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Fig. 1 Coherent imaging uses computation as lenses, i.e. lensless imaging. When a coherent wave illuminates a noncrystalline specimen, shown in Fig. 1, the far-field diffraction pattern is continuous and weak. This continuous diffraction pattern can be sampled at a spacing finer than the Nyquist frequency (i.e. the inverse of the specimen size), which corresponds to surrounding the electron density of the specimen with a no-density region [1]. The higher the sampling frequency, the larger the no-density region. When the no-density region is larger than the electron density region, it has been shown that the phases are uniquely encoded inside the diffraction pattern [2] and can be directly recovered by using an iterative process that takes advantage of information such as the fact that electron density outside the object is zero and within the object is positive [3].
Fig. 2 The first experiment of coherent imaging in three dimensions. (a) A SEM image of a 3D nanoscale specimen, which shows the surface structures, but not the internal structures. (b) A coherent X-ray diffraction pattern from (a). (c) An image reconstructed from (b), showing both the surface and internal structures. (d) Iso-surface rendering of a 3D image reconstructed from thirty-one 2D diffraction patterns. (See ref. 6 for details) The idea of imaging noncrystalline specimens by using coherent X-rays was first suggested by Sayre in 1980 [4]. It was not until in 1999 that the first experimental demonstration was carried out by Miao et al [5]. Since then, a few groups have successfully conducted coherent imaging experiments in both two and three dimensions by using either X-rays or electrons. Fig. 2 shows the first experiment of coherent imaging in three dimensions, which reveals internal structures of a nanoscale material not accessible to scanning probe microscopy. The application to biological samples has also been pursued [7]. The samples were E. Coli bacteria with manganese labeling of histidine-tagged yellow fluorescent proteins. Fig. 3(a) shows an image directly reconstructed from an coherent X-ray diffraction pattern. The reconstructed bacteria contain dense regions that probably represent the histidine-tagged proteins labeled with manganese and a semi-transparent region that is devoid of proteins. The observation was confirmed by both transmission and fluorescence microscopy images shown in Fig. 3(b).
(a) (b) Fig. 3 Coherent X-ray imaging of E. coli bacteria. (a) An image directly reconstructed from a coherent X-ray diffraction pattern. The dense regions inside the bacteria are likely the distribution of proteins labeled with KMnO4. The semi-transparent regions are devoid of yellow fluorescence proteins. (b) Individual bacteria are seen using transmitted light (A, D) and fluorescence (B, E), where the yellow fluorescence protein (green) is seen throughout most of the bacteria except for one small region in each bacterium that is free of fluorescence (arrows). C and F show the fluorescent image superimposed on the transmitted light image. (See ref. 7 for details) While coherent X-rays have been successfully used to image a variety of specimens, the principle can also be extend to optical lasers and electrons. Indeed, we recently proposed a 3D electron diffraction microscope based on coherent electron diffraction and the oversampling method [8]. The demonstration experiment of 2D electron diffraction microscopy has just been carried out by Prof. ZuoÕs group to image a double-wall carbon nanotube at 1 resolution, revealing the structure of two tubes of different helicities [9]. So what is the future of coherent imaging? Well, with the appearance of more coherent sources and faster computers, it is safe to predict that coherent imaging will have a very bright future. Our group will continue to stay at the frontier of this new and exciting field. We will keep improving the spatial resolution and make the image reconstruction faster and more reliable. Meanwhile, we will also pursue its applications in nanoscience and biology by using optical lasers, coherent X-rays and electrons. In the long run, in a combination of the X-ray free electron lasers such as the Linac Coherent Light Source at Stanford Linear Accelerator Center, coherent imaging could potentially be used to determine the 3D structure of single particles down to the single atom level [10, 11]. References
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