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The purpose of this paper is to give a general overview of the phase problem; to discuss existing iterative phase reconstruction algorithms, aimed to solve the problem; to consider their peculiar properties and differences. In addition, the recent developments in coherent diffraction imaging are reviewed, with an emphasis on the impact that this technique has on biophysics, biochemistry and nanoscience. Various lens-based optical techniques, starting from conventional optical microscopy to more advanced methods, such as phase-contrast, fluorescence, confocal and electron microscopy are based on the exploiting of lenses to reproduce an image of the target object.
The development of these techniques revolutionized many of scientific fields, especially biology, chemistry, medicine and physical sciences. Nowadays new methods of imaging have been appeared, among which the coherent diffraction imaging deserves a special attention, as one of the most promising methods of high-quality imaging of complex objects, including the imaging on the nanometre length scale. Coherent diffraction imaging (CDI) is a modern approach of 2-dimensional and 3-dimensional reconstruction of an object’s image on the basis of its diffraction pattern, which is recorded as a result of illumination of the object by a coherent beam of x-rays, electrons or protons and subsequent backscattered reflection.
The collected diffraction pattern is measured and used for obtaining the image via iterative computational algorithms rather than via lenses (see Fig.1). Because of an image of a target object is created without the use of lenses or other optics, the method is also often called “lensless imaging.” Such technique allows avoiding an excessive aberration and improving a quality of image, increasing its resolution. CDI involves the “phase problem” related to the loss of the information that describes
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