High-precision 3D crystal axis orientation measurement in uniaxial crystals via frequency-domain weak measurement with phase compensation

Abstract

Weak measurement is an effective approach for detecting small phase shifts. In this work, a method is proposed for determining the three-dimensional orientation of the optical axis in uniaxial crystals, based on frequency-domain weak measurement. The $C$-axis orientation is decomposed into a transverse azimuthal angle $\chi$ (in the plane perpendicular to the optical axis) and a longitudinal cut angle $\theta$ (along the optical axis), and quantitative relationships are established between these angles and the induced phase shifts. By leveraging the weak-value amplification effect, small phase variations are transformed into measurable spectral shifts, enabling decoupled measurements of $\chi$ and $\theta$. The angular resolution for $\chi$ is $1.9\times {10}^{-3}{}^{\circ }$, and the phase resolution for $\theta$ is $2.5\times {10}^{-5}\text{rad}$. Furthermore, a phase compensation strategy was validated and successfully applied to large cut angle measurements, extending the dynamic range while maintaining high sensitivity. Excellent consistency is observed in repeated measurements of cut angles across four selected sapphire crystals. This approach provides a non-destructive, high-precision solution for crystal processing quality evaluation, offering new possibilities for optimizing polarization-sensitive devices.