Velocity demodulation of near-field time-stretched photon Doppler velocimetry system uses Gerchberg–Saxton algorithm

In the transient high-speed measurement scene, time-stretched dispersion Fourier transform technology is presented as an effective solution to reduce the bandwidth limit of electrical digital-to-analog conversion devices, which can realize the mapping from frequency domain to time domain by introducing sufficient amount of group time delay by dispersion elements, such as single-mode fibers. However, the introduction of long-distance single-mode fiber greatly reduce the intensity of optical signal. In our work, we introduce the Gerchberg-Saxton phase recovery algorithm into the velocity signal analysis to recover the interference signal from the two sufficient diversities incompletely stretched temporal envelope. The two envelopes are stretched by L₁=10 km and L₂=15 km single-mode fiber, which recorded with the dispersion D₁=180 ps/nm and D₂=270 ps/nm respectively. With the additional iterations, the phase error and magnitude tend to be stable, which are both below 0.3. We also compare the error of the algorithm under different dispersion ratios D(=D₁/D₂). The results show that the demodulated error will be affected by the change of the value of D. Our work lays a foundation for the subsequent debugging of the time-stretched photon Doppler velocimetry system, and also provides support for transient high-speed measurement.