Abstract
Previously we showed that the "bootstrap method," a well-known statistical technique, can be used to automatically compute error bars in ultrashort pulse measurements using frequency-resolved optical gating (FROG) without the need for additional measurements or traditional error analysis. Here we extend the bootstrap method to pulse measurement in the presence of ambiguities, where traditional error bars would give misleading information. As a result, we provide a new approach to displaying this uncertainty, which nicely reveals the richness of information available (or perhaps unavailable) in a FROG trace (or other measurement) in the presence of ambiguities.
Highlights
IntroductionThe only available measure of an ultrashort laser pulse was the autocorrelation
For many years, the only available measure of an ultrashort laser pulse was the autocorrelation
The bootstrap technique applied to frequency-resolved optical gating (FROG) involves running the FROG retrieval algorithm numerous times for a given trace, but on a resampled data set from that trace each time
Summary
The only available measure of an ultrashort laser pulse was the autocorrelation. In the presence of this ambiguity, the bootstrap method, as previously described, would yield a nearly flat phase with increasingly large error bars as time (or frequency) approaches the plot edges This is in strong contrast to our knowledge of the pulse phase from the measurement, which is that it is quite accurately either one parabola or the other, and definitely not flat. We point out here that the bootstrap method in its most general form yields, error bars, and the entire probability distribution for each value.[8,9] With this observation, we show that plotting all of the retrieved intensity-and-phase solutions obtained from the bootstrap technique nicely reveals the true solution and its potential ambiguities It reveals the true probability distribution of the measured intensity and phase at each point and is the most general display of the rich information available for the pulse from the data. The remainder of this paper describes the details of the implementation of this more general approach to error in FROG measurements of ultrashort pulses
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