Knowing the distribution of a magnetic field in bulk materials is important for understanding basic phenomena and developing functional magnetic materials. Microscopic imaging techniques employing X-rays, light, electrons, or scanning probe methods have been used to quantify magnetic fields within planar thin magnetic films in 2D or magnetic vector fields within comparable thin volumes in 3D. Some years ago, neutron imaging has been demonstrated to be a unique tool to detect magnetic fields and magnetic domain structures within bulk materials. Here, we show how arbitrary magnetic vector fields within bulk materials can be visualized and quantified in 3D using a set of nine spin-polarized neutron imaging measurements and a novel tensorial multiplicative algebraic reconstruction technique (TMART). We first verify the method by measuring the known magnetic field of an electric coil and then investigate the unknown trapped magnetic flux within the type-I superconductor lead.
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