# Frequency-Resolved Optical Gating Recovery via Smoothing Gradient

## TL;DR

This paper introduces a new algorithm for reconstructing ultrashort laser pulses from FROG data, which is more effective with incomplete data and is simple, scalable, and theoretically sound.

## Contribution

The paper proposes a novel smoothing gradient-based algorithm for FROG pulse recovery, improving performance with incomplete data and providing convergence guarantees.

## Key findings

- Outperforms state-of-the-art with incomplete FROG traces
- Computational cost comparable to existing methods
- Converges to critical points near the true solution

## Abstract

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.