We analyze measurement schemes under which 3D unwrapped phase retrieval can be reduced to projection tomography. A key component is the deployment of a coded aperture.
Our motivation is to leverage highly successful projection-based techniques in cryo-EM to process diffraction data collected under measurement uncertainties such as sample heterogeneities, unknown orientations and positions.
First, with the introduction of a beam splitter, the dataset of diffraction patterns is reducible to that of projections under measurement uncertainties.
Second, without a beam splitter, this data reducibility holds true for random conical tilt and orthogonal tilt schemes widely used in cryo-EM.
Finally, the resulting phase unwrapping problem for 3D projection tomography can be solved by schemes including as special cases the conical tilting at a conical angle slightly greater than pi/4, the orthogonal dual-axis tilting and a combination of a conical tilting and an orthogonal single-axis tilting.
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