<p>Biaxial anisotropy, arising from distinct optical responses along the three principal directions, underlies the complex structure of many crystalline, polymeric and biological materials. However, existing techniques such as X-ray diffraction and electron microscopy require specialized facilities or destructive preparation for full three-dimensional information. Here we introduce incoherent dielectric tensor tomography, a non-interferometric optical imaging method that quantitatively reconstructs three-dimensional dielectric tensor under incoherent, polarization-diverse illumination. By combining polarization diversity and angular-spectrum modulation, the proposed method achieves a speckle-free and vibration-robust mapping of biaxial birefringence with submicrometre resolution. Simulations and experiments on uniaxial and biaxial samples validate its quantitative accuracy. Applied to mixed and polycrystalline materials, the proposed method distinguishes crystal types by their birefringent properties and reveals three-dimensional grain orientations and boundaries. This approach establishes the proposed method as a practical and accessible tool for quantitative, label-free characterization of biaxial anisotropy in diverse materials.</p>