| In recent years, due to the continuous progress of the X-ray source, high sensitivity and high stability of X-ray detector, elaborate micro-/nano-fabrication technology for X-ray optical components, high precision mechanical platform and control systems, nano CT imaging technology has obtained the significant development. The hard X-ray nano CT has many outstanding features, such as large penetration depth, high depth of focal, high resolution, no need vacuum environment, containing a variety of material absorption edges, as well as three-dimensional imaging. It has been applied to materials science, microelectronics industry, environmental engineering and energy science. Because of "water window", Soft X-ray nano CT could keep biology sample "fresh" while obtains high contrast imagings. It has broad potential in a variety of fields, including drug research, life science, nanoparticles, etc. Therefore, nano CT imaging technology with unique advantages, can make up the gap of electron microscope and optical microscope.To obtain the accurate, clear and meaningful information, a series of imaging processing steps are required, including pre-processing,3-D reconstruction, imaging segmentation, calculation and analysis. The pre-processing step of projections is preparation of the series of subsequent processing steps. During pre-processing step, the errors of bad pixels, uneven brightness, noise and rotation axis missing alignment need to be corrected. Imaging reconstruction is the key step, which transform 2-D projections to 3-D structure information. However, the missing wedge, which is due to a restricted rotation range, is a major challenge for reconstuction of high quality imagings. Therefore, it is significant to develop a suitable reconstruction algorithm to conquer the problem. A hard X-ray nano-CT and soft X-ray nano-CT have been built in the NSRL (National Synchrotron Radiation Laboratory) successively since 2007. The main contributions of this thesis are described as follows:1. We summarized the advantages and characteristics of the X-ray nano-microscopy imaging techniques. The principles and the main optical elements parameters of hard X-ray nano-CT and soft X-ray nano-CT were reviewed. We selected a few typical examples to illustrate the unique advantages of hard X-ray nano-CT: urchin-like zinc silicate forming self-assembled, defects during the assembly became visible, which was not detectable with other techniques; The dynamics of CuO volume expansion during electrochemical lithiation-delithiation was record: mitotic yeast cell imagings were obtained in the phase contrast mode, which has the ability to image large biology samples with high contrast. Several examples were selected to demonstrate the value of the soft X-ray nano-CT, such as vaccinia virus infected cells, red blood cells infected with Plasmodium, effects of drugs on cells, immunogold-labeled stem cells, microgel particles and droplets particle interactions. We also demmonstrated the correlative imaging of samples using soft X-ray nano-CT with fluorescence and nanoscale NEXAFS.2. A variety of nano-CT image pre-processing algorithms were proposed to improve the quality of the raw projections. To correct the shift deviation of the rotation axis, a automatic correction algorithm was proposed, which based on the gold particle trajectory tracked. The most important step of the algorithm is that makes the central sheleton of the gold particle to a smooth sine curve. According to the characteristics of the projection data, an projection normalization algorithm was presented to effectively make the brightness among different projections homogeneously. A background noise removed algorithm based on the threshold filter was proposed to make the background "clean". The results of all these algorithms lay the foundation for later reconstruction.3. After researching the basic princeples of CT imaging, the traditional filtere back projection algorithm and iterative recnstruction algorithms were introduced. A total variation based nano-CT reconstruction algorithm was propoed which based on the theory of compressive sensing. A series of simulated data with limited angle range and noise were applied to test the algorithm performance. Two data collected from hard and soft X-ray nano-CT, respectively, were reconstructed through different algorithms. The results showed that the total variation based new algorithm has obvious advantages compared with traditional reconstruction algorithms.4. Discrete tomography is widely applied in nano-CT, industrial CT, and transmission electron microscopy, etc. However, discrete tomography reconstruction algorithm are over reliance on the prior knowledge of graylevels which is difficult to obtained in practice, and the quality of the reconstruction are declining as the number of gray imaging increasing. In this thesis, a new discrete tomography reconstruction algorithm was proposed, in which each independent region of homogeneous material was chosen as a research object, instead of the grey values. The grey values of each discrete region were estimated according to the solution of the linear projection equations. The algorithm could obtain high quality multiple grey imaging without the prior knowledge of the grey levels. A series of experiments were carried out to verify the stability, convergence, precision of the algorithm. And the limitation of the grey number was also tested. The results shows that the new discrete algebraic reconstruction technique is capable of achieving high quality reconstructions with projections in a limited angle range and without prior knowledge of grey levels.
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