The precise measurement of spatial attitude parameters is critical for applications in inertial navigation, industrial monitoring, instrument calibration, quantum metrology, etc. In this work, we theoretically investigate and experimentally realize the simultaneous measurement of the yaw and pitch angles using a Hermite-Gaussian-postselected double weak value system integrated with two sets of high-order-mode balanced homodyne detections, thereby achieving a complete characterization of the beam deflection. Signals of the yaw and pitch angles that are involved in TEM
10 and TEM
01 modes output from two dark ports of the system can be measured independently. As a result, the obtained minimum measurable yaw and pitch angles of beam deflection are 83 prad and 89 prad, respectively. Meanwhile, the corresponding displacements are 0.79 pm and 0.85 pm, respectively. This work expands the beam deflection measurement to two dimensions, which provides a new insight for future high-precision multi-parameter spatial precise detection.
We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 400+/-200 frad and the linear travel of a piezo actuator down to 14+/-7 fm.