Differential interference metrology in crystal optics

Conventional differential interference contrast (DIC) microscopy is inherently qualitative and lacks metrological capability, whereas high-precision techniques such as weak value amplification impose stringent experimental requirements. Here, we present a compact transmissive differential interferometric measurement system based on a birefringent crystal. By functioning as an interference element, the crystal enables quantitative differential interference measurements in both real space and momentum space. This approach avoids the dependence of weak value amplification on weak coupling and non-orthogonal state selection, while retaining and utilizing the inherent birefringent phase information of the crystal. We propose two modulation strategies and establish a unified theoretical model linking microscopic crystal parameters to macroscopic interferometric observations. Based on this model, the system can achieve an angular resolution on the order of 10−9 rad, which exceeds that of typical commercial polarimeters, and detects displacements as small as 0.35 nm, demonstrating nanometer-scale sensing capability. Owing to its compact design and tunable parameters, this system offers a compact quantitative approach for high-precision applications, including chiral sensing, nanometrology, and quantum material analysis.