Overcoming the limitation of phase retrieval using Gerchberg-Saxton-like algorithm in optical fiber time-stretch systems.

We investigate the fundamental limitation of the full-field retrieval of optical pulses based on a time-equivalent Gerchberg-Saxton (GS)-like algorithm, in which the Fourier transformation of the temporal signal is performed by the group velocity dispersion (GVD) of optical fibers. The insufficient knowledge of the input pulse intensity fundamentally limited by the bandwidth of the photodetector influences the accuracy of the retrieved phase using the algorithm. To this end, we propose a modified GS algorithm, which involves multi-step intensity-only measurements, to mitigate this limitation. By studying the influence of spectral phase and amplitude modulations on the retrieval error, we show that the modified GS algorithm demonstrates a significant improvement in phase retrieval accuracy. More importantly, we anticipate the present study will provide valuable insight in understanding how the spectral variation generally influences the recovery accuracy in time-stretch-based GS algorithm, and thus identify its potential applications, particularly for those requiring ultrafast measurements.