## 4 Double Blind FROG
Trace 2 and the improved version of \(E_{1}(t)\) (acting as the gate pulse) are used to retrieve \(E_{2}(t)\). After one complete cycle, both improved versions of \(E_{1}(t)\) and \(E_{2}(t)\) are used as the inputs for the next cycle. This process is repeated, until the two DB PG FROG traces generated from \(E_{1}(t)\) and \(E_{2}(t)\) match the experimentally measured traces, that is, the difference between the measured and retrieved traces is minimized. Standard noise-reduction and background subtraction are performed on the two measured traces before running the retrieval algorithm. The convergence of DB FROG is defined, similarly to other standard FROG techniques, by the G-error (the root-mean-square difference of the measured and retrieved traces), one for each DB PG FROG traces. The DB FROG algorithm was tested with simulated DB PG FROG traces. Complex pulses with time-bandwidth-products (TBPs) of \(\sim\)7 were successfully retrieved from simulated traces, even with 1% Poisson noise added to simulate experimental conditions. Figure 10 shows one of the pulse pairs. The traces yielded 0.085% G-error, which indicated a good fit. The retrieved pulses agreed very well  
Figure 10: Simulations of DB PG FROG for two complex pulses. The two “measured” traces (**a**) and (**c**) are shown in the traces labeled “Simulation”, and their retrieved traces (**b**) and (**d**) are shown to their immediate right. The retrieved intensities and phases are shown in (**e**) to (**h**) by the solid-color lines. The actual intensity and phase of the simulated pulses are shown as dashed black lines. Both of these simulated complex pulses have time-bandwidth products of about seven, and 1% additive Poisson noise was added to the simulated traces to simulate noisy measurements [25]. with the actual pulses used to generate the traces for retrieval. No nontrivial ambiguities were found in the numerical work, except for the well-known trivial ambiguities of most pulse-measurement techniques, the zeroth and first-order spectral phase. A pair of complex pulses was used to test its measuring ability. The measured and retrieved traces are shown in Figure 11. Trace 1 measured a chirped pulse train. It was generated by an etalon and chirped by 2 cm SF11 glass block. Trace 2 measured a chirped double pulse. It was generated by a Michelson interferometer with a tunable delay arm and chirped by 4 cm of SF11 glass. Both traces yielded G-error of \(\sim\)0.8%. Temporal intensity distortions were observed in both pulses, a well-known characteristic of chirped-pulse beating, as expected. Independent measurement of the spectrum made with a spectrometer for both pulses were plotted in black dashed-line. The spectral peak locations match very well between the DB PG FROG and spectrometer measurements, confirming that the retrieved pulses are indeed correct. After the demonstration of DB PG FROG to measure two unknown pulses with the same center wavelength and bandwidth, it was used to measure a pair of pulses with two different center wavelengths and bandwidths. This is an important feature of DB PG FROG, which the measurement of pulses without a precise phase-matching condition. The experimental setup (shown in Figure 12) is slightly modified from the original setup such that each beam path uses a separated pair of focusing and collimating lens to avoid chromatic aberration. The two-color measurement was made with a pair of pulses with center wavelengths of 400 nm and 800 nm (blue and red). The measured and retrieved traces are shown in Figure 13. A well-separated double pulse in red was generated by a Michelson interferometer, while the blue pulse was a simple pulse. The G-errors were 0.8% and 0.5% for the blue pulse and red pulse, respectively. The spectra of both red and blue pulses were measured independently and plotted in black dashed-lines. The spectral  
Figure 11: The measured trace for (**a**) a chirped pulse train and (**c**) a chirped double pulse.