Imaging without lenses

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.
2
Experiment

• Layout of the diffraction chamber used for this
  experiment at BL 9.0.1 at Advanced Light Source,
  LBL

Sample
Sample 50 nm gold balls randomly distributed on
SiN window (100nm thickness and 2?2
?m2) ?2.1nm (588 eV) Detector 1024 ? 1024
Princeton back-illuminated CCD
Au 50nm
SiN 100nm
Si substrate
Side view of sample
3
Phase retrieval with blind support
b0.9 feedback s2 gaussian width
(pixels) t0.2 threshold
known, j unknown s
support estimated from Patterson function
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.
Missing low frequency components are treated as
free parameters.
4
image reconstruction with shrink-wrapping support
Measured x-ray diffraction pattern
1
20
100
1000
Object support constraint
Object
SEM x-ray
Iterative reconstruction techniques require a
known shape (support) of the object. Previous
work has obtained that by x-ray 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. This will enable single-molecule
diffraction and high-resolution imaging of
dynamic systems.
300 nm
5
Clusters of gold spheres
3D single cluster
5-7 clusters
8 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 two-clusters objects
6
Gray-scale images and complex objects
bugs with different histograms
Rec. image
Rec. Supp.
Orig. image
Histogram
Without beamstop
With beamstop
Number of electrons for a given density
The greyscale image demonstrates that the
algorithm does not depend on any atomicity
constraint provided by the gold balls.
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.
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
Complex probe
Amplitude after probe
Comparison of the reconstructed, support and
original object amplitudes the real part is
shown, blue is negative, red/yellow is positive.
(each ball is multiplied by a constant phase)
7
Shrink-wrap vs HIO
Original object
Even for low noise, HIO can achieve a reasonable
reconstruction only if the support mask is set to
the boundary known at essentially the same
resolution to which we are reconstructing the
object.
s indicates the size in pixels of the gaussian
used to obtain the low resolution version
Supports obtained by thresholding a low
resolution version of the original object.
Supports
(iter) 0 50 75 125 250 500 2000
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 the support will be influenced by the noise,
and the algorithm will be unable to converge to
the correct boundary.
1, s0.5
2, s5
Notice that for complex objects, both the
R-factor (error in reciprocal space) and the HIO
errors do not correspond to the real error
(1-Xcorr)
3, s25
4,Patterson
adjusting support
increasing noise level (log2 scale, a.u.)
8
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 window with hollow pyramid
Silicon nitride film
10 ?m
Compact, precision rotation stage
experiment
simulation
We collected a complete data set with over 140
views with 1 angular spacing. Analysis is under
way
Sample, prealigned on rod
Precision v-groove
9
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. arXivphysics/0306174 3
H. He et al. Phys. Rev. B, 174114 (2003) 4
H. He, et al. Acta Cryst. A59, 143 (2003)