Suppression of frequency-mixing effect for pm-level heterodyne interferometers based on "zero coupling" optical path length control.

Optical path length (OPL) noise resulting from stray light significantly constrains interferometry displacement measurements in the low-frequency band. This paper presents an analytical model considering the presence of stray light in heterodyne laser interferometers. Due to the cyclic nonlinear coupling effect, there will be some special OPLs of stray light, minimizing the frequency-mixing impact to zero. Consequently, we propose a noise suppression scheme that locks the OPL of stray light at the zero coupling point. Therefore, we significantly enhanced the interference displacement measurement noise within the low-frequency band. Experimental results show that the interferometer achieves a displacement noise level lower than 6 pm/Hz1/2 covering 1 mHz.

External right-angle measurement using a two-autocollimator system.

We report on a non-contact method for external right-angle measurement using two autocollimators. A precise mathematical model is deduced to evaluate and deduct the measuring error. The values measured with our method are very coincident compared with the results measured by a ZYGO interferometer. The measuring accuracy is superior to 0.1 arcsec for the right-angle errors within 3.0 arcsec and becomes 0.4 arcsec for the extended right-angle errors within 8.0 arcsec. This method can be widely used in situations for external right-angle measurement, such as angle measurement for the body of torsion balance and test mass in spaceborne laser interferometry.

Inter-satellite laser link acquisition with dual-way scanning for Space Advanced Gravity Measurements mission.

Laser link acquisition is a key technology for inter-satellite laser ranging and laser communication. In this paper, we present an acquisition scheme based on the differential power sensing method with dual-way scanning, which will be used in the next-generation gravity measurement mission proposed in China, called Space Advanced Gravity Measurements (SAGM). In this scheme, the laser beams emitted from two satellites are power-modulated at different frequencies to enable the signals of the two beams to be measured distinguishably, and their corresponding pointing angles are determined by using the differential power sensing method. As the master laser beam and the slave laser beam are decoupled, the dual-way scanning method, in which the laser beams of both the master and the slave satellites scan uncertainty cones simultaneously and independently, can be used, instead of the commonly used single-way scanning method, in which the laser beam of one satellite scans and that of the other one stares. Therefore, the acquisition time is reduced significantly. Numerical simulation and experiments of the acquisition process are performed using the design parameters of the SAGM mission. The results show that the average acquisition time is less than 10 s for a scanning range of 1-mrad radius with a success rate of more than 99%.

Analysis of non-linearity in differential wavefront sensing technique.

An analytical model of a differential wavefront sensing (DWS) technique based on Gaussian Beam propagation has been derived. Compared with the result of the interference signals detected by quadrant photodiode, which is calculated by using the numerical method, the analytical model has been verified. Both the analytical model and numerical simulation show milli-radians level non-linearity effect of DWS detection. In addition, the beam clipping has strong influence on the non-linearity of DWS. The larger the beam clipping is, the smaller the non-linearity is. However, the beam walking effect hardly has influence on DWS. Thus, it can be ignored in laser interferometer.

Note: Inter-satellite laser range-rate measurement by using digital phase locked loop.

This note presents an improved high-resolution frequency measurement system dedicated for the inter-satellite range-rate monitoring that could be used in the future's gravity recovery mission. We set up a simplified common signal test instead of the three frequencies test. The experimental results show that the dominant noises are the sampling time jitter and the thermal drift of electronic components, which can be reduced by using the pilot-tone correction and passive thermal control. The improved noise level is about 10(-8) Hz/Hz(1/2)@0.01Hz, limited by the signal-to-noise ratio of the sampling circuit.

A dual-heterodyne laser interferometer for simultaneous measurement of linear and angular displacements.

Picometer laser interferometry is an essential tool for ultra-precision measurements in frontier scientific research and advanced manufacturing. In this paper, we present a dual-heterodyne laser interferometer for simultaneously measuring linear and angular displacements with resolutions of picometer and nanoradian, respectively. The phase measurement method is based on cross-correlation analysis and realized by a PXI-bus data acquisition system. By implementing a dual-heterodyne interferometer with a highly symmetric optical configuration, low frequency noises caused by the environmental fluctuations can be suppressed to very low levels via common-mode noise rejection. Experimental results for the dual-heterodyne interferometer configuration presented demonstrate that the noise levels of the linear and angular displacement measurements are approximately 1 pm/Hz(1/2) and 0.5 nrad/Hz(1/2) at 1 Hz.

Fundamental limits on the digital phase measurement method based on cross-correlation analysis.

Ultra-precision phase measurement is a key technology for state-of-the-art laser interferometry. In this paper we present a fully digital phase measurement method based on cross-correlation analysis, and analyze the measurement errors caused by sampling quantization, intrinsic white noise and non-integral-cycle sampling. The last error source results in a cyclic error that has not been reported ever. We used a high-performance data acquisition system to carry out the cross-correlation-based phase measurement, and obtained a noise level of 1.2 × 10(-6) rad/Hz(1/2)[commercial at]1 Hz. Moreover, the cyclic phase error of about 10(-2) rad/Hz(1/2), caused by non-integral-cycle sampling, had been observed. In order to demonstrate the application of this precision phase measurement method, an ultra-precision heterodyne laser interferometer, consisting of digital phase measurement system and ultra-stable optical bench, was constructed for displacement measurement. The experimental results showed that a measurement resolution of 63 pm had been achieved.