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.