Yb. Zheng et Pc. Doerschuk, ITERATIVE RECONSTRUCTION OF 3-DIMENSIONAL OBJECTS FROM AVERAGED FOURIER-TRANSFORM MAGNITUDE - SOLUTION AND FIBER X-RAY-SCATTERING PROBLEMS, Journal of the Optical Society of America. A, Optics, image science,and vision., 13(7), 1996, pp. 1483-1494
Reconstruction of objects based on solution x-ray scattering and fiber
x-ray diffraction both involve measurements that are averages of the
magnitude squared of the Fourier transform of the electron density and
involve electron densities with symmetries. We describe an iterative
algorithm for such problems that is a generalization of the Gerchberg-
Saxton algorithm from two dimensions (where the measurement is the mag
nitude squared of an unknown complex number) to n dimensions (where th
e measurement is the norm squared of an unknown n vector). An example
of the reconstruction, for solution x-ray scattering from cowpea mosai
c virus, is described. (C) 1996 Optical Society of America.