Heterodyne interferometer for displacement measurement with amplitude quadrature and noise suppression

Abstract

The high precision displacement measurement in nanoscale is crucial to many applications. We present a heterodyne interferometry with differential phase to amplitude conversion scheme for displacement measurement in nanoscale. In this approach, the differential phase introduced by the displacement is converted into the amplitudes of heterodyne signals in quadrature. Meanwhile, the heterodyne signals in phase quadrature are also achieved so that the displacement can be determined from the amplitude ratio of the quadrature signals, and the direction of displacement can be determined from the phase quadrature. Since the differential phase to quadrature amplitude conversion is achieved through the optical addition and subtraction by polarization tuning, which are based on differential detection concept. Thus the proposed method benefits from the features of differential detection with common phase noise and correlated amplitude noise rejection and that of quadrature detection with real time and wide dynamic range of phase measurement. To demonstrate the capability of proposed method in differential phase measurement, we measure the displacement drove by a commercially available PZT pusher and found close agreement between the experiment and the theory. The experimental evidence of noise suppression is also found with spectral measurements, which demonstrates the resolution of displacement measurement at 60 pm and minimum detectable differential phase of 5.6 × 10 −6 rad/ Hz over 50 kHz.