یک بازیابی فاز چند تصویری قوی A robust multi-image phase retrieval

1. Introduction Iterative phase retrieval has been a powerful tool to reconstruct the complex amplitude of sample by the back-and-forth beam propagation between the measuring plane and the sample plane with the addition of different constraints. To date, iterative phase retrieval technique has been successfully applied in encryption [1,2], electron microscopy [3], quantum imaging [4], super-resolution imaging [5]. As the origin of iterative phase retrieval algorithm, Gerchberg-Saxton (GS) algorithm [6] reconstructs the phase of sample with a pair of known amplitude distribution at the sample plane and the measuring plane. Its low convergence speed and much sensitivity to the initial value, however, restrict its application. Moreover, another limitation of GS algorithm lies on that the amplitude distribution of sample has to be determined, which usually imposes more complexity in experimental setup. Thus, based on the origin, hybrid input output (HIO) algorithm [7] was brought up by using the support constraint to increase the convergence speed. In spite of higher convergence speed and high precision, both algorithms require that the support constraint should be tight. To overcome these limitations, multi-image phase retrieval algorithms have been proposed [8–18] afterwards. They introduce variable optical system parameters to generate multiple measurements and get rid of the prior knowledge of amplitude distribution at the sample plane. The methodology can be divided into two categories: lateral and axial scanning strategies. As a lateral scanning technique, the ptychographic iterative engine (PIE) algorithm [8] shifts an aperture or a pinhole to create a series of overlapped diffraction patterns at the measuring plane. Its demanding shifting operation slows down the reconstruction and leads to a long acquisition time, which is then improved by LED array microscope [9], parallel calculation [10], and modulation imaging with a measured loose support [11]. Recently, these lateral scanning methods, such as single-shot pychography [12] and Fourier pychographic microscopy [5], have made lots of achievements theoretically and experimentally.