Incoherent dielectric tensor tomography for quantitative 3D measurement of biaxial anisotropy

Biaxial anisotropy, arising from distinct optical responses along 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 and cannot provide full three-dimensional (3D) information. Here we introduce incoherent dielectric tensor tomography (iDTT), a non-interferometric optical imaging method that quantitatively reconstructs the 3D dielectric tensor under incoherent, polarization-diverse illumination. By combining polarization diversity and angular-spectrum modulation, iDTT achieves speckle-free and vibration-robust mapping of biaxial birefringence with submicron resolution. Simulations and experiments on uniaxial and biaxial samples validate its quantitative accuracy. Applied to mixed and polycrystalline materials, iDTT distinguishes crystal types by their birefringent properties and reveals 3D grain orientations and boundaries. This approach establishes iDTT as a practical and accessible tool for quantitative, label-free characterization of biaxial anisotropy in diverse materials.