Real space iterative reconstruction for vector tomography (RESIRE-V)

Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method

Tomographic reconstruction of 3-D vector fields using inner product probes

Inner product probe measurements are defined for tomographic reconstruction of 3-D vector fields. It is shown that one set of measurements is required to reconstruct an irrotational field, two are required to reconstruct a solenoidal field, and special probes are required to reconstruct the components of an arbitrary field. I. INTRODUCTION In recent years there has been a growing interest in tomographic reconstruction of vector fields [1, 2, 3, 4]. The primary driving force has been the realization that certain applications such as ultrasonic imaging [5], flow imaging [6, 7], and ocean acoustic tomography [8, 9] have measurements that are inherently line integrals of the inner product of the vector field with a fixed unit vector. Norton [2] laid the groundwork for a theoretical treatment of this problem by showing that through a decomposition of the vector field into its irrotational and solenoidal components, conventional line integral projections --- i.e., where the integral of the..

Kerr electro-optic tomography for determination of nonuniform electric field distributions in dielectrics

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 255-260).by Afşin Üstündağ.Ph.D