Sequential on-line construction for ensemble phase-retrieved images

The reconstruction of a target image from its diffraction pattern is referred to as “diffractive imaging,” and this has been focused as a new microscopy. Fourier phase retrieval is required during the imaging process by means of numerical computations using computers. However, it is difficult to establish a complete convergence using an incomplete diffraction pattern such as experimental data in the retrieving process. A simple averaging procedure by weak phase-retrieved results using different initials is often used. Recently, the spherical shell structure of the retrieved images has been investigated and the center of the shell is to be a superior retrieved result. Therefore, it is important to construct such a structure by the retrieved images in order to reconstruct the target image. In this paper, a novel sequential on-line algorithm for effectively constructing the spherical shell structure of the images is introduced. A numerical demonstration is also presented using the Fourier intensities contaminated with Poisson noise.