Research on object reconstruction from Fresnel intensities using phase retrieval methods

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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