Properties in crystalline and ordered materials tend to be anisotropic, with their orientation affecting the macroscopic behavior and functionality of materials. The ability to image the orientation of anisotropic material properties in three dimensions (3D) is fundamental for the understanding and functionality-driven development of novel materials. With the development of x-ray linear dichroic orientation tomography (XL-DOT), it is now possible to non-destructively map 3D orientation fields in micrometer-sized samples. In this work, we present the iterative, gradient-based reconstruction algorithm behind XL-DOT that can be used to map orientations based on linear dichroism in 3D. As linear dichroism can be exhibited by a broad spectrum of materials, XL-DOT can be used to map, for example, crystal orientations as well as ferroic alignment, such as ferroelectric and antiferromagnetic order. We demonstrate the robustness of this technique for orientation fields that exhibit smoothly varying and granular configurations, and subsequently identify and discuss optimal geometries for experimental data acquisition and optimal conditions for the reconstruction. We anticipate that this technique will be instrumental in enabling a deeper understanding of the relationship between material structures and their functionality, quantifying, for example, the orientation of charge distributions and magnetic anisotropies at the nanoscale in a wide variety of systems—from functional to energy materials.