Hsien-Chi Yeh

TianQin: a space-borne gravitational wave detector

TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the major constituents of the experiments error budget and discuss the projects overall feasibility. Given the current level of technology readiness, we expect TianQin to be flown in the second half of the next decade.

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.

Intersatellite laser ranging with homodyne optical phase locking for Space Advanced Gravity Measurements mission

In this paper, we present the scheme and the preliminary results of an intersatellite laser ranging system that is designed for the Earths gravity recovery mission proposed in China, called Space Advanced Gravity Measurements (SAGM). The proposed intersatellite distance is about 100 km and the precision of inter-satellite range monitoring is 10 nm/Hz(1/2) at 0.1 Hz. To meet the needs, we designed a transponder-type intersatellite laser ranging system by using a homodyne optical phase locking technique, which is different from the heterodyne optical phase-locked loop used in GRACE follow-on mission. Since an ultrastable oscillator is unnecessary in the homodyne phase-locked loop, the measurement error caused by the frequency instability of the ultrastable oscillator need not be taken into account. In the preliminary study, a heterodyne interferometer with 10-m baseline (measurement arm-length) was built up to demonstrate the validity of the measurement scheme. The measurement results show that a resolution of displacement measurement of about 3.2 nm had been achieved.

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.

A self-analyzing double-loop digital controller in laser frequency stabilization for inter-satellite laser ranging

We present a digital controller specially designed for laser frequency stabilization in the application of inter-satellite laser ranging. The prototype of controller is developed using field programmable gate arrays programmed with National Instruments LabVIEW software. The controller is flexible, self-analyzing, and easily optimized with build-in system analysis. Application and performance of the controller to a laser frequency stabilization system designed for spaceborne scientific missions are demonstrated.

Note: Digital laser frequency auto-locking for inter-satellite laser ranging

We present a prototype of a laser frequency auto-locking and re-locking control system designed for laser frequency stabilization in inter-satellite laser ranging system. The controller has been implemented on field programmable gate arrays and programmed with LabVIEW software. The controller allows initial frequency calibrating and lock-in of a free-running laser to a Fabry-Pérot cavity. Since it allows automatic recovery from unlocked conditions, benefit derives to automated in-orbit operations. Program design and experimental results are demonstrated.

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 futures 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.

Development of a 170-mm hollow corner cube retroreflector for the future lunar laser ranging

Over the past 50 years, lunar laser ranging has made great contributions to the understanding of the Earth–Moon system and the tests of general relativity. However, because of the lunar libration, the Apollo and Lunokhod corner-cube retroreflector (CCR) arrays placed on the Moon currently limit the ranging precision to a few centimeters for a single photon received. Therefore, it is necessary to deploy a new retroreflector with a single and large aperture to improve the ranging precision by at least one order of magnitude. Here we present a hollow retroreflector with a 170-mm aperture fabricated using hydroxide-catalysis bonding technology. The precisions of the two dihedral angles are achieved by the mirror processing with a sub-arc-second precision perpendicularity, and the remaining one is adjusted utilizing an auxiliary optical configuration including two autocollimators. The achieved precisions of the three dihedral angles are 0.10 arc-second, 0.30 arc-second, and 0.24 arc-second, indicating the 68.5% return signal intensity of ideal Apollo 11/14 based on the far field diffraction pattern simulation. We anticipate that this hollow CCR can be applied in the new generation of lunar laser ranging.

A preliminary prototype of laser frequency stabilization for spaceborne interferometry missions

A preliminary prototype of spaceborne laser frequency stabilization system for inter-satellite laser ranging missions has been constructed and demonstrated on ground. The system is based on hydroxide-catalysis bonding and fiber optics. The laser frequency control is driven by an in-house-designed digital controller featuring self-analysis and auto-locking functions. Laser frequency noise less than 30 Hz/Hz1/2 from 0.7 Hz to 10 Hz has been measured by beat note analysis. The laser stabilization system has been tested on a laser interferometer test bed. Preliminary experimental results are reported in this paper.

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.