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Imaging without lenses
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
S. Marchesini, H.N. Chapman, S.P. Hau-Riege, A. Noy
U. Weierstall, J.C.H. SpenceH. He, M. R. Howells,
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.
Sample: 50 nm gold balls randomly distributed on SiN window (~100nm thickness and 22 m2)
=2.1nm (588 eV)Detector: 1024 1024 Princeton back-illuminated CCD
Experiment
Layout of the diffraction chamber used for this experiment at BL 9.0.1 at Advanced Light Source, LBL
Zone plate monchromator Energy dispersion
slit . 25 micronsField limiting aperture. 5 microns
Sample Gold balls on SiN.
80 mm. 25 mm 105 mm
Undulator
Mirror 2and PT 2
Long WD ExternalOptical Microsocope
Beam stops
RemovablePhotodiode 1, Absorption filter.
Mirror 1Phosphor
Sample
SiN 100nm
Si substrate
Au 50nm
Side view of sample
Phase retrieval with blind support
=0.9 feedback
=2 gaussian width (pixels)
t=0.2 threshold
known, unknown
s support estimated from Patterson function
)()( kk IF
))FFT(I()p( kr
support
random
Amplitude constraint
Hybrid Input Output new support
Every 20 iterations
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.
image reconstruction with shrink-wrapping support
Measured x-ray diffraction pattern
1 20 100 1000
300 nm
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.
SEM x-ray
Objectsupport
constraintObject
Clusters of gold spheres
Single clusters
2-4 clusters
5-7 clusters 8 clusters
3D single cluster
These simulations show that the algorithm works not only for two-clusters objects
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.
Gray-scale images and complex objects
Rec. image
Rec. Supp.
Orig. image
With beamstop
Without beamstop
Histogram
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.
Original object Complex
probeAmplitude after probe
Comparison of the reconstructed, support and original object amplitudes the real part is shown, blue is negative, red/yellow is positive.
The use of focused illumination will allow users to select either one or two-part objects (which may be complex) from a field.
(each ball is multiplied by a constant phase)
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.
bugs with different histograms
adjusting supportSupport 1Support 2Support 3Support 4
0 2 4 6 8 10 12 14 160
0.5
1
HiO
err
or
0 2 4 6 8 10 12 14 160
0.5
1R
fact
0 2 4 6 8 10 12 14 160
0.5
1
1-xc
orr
increasing noise level (log2 scale, a.u.)
Shrink-wrap vs HIO
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.
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.
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 ofthe support will be influenced by the noise, and the algorithm will be unable to converge to the correct boundary.
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 ofthe support will be influenced by the noise, and the algorithm will be unable to converge to the correct boundary.
1, σ=0.5 2, σ=5
3, σ=25 4,Patterson
Original object
Supports obtained by thresholding a low resolution version of the original object.
Supports obtained by thresholding a low resolution version of the original object.
adjusting support
(iter)0
50
75
125
250
500
2000
Supports
σ indicates the size in pixels of the gaussian used to obtain the low resolution version
σ indicates the size in pixels of the gaussian used to obtain the low resolution version
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)
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)
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
1 m
Silicon nitride pyramid decorated with Au spheres
Cross-section
Silicon
Silicon nitride film
Silicon nitride window with hollow pyramid
10 m
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
[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)
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.