Frequency-sweeping interferometry for intersatellite baseline metrology in array telescope formation

Space-based distributed array telescope formations, through multi-telescope collaborative observation and long-baseline optical interferometry, can significantly enhance deep space exploration capabilities, providing key technological support for missions such as asteroid monitoring and the search for extraterrestrial life. However, the measurement and control performance of such formations is highly dependent on the precision of intertelescope baseline measurements. Frequency-sweeping interferometry (FSI) technology, with its significant advantages—including freedom from the ambiguity range limitation, capability for non-cooperative target measurement, strong anti-interference ability in complex space environments, and high maturity of core components—has emerged as the most promising technical approach for baseline measurement in space-based distributed array telescope formations. Nevertheless, advancing this technology toward aerospace engineering applications still faces two major challenges: suppressing optical frequency-sweep nonlinearity and eliminating dynamic ranging errors. Currently, using electro-optic modulation to generate highly linear, synchronized, symmetrically sweeping positive and negative sidebands—establishing a frequency-sweeping interferometry system based on electro-optic sideband modulation—represents an effective method to address the issues of sweep nonlinearity and Doppler dynamic error. However, frequency-sweeping interferometry systems based on electro-optic sideband modulation lack a traceable on-orbit optical frequency-sweep reference, making it difficult to ensure long-term stable measurement and accuracy maintenance on orbit. Therefore, further research into high-precision electro-optic sideband modulation-based frequency-sweeping interferometry methods with traceable sweep references is of great significance for advancing the development of baseline measurement technology for space-based distributed array telescope formations.

Recently, in a research article published in Space: Science & Technology, Academician Weimin Bao's team at Xidian University proposed a double-sideband frequency-sweeping interferometry (DSB-FSI) technique based on Fabry–Pérot (F-P) etalon calibration. The study established an intersatellite baseline measurement architecture comprising an electro-optic modulation-based double-sideband frequency-swept laser source module, an F-P etalon-based optical frequency-sweep rate calibration module, and an optical hybrid quadrature detection module. By acquiring beat signals generated by the symmetrically sweeping sidebands through quadrature detection, the Doppler error in dynamic ranging is eliminated. Online calibration of the optical frequency-sweep rate is achieved based on the time-domain intervals of the F-P etalon's resonance peaks. Experimental results demonstrate that the ranging system reduces measurement drift error from 20.11 μm to 13.38 μm over a 5.7 m baseline, improving stability by 33.47%. The ranging accuracy reaches 44.30 μm over a 10 m range. Within a velocity range of 5–20 mm/s, the system exhibits a displacement measurement linearity better than 0.99999, a velocity measurement deviation of less than −16.80 μm/s, and a vibration measurement error of less than 0.08 μm. This study provides a feasible technical solution for high-precision and stable intersatellite baseline measurement in the "MEAYIN" project.

First, the authors focused on the urgent need for high-precision, high-stability intersatellite baseline measurements in space-based distributed array telescope formations and proposed a frequency-sweeping interferometry (FSI) ranging technique based on electro-optic sideband modulation. As shown in Figure 1, in the "MEAYIN" project, multiple sub-telescopes must maintain a coplanar, cophased, and conformal formation configuration. The measurement precision and stability of the formation baseline directly affect the resolution of the distributed formation imaging system. Existing laser frequency-sweeping interferometry techniques face two major challenges: ranging errors introduced by sweep nonlinearity and dynamic error amplification caused by Doppler frequency shifts resulting from target motion. The research team proposed a frequency-sweeping interferometry ranging technique based on electro-optic sideband modulation. By applying electro-optic intensity modulation to a single-wavelength continuous-wave laser using a lithium niobate dual-drive Mach-Zehnder modulator (MZM), strictly synchronized, oppositely sweeping sidebands with extremely low sweep nonlinearity are generated. High-precision dynamic measurement and calculation of absolute distance to the target are achieved through optical quadrature detection, overcoming the ranging errors caused by sweep nonlinearity and Doppler frequency shifts.

Second, to address the lack of a frequency-sweep reference in the electro-optic sideband modulation-based frequency-sweeping interferometry ranging system, the authors innovatively introduced an F-P etalon to achieve online calibration of the optical frequency-sweep rate. As shown in Figure 2, when the positive and negative frequency-sweep sideband lasers are injected into the F-P etalon, two sets of periodic time-domain pulses are generated, corresponding to the optical frequency-sweep processes of the positive and negative sidebands, respectively. The frequency-sweep range between adjacent pulses corresponds to the free spectral range (FSR) of the F-P etalon, which is determined solely by the optical cavity length of the etalon. By measuring the time intervals between the pulse sequences, online monitoring of the optical frequency-sweep rate can be achieved, enabling precise compensation of the measurement results. Compared to alternatives such as gas absorption cells and optical frequency combs, the F-P etalon is a passive device characterized by a compact structure and high cavity length stability, resulting in lower system complexity and cost, as well as reduced difficulty for aerospace engineering implementation. As shown in Figure 3, the ranging system consists of core modules including a narrow-linewidth laser, an electro-optic modulation module, a quadrature photodetection module, and an F-P etalon. The relevant components have high technological maturity and demonstrate potential for aerospace engineering applications. The proposal of this online optical frequency-sweep rate calibration method lays a technical foundation for the on-orbit application of frequency-sweeping interferometry ranging technology.

Finally, the authors experimentally validated the online monitoring effect of the optical frequency-sweep rate and the measurement performance of the ranging system using the proposed method. Ranging experiments were conducted with a step size of 1 mm using a high-precision linear guided rail. As shown in Figure 4, the measurement results demonstrate that the maximum standard deviation of the electro-optic double-sideband frequency-sweeping interferometry ranging system is only 2.38 μm, which is far superior to the results obtained from single-sideband frequency-sweeping interferometry. The linearity of the displacement measurement results reaches 0.99998. As shown in Figure 5, in a one-hour continuous measurement experiment over a 5.7 m baseline length, the ranging fluctuation range without online optical frequency-sweep rate calibration using the F-P etalon was 20.11 μm. After online calibration, this fluctuation range was reduced to 13.38 μm, and the deviation distribution was concentrated from ±10 μm to ±5 μm. As shown in Figure 6, through metrological comparison with a commercial laser interferometer, the ranging system achieved a measurement accuracy of 44.30 μm over a 10 m range. In dynamic measurement experiments, the displacement measurement linearity of the ranging system was better than 0.99999 within a velocity range of 5–20 mm/s, with a maximum velocity measurement deviation of −16.80 μm/s. Within a vibration frequency range of 50–500 Hz, the amplitude measurement error was less than 0.08 μm, and the relative error was below 4.01%. The study also points out that the compensation effect of the optical frequency-sweep rate using this method is limited by factors such as the number of F-P pulses within the sweep bandwidth and the accuracy of peak extraction. Future work could further improve the long-term on-orbit compensation effect of the optical frequency-sweep rate and enhance the measurement performance of the ranging system by designing resonant cavities with higher spectral resolution and better environmental robustness of the optical cavity length, as well as by developing high-precision algorithms for pulse peak extraction. The frequency-sweeping interferometry ranging system with electro-optic sideband modulation, featuring an online traceable optical frequency-sweep rate established in this study, provides a feasible technical solution for high-precision and stable intersatellite baseline measurement in the "MEAYIN" project.

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