Demodulation for sinusoidal frequency/phase modulation interferometer using artificial harmonic series signal and phase-locked loop

Abstract

A new demodulation method for sinusoidal frequency/phase modulation (SFM/SPM) interferometers using an artificial harmonic series signal and a phase-locked loop (PLL) is proposed in the paper. Utilizing a laser diode (LD) as the light source and an electric optic modulator (EOM), frequency/phase modulations of the LD light can be achieved by modulating the LD injection current or the driving voltage to the EOM. The SFM/SPM interference signals for the displacement measurement has have the form of cos(msinωmt+θ), where m, ωm and φ are a modulation index, a modulation frequency and a phase change due to optical path movement, respectively. Therefore, the SFM/SPM interference signals is composed by a series of harmonics of the modulation frequency. The two adjacent (2k and 2k+1: k is integer) harmonics include the displacement information. By using the two harmonics, a Lissajous diagram can be drawn to obtain the displacements. In the conventional way, the two harmonics can be demodulated by two lock-in amplifiers. In this paper, we propose new demodulation method for SFM/SPM interferometers using an artificial hormonic series signal and the PLL, which are installed in field programable gate array (FPGA), to obtain sub-picometer (μrad) resolution. An artificial hormonic signals with the form of sin(msinωmt+θ) can be made virtually by the FPGA, where θ is the target phase controlled by the PLL. The output signal from the interferometer will be firstly digitized by the FPGA, and the digitized output signal and the artificial harmonic series signal are multiplied by a mixer, then the mixer output signal is inserted to a low pass filter (LPF). Then the LPF output signal should be -sin(φ-θ)~-(φ-θ) (if (φ-θ) is sufficiently small). In the system, modulation index should be fixed to some value. To set the LPF output signal (-(φ-θ)) to null, the target phase θ of the virtual artificial harmonic signal is controlled by the PLL. In the paper, we discuss the principle, experimental system and results.