Latychevskaia Tatiana, Longchamp Jean-Nicolas, Fink Hans-Werner
Institute of Physics, University of Zurich, Winterthurerstrasse 190, CH-8057, Switzerland.
Opt Express. 2012 Dec 17;20(27):28871-92. doi: 10.1364/OE.20.028871.
The phase problem is inherent to crystallographic, astronomical and optical imaging where only the intensity of the scattered signal is detected and the phase information is lost and must somehow be recovered to reconstruct the object's structure. Modern imaging techniques at the molecular scale rely on utilizing novel coherent light sources like X-ray free electron lasers for the ultimate goal of visualizing such objects as individual biomolecules rather than crystals. Here, unlike in the case of crystals where structures can be solved by model building and phase refinement, the phase distribution of the wave scattered by an individual molecule must directly be recovered. There are two well-known solutions to the phase problem: holography and coherent diffraction imaging (CDI). Both techniques have their pros and cons. In holography, the reconstruction of the scattered complex-valued object wave is directly provided by a well-defined reference wave that must cover the entire detector area which often is an experimental challenge. CDI provides the highest possible, only wavelength limited, resolution, but the phase recovery is an iterative process which requires some pre-defined information about the object and whose outcome is not always uniquely-defined. Moreover, the diffraction patterns must be recorded under oversampling conditions, a pre-requisite to be able to solve the phase problem. Here, we report how holography and CDI can be merged into one superior technique: holographic coherent diffraction imaging (HCDI). An inline hologram can be recorded by employing a modified CDI experimental scheme. We demonstrate that the amplitude of the Fourier transform of an inline hologram is related to the complex-valued visibility, thus providing information on both, the amplitude and the phase of the scattered wave in the plane of the diffraction pattern. With the phase information available, the condition of oversampling the diffraction patterns can be relaxed, and the phase problem can be solved in a fast and unambiguous manner. We demonstrate the reconstruction of various diffraction patterns of objects recorded with visible light as well as with low-energy electrons. Although we have demonstrated our HCDI method using laser light and low-energy electrons, it can also be applied to any other coherent radiation such as X-rays or high-energy electrons.
相位问题在晶体学、天文学和光学成像中是固有的，在这些成像中，仅检测到散射信号的强度，而相位信息丢失，必须以某种方式恢复相位信息才能重建物体的结构。分子尺度的现代成像技术依赖于利用新型相干光源，如X射线自由电子激光，以实现可视化单个生物分子而非晶体等物体的最终目标。在这里，与晶体情况不同，晶体结构可通过模型构建和相位细化来求解，而单个分子散射波的相位分布必须直接恢复。相位问题有两种众所周知的解决方案：全息术和相干衍射成像（CDI）。这两种技术都有其优缺点。在全息术中，散射复值物体波的重建直接由一个定义明确的参考波提供，该参考波必须覆盖整个探测器区域，这通常是一个实验挑战。CDI提供了尽可能高的、仅受波长限制的分辨率，但相位恢复是一个迭代过程，需要一些关于物体的预定义信息，且其结果并不总是唯一确定的。此外，衍射图案必须在过采样条件下记录，这是能够解决相位问题的一个先决条件。在这里，我们报告了如何将全息术和CDI合并为一种更优的技术：全息相干衍射成像（HCDI）。可以通过采用改进的CDI实验方案来记录在线全息图。我们证明，在线全息图的傅里叶变换幅度与复值可见度相关，从而提供了衍射图案平面中散射波的幅度和相位信息。有了相位信息，衍射图案过采样的条件可以放宽，并且可以快速、明确地解决相位问题。我们展示了用可见光以及低能电子记录的物体的各种衍射图案的重建。虽然我们已经使用激光和低能电子展示了我们HCDI方法，但它也可以应用于任何其他相干辐射，如X射线或高能电子。
