TY - JOUR
T1 - Frequency-Resolved Optical Gating Recovery via Smoothing Gradient
AU - Pinilla, Samuel
AU - Bendory, Tamir
AU - Eldar, Yonina C.
AU - Arguello, Henry
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-To-implement. Empirically, our approach outperforms the state-of-The-Art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-The-Art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://github.com/samuelpinilla/FROG.
AB - Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-To-implement. Empirically, our approach outperforms the state-of-The-Art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-The-Art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://github.com/samuelpinilla/FROG.
KW - FROG
KW - Pulse reconstruction
KW - phase retrieval
KW - smoothing gradient technique
KW - spectral algorithm
KW - ultrashort pulse characterization
UR - http://www.scopus.com/inward/record.url?scp=85077808745&partnerID=8YFLogxK
U2 - 10.1109/TSP.2019.2951192
DO - 10.1109/TSP.2019.2951192
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AN - SCOPUS:85077808745
SN - 1053-587X
VL - 67
SP - 6121
EP - 6132
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 23
M1 - 8890893
ER -