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

Abstract

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.

A Smoothing Stochastic Phase Retrieval Algorithm for Solving Random Quadratic Systems

“…x 2 , where dr(•, •) has been defined in (1). We also evaluated the performance using the empirical success rate for 100 Monte Carlo runs.…”

“…Phase retrieval is an inverse problem that consists of recovering a signal from the squared modulus of some linear transforms, which has proved efficient in in various applications such as, optics [1], astronomy [2] and X-ray crystallography [3,4,5,6]. Recent works [7,8,9] have been proposed to solve the phase retrieval problem by optimizing a non-convex and non-smooth objective function with a gradient descent algorithm based on the Wirtinger derivative with an appropriate initialization.…”

Reducing the variability in random-phase initialized Gerchberg-Saxton Algorithm

“…The decade of the 90's was specially productive due to the development of Personal Computers and Liquid Crystal Displays (LCDs) [2]. In the recent years, this application has become an increasing interest motivated, specially, by the display industry and 3D imaging systems, leading to an increment of the number of published works about this topic [3][4][5][6][7][8][9][10]. These fields, compared to planar optics, require an elevated number of pixels increasing notably the computation time.…”

Real-time characterization of spectral coherence of ultrafast laser based on optical time-stretch

“…While optical time stretch has opened a new avenue for spectrally-resolved single-shot characterization at an ultrahigh speed, majority of the existing effort focuses on intensity measurement and analysis [24][25][26][27]. Although phase retrieval from single pulses is possible with iterative computational techniques [28], the phase accuracy is inherently limited by the time-bandwidth product, not to mention that the increased experimental complexity due to the required multiple/cascaded measurements [29]. To date, there is apparently a missing element in the optical time stretch technique that enables ultrafast broadband pulse-to-pulse phase variation measurement in real-time.…”