In a study published in Optics Communications, a research group led by YU Tao from the Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP) of the Chinese Academy of Sciences proposed a new analytical phase readout algorithm for deep frequency modulation interferometry (DFMI).

The method improves phase measurement accuracy and simplifies signal processing by eliminating the need to explicitly estimate modulation parameters. This offers a promising approach for developing compact interferometric measurement systems for space gravitational wave detection.

Space-based gravitational wave detection requires precise measurements of tiny changes in the distances between freely falling test masses. Laser interferometry provides a powerful means of detecting these minute displacements by measuring variations in optical phase. However, conventional interferometric systems often require complex optical arrangements and electronic components, creating challenges for spacecraft applications. DFMI offers a simpler alternative, but existing phase readout methods typically rely on estimating several modulation parameters before recovering the desired phase. Fluctuations and errors in these intermediate estimates can reduce measurement accuracy.

To address this limitation, the researchers developed an analytical algorithm that recovers the interferometric phase directly without explicitly estimating the modulation phase or depth. Rather than calculating these parameters separately, the researchers combined information from multiple harmonic components of the interferometric signal to eliminate their influence on the phase recovery process. This approach reduced the possibility of intermediate estimation errors propagating into the final measurement result.

The researchers established a phase recovery procedure combining harmonic signal processing and mathematical operations to suppress modulation-related disturbances. Then, they conducted numerical simulations under different modulation conditions, including phase fluctuations, transmission delays, and measurement noise. They evaluated the accuracy and stability of the proposed algorithm under conditions relevant to high-precision interferometric measurements by comparing it with a conventional stepwise phase recovery method.

The results showed that the proposed algorithm achieved a root-mean-square phase error of 2.362 μrad under the selected simulation conditions, which is approximately 52.78% lower than the error achieved with the conventional method. The measurement error approached the theoretical precision limit, demonstrating the efficient extraction of phase information from the interferometric signal.

In addition, the researchers designed a field-programmable gate array (FPGA)-oriented processing architecture and verified its functionality through fixed-point simulations, obtaining a phase error of 2.663 μrad. These findings indicate the potential of the algorithm for efficient hardware implementation.

This study offers a promising approach to improving the precision and efficiency of laser-based measurements for space gravitational wave detection. By enabling more accurate phase measurements with simpler signal processing, the new algorithm could help scientists detect the extremely small changes in distance caused by gravitational waves. It may also support the development of more compact and reliable measurement systems for future space missions.

Beyond gravitational wave detection, this method could contribute to advancements in high-precision laser interferometry and space-based scientific instruments, opening new possibilities for exploring the universe through increasingly sensitive measurements.