## 5 Summary  
Several ultrashort pulse measurement techniques have attempted to solve the two-pulse measurement problem. The earliest attempt, Blind FROG, found limited application in characterizing fs-pulses, due to the existence of nontrivial ambiguities. The experimental apparatus and retrieval algorithm developed for Blind FROG, however, inspired other measurement techniques that can solve the two-pulse measurement problem. Based on the idea of Blind FROG, CRAB has performed simultaneous attosecond and femtosecond pulse retrieval. No nontrivial ambiguities are known in CRAB reconstruction, because the signal field generation mechanism takes a different form than that of the originally proposed sum-frequency-generation Blind FROG. The generalized projections reconstruction algorithm is robust and requires no extra information for the pulses to converge.  
For pairs of unknown fs-pulses, VAMPIRE was developed to avoid the nontrivial ambiguities found in Blind FROG. It introduces a spectral phase modulator and a temporal phase modulator into the experimental apparatus in order to break the symmetry of the measured spectrogram. These additional modulators add significant extra complexity to the apparatus, but they effectively remove the nontrivial ambiguities resulting from a symmetric spectrogram. The reconstruction algorithm applies the Gerchberg-Saxton algorithm to solve rows of 1D phase retrievals, which gives a reliable way to generate the initial guess. The spectra of both pulses are measured and used as the constraint in the problem. The SVD algorithm provides a fast and robust way to reconstruct the spectral phase information of the unknown pulses. However, the requirement of using the measured spectra of the unknown pulses as constraints adds additional complication to the VAMPIRE technique.  
A recently developed technique based on the original Blind FROG, called DB FROG, accomplishes the two-pulse measurement task without such constraints or complexity. It slightly modifies Blind FROG by adding an extra polarizer and an extra spectrometer to measure an extra FROG trace. The retrieval algorithm solves a pair of linked XFROG problems using a modified algorithm based on the standard XFROG one. The algorithm requires no additional information from the pulses and finds no nontrivial ambiguities, as determined from numerical simulations. If implemented in the PG geometry, there is no constraint on the spectra of the pulses, due to the unlimited phase-matching bandwidth of the nonlinear optical interaction. This implies that DB PG FROG can be used to measure pulse pairs at any central wavelengths and with any bandwidths.  
Ultrashort-pulse characterization techniques allow researchers to gain more understanding of their experimental tools. These advances in two-pulse measurement now permit ever more general and arbitrary pulse pairs to be measured. And in the near future, it may even be possible, using them, to measure extremely complex pulse pairs, such as supercontinuum and the seed pulse that generates it simultaneously on a single-shot.  
This work was supported by the National Science Foundation, Grant #ECCS-1028825, and the Georgia Research Alliance. The authors gratefully thank [PERSON] and [PERSON] for the insightful discussion and the help in manuscript preparation. They would also like to thank the OSAfor the permission to reprint Figures 2, 9-13 [18, 25, 26], and IOP for the permission to reprint Figures 3-8 [22, 24].