phase retrieval
Phase retrieval
Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex spectrum $${\displaystyle F(k)}$$ , of amplitude $${\displaystyle |F(k)|}$$ , and phase $${\displaystyle \psi (k)}$$ $${\displaystyle F(k)=|F(k)|e^{i\psi (k)}=\int _{-\infty }^{\infty }f(x)\ e^{-2\pi ik\cdot x}\,dx}$$ where x is an M-dimensional spatial coordinate and k is an M-dimensional spatial frequency coordinate. Phase retrieval consists of finding the phase that satisfies a set of constraints for a measured amplitude. Important applications of phase retrieval include X-ray crystallography, transmission electron microscopy and coherent diffractive imaging, for which $${\displaystyle M=2}$$ . Uniqueness theorems for both 1-D and 2-D cases of the phase retrieval problem, including the phaseless 1-D inverse scattering problem, were proven by Klibanov and his collaborators (see References).
Read more about 'Phase retrieval' at: WikipediaWikipedia contributors. "Phase retrieval." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, Oct. 14, 2024.
