This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for {strong phase objects} and { weak phase objects}, including: (i) {\em Unique determination of (phase) projections from diffraction patterns} -- General measurement schemes with coded and uncoded apertures are proposed and shown to ensure unique conversion of diffraction patterns into the phase projection for a strong phase object (respectively, the projection for a weak phase object) in each direction separately without the knowledge of relative orientations and locations. (ii) {\em Uniqueness for 3D phase unwrapping} -- General conditions for unique determination of a 3D strong phase object from its phase projection data are established, including, but not limited to, random tilt schemes densely sampled from a spherical triangle of vertexes in three orthogonal directions and other deterministic tilt schemes. (iii) {\em Uniqueness for projection tomography} -- Unique determination of an object of $n^3$ voxels from generic $n$ projections or $n+1$ coded diffraction patterns is proved. This approach has the practical implication of enabling classification and alignment, when relative orientations are unknown, to be carried out in terms of (phase) projections, instead of diffraction patterns. The applications with the measurement schemes such as single-axis tilt, conical tilt, dual-axis tilt, random conical tilt and general random tilt are discussed.
翻译:本文为三维阶段的检索单独开发了独特性理论,使用有限的、离散的相片对象和{弱相对象的测量数据,包括:(一) 确定来自分折模式的三维强对象的独特性(阶段) {强相} 和{弱相对象},包括:(一) 确定来自分折模式的(阶段)预测的(阶段) —— 提出并展示有编码和未编码孔径的通用测量计划,以确保将偏差模式单独转换到一个强相位对象的阶段预测(分别是,对弱相向对象的预测),而没有了解相对方向和地点。 (二) 3D阶段不透明性预测的三维强相异性 : 其阶段预测数据的独特性确定三维强对象的(阶段) -- -- 确定了独特的一般条件,包括但不限于从三个或不同方向的球形的脊椎和其他确定性倾斜向的随机偏移方案。 (三) 预测的直径直径直径直线是双向的双向,这种精确度和直径直径直的计算方法,在一般的平面的平面上下进行。