Spectrography: volumetric reconstruction from one or two spectral views

Recently, ‘ankylography’ was proposed to perform a 3D reconstruction from a single exposure of a monochromatic radiation beam. This approach appeared very attractive to reveal structures of important objects such as complex proteins that can be glimpsed only once before they are destroyed by a high-intensity x-ray laser beam. However, this approach does not give a unique solution and is highly unstable when the number of voxels is not too small. In this paper, we acquire one or two polychromatic diffractive views with energy-sensitive detectors simultaneously. Specifically, a spectrography system may consist of two spectral coherent imaging chains perpendicular to each other. As a result, multiple Ewald spheres of different radii can be simultaneously measured in the Fourier space, and an image volume can be practically reconstructed. To evaluate the performance of spectrography, the hybrid input-output algorithm is implemented for phase retrieval and improved with a lower dimensional subspace saddle-point optimization technique proposed by Marchesini. For different configurations of the proposed spectrography scheme, extensive numerical tests are conducted, yielding encouraging results.