High-sensitivity and high-resolution collaborative determination of birefringence coefficient using weak measurement

We present a high-sensitivity and high-resolution birefringence coefficient determination system for nm-level membrane films based on weak measurement, addressing the sensitivity-resolution trade-off. A tunable bandwidth light source is exploited to achieve complementary momentum (P-pointer) and intensity (I-pointer) measurements,enabling calibration-free operation across various bandwidths, and to realize high-precision phase difference monitoring of the measured membranes.This method maps the birefringence effect to a weak-value amplified signal of spectral shift and light intensity. The optimal resolution, achieved at a spectral width of 6 nm, is $1.5 \times 10^{-8}$ RIU, while the optimal sensitivity is achieved when the light source is a narrow-linewidth coherent laser, reaching 4710 mV/RIU. The linear range of the system covers a broad birefringence coefficient range for crystals,from $10^{-6}$ to 0.1. Furthermore, the auxiliary optical path eliminates substrate interference, achieving a detection limit of the birefringence coefficient as low as $10^{-8}$ RIU.This approach, characterized high precision, high sensitivity, and strong robustness, provides an effective solution for the detection of optical nano-thin membrane parameters.