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Phase‐Retrieval Algebraic Solution Based on Window Modulation
Author(s) -
Huang Jianhui,
Jin Huiliang,
Ye Qian,
Meng Guoxiang
Publication year - 2018
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201800063
Subject(s) - phase retrieval , algebraic number , phase (matter) , computer science , diffraction , algebraic equation , algorithm , field (mathematics) , fourier transform , phase problem , algebraic solution , optics , nonlinear system , mathematics , mathematical analysis , physics , differential equation , pure mathematics , quantum mechanics , ordinary differential equation , differential algebraic equation
Phase retrieval is to recover the object amplitude and phase from the diffraction patterns. Here, an algebraic method is presented to solve the phase retrieval problems of arbitrary 2D complex‐valued objects, without the requirements of numerous iterations, object prior knowledge, and precise experimental setups. The key step is to extract the far‐field phase from the diffraction patterns. It is demonstrated by rigorous theoretical derivation that three window‐shaped modulations are sufficient to establish a system of linear equations related to the far‐field phase, from which the far‐field phase is solved approximately with only algebraic calculations. Then, an efficient iteration scheme is designed to optimize the direct approximate solution. After a few iterations, the direct solution is improved quickly and very close to the exact solution. With the advantages of high speed and high accuracy to general phase retrieval problems, the proposed algebraic method may be helpful to the Fourier imaging systems in which interferometric techniques are not applicable.