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We experimentally realize a great precision enhancement in the small tiltmeasurement by using a Sagnac interferometer and balanced homodyne detection(BHD) of high-order optical modes, together with the weak value amplification(WVA) technique. Smaller minimum measurable tilt (MMT) and highersignal-to-noise ratio (SNR) can be obtained by using BHD, compared with thesplit detection (SD). The precision of 3.8 nrad can be obtained under ourpresent experimental condition. It is shown that combining WVA technique andBHD can strengthen each other's advantages and can behave better for somespecial application scenarios, such as extremely weak output, wider measurementbandwidth, etc. Moreover, the precision can be further enhanced by experimentalparameter optimization.

Realization of higher Precision in Interferometric-weak-value-based Small-tilt Measurement