X-ray Microscopy
at Stony Brook (6)

1. Why Soft X-ray Microscopy
2. The Scanning Transmission X-ray Microscope
3. X-ray Lenses: Fresnel Zone Plates
4. Example: Biological Applications
5. Example: Environmental Sciences and Cluster Analysis
6. Soft X-ray Diffration and Holography
7. Acknowledgements

Soft X-ray Diffraction

Soft X-ray diffraction is suitable to provide 3D images of cells and other non-crystalline objects at high resolution. The feasibility of the technique has been demonstrated by our group. We have developed an experimental apparatus that will allow for automated data collection (necessary for 3D data sets) and handles cryogenic specimens to minimize radiation damage. The experiments are conducted at beamline 9.0.1 at ALS (Berkeley).

The concept of lensless imaging was first conceived of by David Sayre in 1980, the idea is to record the far field diffraction pattern rather than use a lens to focus the diffracted light to an image. The far field diffraction patteren is then inverted to an image via a computational alogrithm,utilising the oversampling of the object to uniquely recover the phase. The first demonstration of this was acheived in our group in 1999 by Miao et al. with the reconstruction of a test pattern.

Experimental setup for diffraction microscopy.

There are several advantages to not using a lens to form the image, there are no depth of focus problems or spherical aberations to worry about, but most importantly there is no limitations of resolution introduced by the lens. In the case of X-rays the resolution of the microscope is limited to the outer most zone width of the Zone plate, which is currently limited to about 60nm resolution, although zone plates of higher resolution have been fabricated they are too inefficent at this point for imaging porposes. With lensless imaging the resolution is only limited by what the detector can collect and the radiation damage to the specimen.

Experimental chamber developed for diffraction
experiments at the ALS.

Assembled diffraction pattern of a freeze dried yeast cell. The central part, where the direct beam is incident on the detector, is blocked out by a beamstop.

Reconstructed 2D image of freeze dried yeast cell to 30nm resolution, from above diffraction pattern. The nucleus, vacules and cell membrane can all be clearly seen in this reconstruction

We also collaborate with Henry Chapmans group from Livermore, who has used our chamber for the reconstruction of a 3D object, a silicon nitride pyramid lined with 50nm gold spheres. Computer algorithms that are used to phase diffraction patterns, have been jointly developed with the Livermore group as well as Veit Elser and Pierre Thibault from Cornell. Computer simulations of the experiment help us understand the experiments and guide us in improving the next experiment.

Images a, b, and c are projection imagies form the reconstruction of the pyramid of gold spheres. Diffration Pattern a is one of the 2D diffraction patterns in the 3D reconstruction.

The reconstruction alogrithms used for reconstruction are based upon the ideas first introduced by Gerchberg & Saxton in 1971. These ideas were later refined by Fienup in the 70's and 80's, and then extend by Elser in 2003. We primarily use Elser's Difference map approach for our reconstructions. These Methods work by cycling between real and reciprocal space modifing the image in real space and the magnitudes in reciprocal space, until there is a convergence of the alogrithm to a unique image.

Outline for reconstruction algorithm.

Key Publications

1. D. Sayre, "Prospects for long-wavelength X-ray microscopy and diffraction", in M. Schlenker, M. Fink, J.P. Goedgebuer, C. Malgrange, J.Ch. Viénot and R.H. Wade (eds.), Imaging Processes and Coherence in Physics 112, Springer-Verlag, Lecture Notes in Physics, 229-235, (1980). [ PDF]

2. J. Miao, P. Charalambous, J. Kirz and D. Sayre, "An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens", Nature 400, 342-344, (1999). [ PDF]

3. V. Elser, "Random projections and the optimization of an algorithm for phase retrieval", Journal of Physics A: Mathematical and General 36, 2995-3007, (2003). [ doi:10.1088/0305-4470/36/12/309] [ PDF]

4. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy", Proceedings of the National Academy of Science 102 (43), 15343-15346, (2005). [ PDF]

5. P. Thibault, V. Elser, C. Jacobsen, D. Shapiro and D. Sayre, "Reconstruction of a yeast cell from x-ray diffraction data", Acta Crystallographica A 62, 248-261, (2006). [ PDF]

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