A phase error of just 2.362 microradians may sound tiny, but it matters when scientists are trying to detect the minute changes in distance caused by gravitational waves. A research team in Changchun has developed a way to make that kind of measurement more accurate while reducing the steps needed to process the signal.
The work, published in Optics Communications, was led by Yu Tao at the Changchun Institute of Optics, Fine Mechanics and Physics, part of the Chinese Academy of Sciences. Space-based gravitational wave detectors rely on laser interferometry: they measure changes in the light’s phase to track tiny shifts between freely falling test masses. Building such instruments for spacecraft is difficult. Traditional systems can require complex optical setups and electronic parts, while errors in signal processing can make a faint measurement less reliable.
The team focused on deep frequency modulation interferometry, or DFMI, a simpler approach to interferometric measurement. Existing DFMI methods generally estimate several modulation settings first, then use those estimates to recover the phase. If the intermediate estimates are affected by noise or fluctuations, their errors can carry through to the final result.
The new algorithm takes a more direct route. It combines information from multiple harmonic components—repeating parts of the measured signal—to recover the interferometric phase without separately estimating the modulation phase or depth. By removing those steps, the method can avoid one source of error spreading through the calculation.
The researchers tested the approach in numerical simulations that included phase fluctuations, transmission delays and measurement noise. They compared it with a conventional, step-by-step phase recovery method. Under the selected simulation conditions, the new method produced a root-mean-square phase error of 2.362 microradians, about 52.78% lower than the conventional method’s error. The result approached the theoretical precision limit, the best accuracy expected under the model’s conditions.
The team also designed a processing layout aimed at a field-programmable gate array, or FPGA—a reconfigurable chip used to carry out calculations in hardware. Fixed-point simulations, which use numbers with set precision, produced a phase error of 2.663 microradians. That test suggests the method could be suited to efficient hardware processing, though it does not by itself demonstrate a working space instrument.
More accurate phase readings could help future missions distinguish the extremely small distance changes linked to gravitational waves. The algorithm may also be useful in other high-precision laser measurements and space science instruments. Its next promise lies in turning a cleaner calculation into compact, dependable hardware for the demanding conditions of a spacecraft.