David Sayre

Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens

The contrast and penetrating power afforded by soft X-rays when they interact with matter makes this form of radiation ideal for studying micrometre-sized objects,. But although soft X-rays areuseful for probing detail too fine for visible light microscopy in specimens too thick for electron microscopy, the highest-resolution applications of X-ray imaging have been traditionally limited to crystalline samples. Here we demonstrate imaging (at ∼75 nm resolution) of a non-crystalline sample, consisting of an array of gold dots, by measuring the soft X-ray diffraction pattern from which an image can be reconstructed. The crystallographic phase problem — the usually unavoidable loss of phase information in the diffraction intensity — is overcome by oversampling the diffraction pattern, and the image is obtained using an iterative algorithm. Our X-ray microscopy technique requires no high-resolution X-ray optical elements or detectors. We believe that resolutions of 10–20 nm should be achievable; this would provide an imaging resolution about 100 times lower than that attainable with conventional X-ray crystallography, but our method is applicable to structures roughly 100 times larger. This latter feature may facilitate the imaging of small whole cells or large subcellular structures in cell biology.

Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2× in each dimension (i.e., oversampling by 4× for 2D and 8× for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop.

Biological imaging by soft x-ray diffraction microscopy

We have used the method of x-ray diffraction microscopy to image the complex-valued exit wave of an intact and unstained yeast cell. The images of the freeze-dried cell, obtained by using 750-eV x-rays from different angular orientations, portray several of the cells major internal components to 30-nm resolution. The good agreement among the independently recovered structures demonstrates the accuracy of the imaging technique. To obtain the best possible reconstructions, we have implemented procedures for handling noisy and incomplete diffraction data, and we propose a method for determining the reconstructed resolution. This work represents a previously uncharacterized application of x-ray diffraction microscopy to a specimen of this complexity and provides confidence in the feasibility of the ultimate goal of imaging biological specimens at 10-nm resolution in three dimensions.

Transmission microscopy of unmodified biological materials. Comparative radiation dosages with electrons and ultrasoft X-ray photons

The minimum radiation dosage in a specimen consistent with transmission microscopy at resolution d and specimen thickness t is calculated for model specimens resembling biological materials in their natural state. The calculations cover 10(4)-10(7) eV electrons and 1.3-90 A photons in a number of microscopy modes. The results indicate that over a considerable part of the (t,d)-plane transmission microscopy on such specimens can be carried out at lower dosage with photons than with electrons. Estimates of the maximum resolutions obtainable with electrons and photons, consistent with structural survival of the specimen, are obtained, as are data on optimal operating conditions for microscopy with the two particles.

An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images

We describe an approach to the high-resolution three-dimensional structural determination of macromolecules that utilizes ultrashort, intense x-ray pulses to record diffraction data in combination with direct phase retrieval by the oversampling technique. It is shown that a simulated molecular diffraction pattern at 2.5-Å resolution accumulated from multiple copies of single rubisco biomolecules, each generated by a femtosecond-level x-ray free electron laser pulse, can be successfully phased and transformed into an accurate electron density map comparable to that obtained by more conventional methods. The phase problem is solved by using an iterative algorithm with a random phase set as an initial input. The convergence speed of the algorithm is reasonably fast, typically around a few hundred iterations. This approach and phasing method do not require any ab initio information about the molecule, do not require an extended ordered lattice array, and can tolerate high noise and some missing intensity data at the center of the diffraction pattern. With the prospects of the x-ray free electron lasers, this approach could provide a major new opportunity for the high-resolution three-dimensional structure determination of single biomolecules.

Reconstruction of a yeast cell from X-ray diffraction data

Details are provided of the algorithm used for the reconstruction of yeast cell images in the recent demonstration of diffraction microscopy by Shapiro, Thibault, Beetz, Elser, Howells, Jacobsen, Kirz, Lima, Miao, Nieman & Sayre [Proc. Natl Acad. Sci. USA (2005), 102, 15343-15346]. Two refinements of the iterative constraint-based scheme are developed to address the current experimental realities of this imaging technique, which include missing central data and noise. A constrained power operator is defined whose eigenmodes allow the identification of a small number of degrees of freedom in the reconstruction that are negligibly constrained as a result of the missing data. To achieve reproducibility in the algorithms output, a special intervention is required for these modes. Weak incompatibility of the constraints caused by noise in both direct and Fourier space leads to residual phase fluctuations. This problem is addressed by supplementing the algorithm with an averaging method. The effect of averaging may be interpreted in terms of an effective modulation transfer function, as used in optics, to quantify the resolution. The reconstruction details are prefaced with simulations of wave propagation through a model yeast cell. These show that the yeast cell is a strong-phase-contrast object for the conditions in the experiment.

X-ray microscopy

The subject of X-ray microscopy (high-resolution X-ray imaging of general nonperiodic structures), an area in which much progress has been made in recent years, is reviewed. The main techniques are briefly described. Achievable performance levels, which for many years were highly speculative, can now be understood with fair accuracy in terms of basic X-ray and specimen properties, and techniques have progressed to the point where actual results are nearing those levels. In terms of specimen size and imaging resolution, X-ray microscopies lie between electron and light microscopy, and are thus suited to imaging extremely large and complex structures; in addition, they demand little or no specimen preparation, and can be used to observe local composition and chemical state as well as structure. Thus X-rays, which have played the leading role in imaging crystallizable materials, may also prove to be highly valuable in the imaging of very large non-crystalline structures. Throughout the treatment, attention is paid to the relationships connecting the subject with X-ray crystallography.

The oversampling phasing method

Sampling the diffraction pattern of a finite specimen more finely than the Nyquist frequency (the inverse of the size of the diffracting specimen) corresponds to surrounding the electron density of the specimen with a no-density region. When the no-density region is bigger than the electron-density region, sufficient information is recorded so that the phase information can be retrieved from the oversampled diffraction pattern, at least in principle. By employing an iterative algorithm, the phase information from the oversampled diffraction pattern of a micrometre-sized test specimen has been successfully retrieved. This method is believed to be able to open a door for high-resolution three-dimensional structure determination of complex and non-crystalline biological specimens, i.e. whole cells and sub-micrometre molecular clusters and micrometre-sized protein crystals. With the possible appearance in the future of X-ray free-electron lasers, it may become possible to image single molecules by recording diffraction patterns before radiation damage manifests itself.

Soft x-ray microscopy with coherent x rays (invited)

The Soft X‐ray Undulator beamline at the NSLS supports a soft x‐ray imaging program including scanning transmission microscopy, scanning photoemission microscopy, Gabor and Fourier transform holography, and large angle diffraction. Zone plates from an LBL Center for X‐ray Optics/IBM collaboration are used as optical elements. The current instrumentation of the beamline and the experimental stations is discussed, along with plans for the future at the NSLS and prospects for imaging programs at third generation sources.

Recent Results from the Stony Brook Scanning Microscope

We have recently completed our first run [21.1] with the Stony Brook scanning microscope at the National Synchrotron Light Source (NSLS), using a Fresnel zone plate fabricated at IBM as the principal focusing element. The brightness of this synchrotron radiation source coupled with our high — resolution optics have made a substantial improvement in resolution and throughput compared with our earlier work [21.2,3] which lacked these features.