Research on object reconstruction from Fresnel intensities using phase retrieval methods

在这项研究中，非干涉重建复振幅物体的衍射强度的方法，其中使用高斯或指数滤波的非迭代相位恢复方法被利用。首先，在激光器的实验中，已经表明激光器的高斯光束能够以激光器波长的约1/10的范围的精度恢复来自物体的衍射波的相位分布。其次，它是第一次表明，二维相位恢复可以解决通过使用非迭代方法，从只有两个远场强度得到的指数滤波器和没有。到目前为止，还没有任何非迭代的方法来恢复这两个远场强度的相位。在上述实验中，激光的高斯光束被用作高斯滤波器。然而，如何对x射线或电子束进行高斯滤波相位恢复是一个研究课题 ...更多信息 电子波因此，第三，圆孔的夫琅和费衍射图案（即，Besinc函数）代替高斯光束被用作对象的照射，因此发现，只要对象的范围被限制在Besinc函数的第一个零点的半径的约1/3内，这样的照射就能够通过本发明的方法从X射线或电子波的衍射强度重建对象。通过对一般复杂物体和具有相位涡的特殊物体的计算机模拟，证明了该方法的有效性。特别是，本方法是能够科普与众所周知的相位恢复方法相比，通过从强度分布求解强度的传输方程的相位分布中的旋涡的存在。然而，在现有的方法中，存在着困难的高斯函数过滤的小目标。因此，提出了该方法的一种扩展。该方法利用狭缝孔径与物体菲涅耳衍射振幅的相关性，间接地进行高斯滤波相位恢复。这种相关性的强度数据是通过测量在菲涅耳带平面上扫描的穿过狭缝孔径的波场的衍射强度来获得的。然后利用傅里叶变换的相位计算技术，从两组扫描狭缝时测得的光强中反演物体菲涅耳区平面内的相位。通过傅里叶逆变换，可以从测量的模量和检索的相位重建对象。少

In this research, the noninterferometric reconstruction method of complex amplitude objects from their diffraction intensities was developed, in which the noniterative phase retrieval method by use of a Gaussian or exponential filtering was utilized. First, in the experiment with a laser, it has been shown that the Gaussian beam of a laser is capable of retrieving the phase distribution of a diffracted wave from the objects with the accuracy of the range from about 1/10 of the laser's wavelength. Secondly, it was first shown that the two-dimensional phase retrieval can be solved by using a noniterative method from only two far-field intensities obtained with and without an exponential filter. So far there has not been any noniterative method for the phase retrieval from such two far-field intensities. In the above experiment, the Gaussian beam of a laser was used as a Gaussian filter. However, it was a subject of inquiry how to do Gaussian filtering for phase retrieval of x-rays or ele … More ctron waves. Thus, thirdly, the Fraunhofer diffraction pattern of a circular aperture (i.e., a besinc function) was used as the object's illumination instead of a Gaussian beam, and so it was found that such an illumination enables the object reconstruction by the present method from the diffraction intensities for x-rays or electron waves, provided that the object's extent is confined within about 1/3 of the first zero's radius of the besinc function. The validity of this method is demonstrated in computer simulations of the reconstructions of a general complex object and a particular object with phase vortices. In particular, the present method is able to cope with the existence of vortices in the phase distribution in contrast with the well-known phase recovery method by solving the transport-of-intensity equation from intensity distributions. However, there exists the difficulty of filtering a small object with Gaussian functions in the present method. Thus, fourthly, an extension of the method was proposed. In the extended method, the Gaussian filtering for phase retrieval is done indirectly by taking the correlation of a slit aperture with the Fresnel diffraction amplitude of an object. The intensity data of such a correlation are obtained by measuring the diffraction intensities of a wave field transmitted through the slit aperture that is scanned on the Fresnel-zone plane. Then the phases in the Fresnel-zone plane of the object can be retrieved from two series of the intensities measured while scanning the slit by a new phase calculation technique using Fourier transforms. The object can be reconstructed from the measured moduls and the retrieved phase by an inverse Fourier transform. Less