The methods discussed in the first part of the present paper rely on optical elements, typically zone plates, to produce an image of the sample under investigation. The ongoing improvement of the spatial resolution of these methods is very likely to ultimately hit some fundamental barriers due to the difficulty of fabricating ever finer structures. Coherent diffractive imaging (CDI), sometimes also referred to as coherent diffraction microscopy, is a method that offers the possibility of removing the need for a lens and so obviating the limitations imposed by the state-of-the-art in fabrication technology.
The method has a long history, originating from an early proposal by the crystallographer David Sayre [25
] in which it was suggested that the methods of crystallography could be adapted to the imaging of samples that do not display periodicity. The manner in which the image is recovered has more in common with electron imaging methods than it does with X-ray crystallography and, indeed, the phase problem is much easier to solve than it is for the case of crystals. The basic underlying principle for CDI is the realization that a finite sample is uniquely defined by its diffraction pattern [26
]. An iterative method based on ideas with origins in electron and visible optics [27
] is used to find an object that is consistent with both the measured diffraction pattern and any a-priori
knowledge possessed about the object.
The basic arrangement of a CDI experiment is shown schematically in . In essence, a coherent beam is used to illuminate the sample and its far-field diffraction pattern is measured. As the beam will typically interact only weakly with the sample, the undiffracted component of the beam is dominant and will damage the detector unless a beam-stop is introduced, precluding the measurement of the beam at very low diffraction angles. Ideally, if the angular subtended by the beam-stop is smaller than the characteristic scale of the variation of the diffraction pattern (ie. the characteristic size of the coherent speckle) then there need not be a significant impact on the reconstruction. The first experimental confirmation did not take place until long after Sayre’s proposal [28
], and this work used an electron microscope image of the sample to replace the data obscured by the beam-stop. In the intervening decade or so, there has been considerable further progress driven by the rapidly growing access to coherent X-ray photons.
Figure 5 (a) Schematic of a coherent diffractive imaging experiment. The sample is illuminated with a nominally coherent beam of X-rays and the resulting diffraction pattern is captured on a suitable detector placed downstream of the sample. Pinhole 1 is used (more ...)
A major requirement for flexible microscopy is the ability to image samples without the need for the sample to be spatially isolated – the sample must have a well-defined and finite spatial extent. Williams et al [29
] introduced the idea of using a curved incident beam (see ), where a zone plate or any other suitable optic is used to create a focus and the sample is placed in the beam diverging from it. The resolution of the resulting image, as with other forms of CDI and crystallography, is limited by the maximum angle at which diffraction is observed (not by the properties of the optics producing the diverging beam) and it has been established that this configuration displays rather more stable and consistent image recovery characteristics [30
]. This configuration, in turn, allowed the finite object to be replaced by the finite illumination of an extended object [31
] and so eliminating the need for the sample to be isolated. Scanning methods also borrowed from electron microscopy [32
] and known diversely as Wigner phase space deconvolution [33
], ptychography [34
] and scanning diffraction microscopy [35
] have also enabled diffractive imaging of extended objects with high resolution. The different names really refer to the analysis methods for the data, with the latter two forms relying on iterative methods, and the Wigner phase-space method using a deterministic Fourier transform based deconvolution method.
As argued in this paper, modern high-resolution microscopy also needs the capacity to image in three dimensions and this has also been convincingly demonstrated for non-biological objects [36
] at a spatial resolution of around 50nm. The application of CDI to biological samples has been developing rapidly. The first convincing demonstration was of a yeast cell in a form that allowed for imaging of both the phase and the amplitude [37
] at a resolution of 30nm. Images have also been published of the malaria-infected red blood cell [38
] and samples of a human chromosome [39
]. In all these cases, the samples were dried prior to imaging.
Realistic biological imaging will require that the sample be prepared in a frozen hydrated state and results of such experiments have been reported very recently for X-rays in the water window obtained at the Advanced Light Source [40
] where a resolution of better than 25 nm was reported for a yeast (S. cerevisiae
) cell (; cryo X-ray tomography of S. cerevisiae
is shown in for comparison). A frozen hydrated Deinococcus radiodurans
bacteria was simultaneously reported from the ESRF [41
] where 8keV X-rays were used to image at a spatial resolution of around ~30nm.
Figure 6 Optical DIC image (left) and X-ray CDI image (right) of a Saccharomyces cerevisiae yeast cell. The arrow in the left indicates the assumed direction of the incident X-ray beam. The red arrow indicates the possible location of a mitochondrion. Reproduced (more ...)
A recent paper by Nelson et al reports high-resolution molecular localization in a specifically labeled cell, and describes an approach to obtain some depth resolution using the phase information to enable “focusing” through the sample using digital methods [42
]. In this manuscript, the authors show that similar images of a yeast cell are obtained using CDI, STXM and SEM. However, none of these images shows the vast array of subcellular organelles that are seen in images of S. cerevisiae
obtained with transmission electron tomography [43
] or X-ray tomography (), indicating that there remains considerable scope for the further development of CDI in bio-imaging.
It has been proposed that using a short pulse of x-rays from a free electron laser could mitigate the effects of radiation damage, with the image being formed from scattered radiation before the specimen is destroyed [44
]; Chapman and colleagues have shown that it is indeed possible to obtain useable diffraction patterns from objects that are in the process of disintegrating [45
]. Unfortunately the damage caused by the extremely powerful laser pulse rules out the use of tomography to retrieve 3D information, as tomography requires many images of the same cell. The remaining option is to average data from many specimens. While this method could, in principal, work with identical particles such as single molecules, it is unlikely to be effective for cell imaging since each cell is unique. Moreover, recent data has shown that the core electrons are removed from light atoms such as carbon and nitrogen in a few femtoseconds, creating hollow atoms [46
] suggesting that the rapid electronic damage effects of the incident pulse must also be considered – the nature of the sample in the Chapman et al paper [45
] was such that it could not test the consequences of electronic damage. However, future experiments will no doubt soon clarify whether high-flux femtosecond pulse imaging can mitigate the effects of radiation damage accompanying biological x-ray imaging.
In summary, CDI has a great deal further to go in order to compete with the state-of-the-art three-dimensional X-ray microscopy, and the available resolution of X-ray zone plates will continue to improve and so the requirements for CDI to be truly competitive in biological X-ray microscopy will continue to become ever more demanding. The image reconstruction algorithms will continue to develop and, in the opinion of the authors, the uncertainty as to whether a given reconstruction is correct in every detail – the problem being that the algorithm might become trapped in a spurious solution (ie. a local minimum in solution space) – remains an issue worthy of further examination. However the ptychography-related methods [33
] and curved beam methods [29
] seem to be more consistent. However CDI does offer very high spatial resolution imaging that is sensitive to both phase and amplitude and so offers a quantitative form of imaging that has considerable potential for biological imaging.