High Precision Phase Measurement For Heterodyne Laser Interferometer

Inter-satellite laser ranging system is used to measure the change in inter-satellite distance for the next generation of the Earth’s gravity recovery (e.g. GRACE Follow-on mission) and the spaceborne gravitational waves detection mission (e.g. LISA, Laser Interferometer Space Antenna). This tiny distance change will induce the phase shift of the beat note between the received and local laser beams. Hence, high precision phase measurement is one of the key techniques in the inter-satellite laser ranging system and is the major research work presented in this thesis.In order to develop a high precision laser ranging system, we constructed a prototype of10-m-baseline heterodyne laser interferometer, and following a transponder-type interferometer with homodyne optical phase-locked loop (OPLL). Besides, a home-made digital PLL-based phasemeter was implemented with an ultra-stable heterodyne interferometer that was built by using silicate bonding technique for demonstrating picometer-level displacement measurement and positioning control.In addition to PLL-based phasemeter, we develop another digital phase detection method based on the cross-correlation analysis. The basic principle is that the sine or cosine value of phase s is proportion to the cross-correlation value at zero time lag of two sinewave signals. The pros and cons between the arcsine and arctangent arithmetics are compared. When the latter method is chosen, the effects of sampling quantization error, intrinsic white noise, and non-integral-cycle sampling error on phase measurement are analyzed. We find that the non-integer-cycle sampling could result in a cyclic error that has not been reported ever. We use a high-performance data acquisition system to carry out the cross-correlation-based phase measurement. A noise level of1.2x10-6rad/Hz1/2@(1mHz～10Hz) is obtained, and the non-integral-cycle sampling error is observed.The application of the phase measurement based on the cross-correlation is limited by the frequency change of the measured (interference) signal. The Doppler-induced frequency shift caused by the relative motion between two satellites is typically more than1MHz, so that the PLL-based phase measurement is a better method for most inter-satellite ranging applications. Therefore, we have develop a PLL-based phasemeter and achieve a background noise (dominated by sampling time jitter and phase readout noise) of about1x10-6rad/Hz1/2. The possible error sources, such as temperature fluctuation and intrinsic white noise, had been investigated. For inter-satellite range-rate monitoring, the direct read frequency (DRF) and differential phase time series (DPS) methods are compared, and the result show that the precisions are limited by the stability of the internal oscillator and the sampling-time jitter, respectively.To demonstrate the useful applications of PLL-based phasemeter, we use it for picometer positioning control and heterodyne optical PLL. A resolution of50pm for positioning control with laser interferometer has been achieved, and the preliminary result of heterodyne optical phase locking will be discussed in the last chapter.