diffraction pattern
SEM
1
x-ray
20
100
Object
support
constraint
Object
1000
Iterative reconstruction techniques require a known shape
(support) of the object. Previous work has obtained that by xray microscopy.
We reconstruct the support and the object simultaneously. No
prior knowledge is needed. The reconstruction gives a better
estimate of the support. The better support gives a better
reconstruction.
300 nm
This will enable single-molecule diffraction and high-resolution
imaging of dynamic systems.
Clusters of gold spheres
3D single cluster
5-7 clusters
This particular 3D cluster was
chosen to have a small number of
balls for visualization purposes the algorithm also works with a
much larger number of balls.
Single clusters
2-4 clusters
These simulations show that the
algorithm works not only for twoclusters objects
8 clusters
Gray-scale images and complex objects
Rec.
Rec.
Orig.
image Supp. image
Histogram
bugs with different histograms
Without
beamstop
With
beamstop
The greyscale image demonstrates
that the algorithm does not depend
on any “atomicity” constraint
provided by the gold balls.
Number of
electrons for a
given density
The use of focused illumination will allow users
to select either one or two-part objects (which
may be complex) from a field.
Original
object
(each ball is multiplied by
a constant phase)
Complex
probe
Amplitude
after probe
The complex object is of particular interest since it is well
known that the reconstruction of complex objects is much more
difficult than real objects, but is possible using either disjoint,
precisely known or specially shaped supports.
Comparison of the reconstructed, support and
original object amplitudes the real part is
shown, blue is negative, red/yellow is positive.
Shrink-wrap vs HIO
1
(iter)
0
50
75
2, σ=5
2
4
6
8
10
12
14
1
Supports
1, σ=0.5
0.5
0 0
σ indicates the size in
pixels of the gaussian
used to obtain the low
resolution version
HiO error
Supports
obtained
by
thresholding a low resolution
version of the original object.
1-xcorr
Original object
adjusting support
Support 1
Support 2
Support 3
Support 4
0.5
0
0
2
4
6
8
10
12
14
1
125
500
Rfact
250
Even for low noise, HIO can
achieve a reasonable
reconstruction only if the
16 support mask is set to the
boundary known at essentially
the same resolution to which
we are reconstructing the
object.
The noise level at which our
algorithm fails to reconstruct
occurs when the noise in real
space becomes larger than
the threshold used to update
the support. At this noise level
the estimate of
16 the support will be influenced
by the noise, and the
algorithm will be unable to
converge to the correct
boundary.
Notice that for complex
objects, both the R-factor
(error in reciprocal space) and
the HIO errors do not
correspond to the real error (1Xcorr)
0.5
2000
3, σ=25
4,Patterson
adjusting support
0 0
2
4
6
8
10
12
14
16
increasing noise level (log2 scale, a.u.)
We just performed 3D diffraction-imaging experiments
•Complete coverage of reciprocal space by sample rotation
•Use a true 3D object that can be well-characterized by independent means
•Will use diffraction data to test classification and alignment algorithms
Silicon nitride pyramid
decorated with Au
spheres
Silicon nitride window
with hollow pyramid
Silicon
Silicon
nitride film
10 m
1 m
Cross-section
Compact, precision rotation
stage
Sample,
prealigned
on rod
Precision
v-groove
experiment
simulation
We collected a
complete
data
set with over 140
views with 1°
angular spacing.
Analysis is under
way
Conclusions
The combination of an apparatus to measure large-angle diffraction patterns with our new method of
data analysis forms a new type of diffraction-limited, aberration-free tomographic microscopy. The
absence of inefficient optical elements makes more efficient use of damaging radiation, while the
reconstruction from a three-dimensional diffraction data set will avoid the current depth-of-field
limitation of zone-plate based tomography. The use of focused illumination will allow users to select
either one or two-part objects (which may be complex) from a field. The conditions of beam energy and
monochromatization used in these preliminary experiments are far from optimum for diffractive imaging
and can be greatly improved to reduce recording times by more than two orders of magnitude. We
expect this new microscopy to find many applications. Since dose scales inversely as the fourth power
of resolution, existing measurements of damage against resolution can be used to show that
statistically significant images of single cells should be obtainable by this method at 10 nm resolution in
the 0.5-10 m thickness range under cryomicroscopy conditions. Imaging by harder coherent X-rays of
inorganic nanostructures (such as mesoporous materials, aerosols and catalysts) at perhaps 2 nm
resolution can be expected. Atomic-resolution diffractive imaging by coherent electron nanodiffraction
has now been demonstrated. The imaging of dynamical systems, imaging with new radiations for
which no lenses exist, and single molecule imaging with X-ray free-electron laser pulses remain to
be explored.
[1] S. Marchesini, et al. arXiv:physics/0306174
[3] H. He et al. Phys. Rev. B, 174114 (2003)
[4] H. He, et al. Acta Cryst. A59, 143 (2003)