3D Image Reconstruction - Determination of Pattern Orientation

The problem of determining the euler angles of a randomly oriented 3-D object from its 2-D Fraunhofer diffraction patterns is discussed. This problem arises in the reconstruction of a positive semi-definite 3-D object using oversampling techniques. In such a problem, the data consists of a measured set of magnitudes from 2-D tomographic images of the object at several unknown orientations. After the orientation angles are determined, the object itself can then be reconstructed by a variety of methods using oversampling, the magnitude data from the 2-D images, physical constraints on the image and then iteration to determine the phases