High-resolution Interferometric Diagnostics for Ultrashort Pulses

7.5 Comparison of results with simulationerror. Only for the highest harmonics at the extremes of the gas jet scan, where the signal was extremelyweak, did shot-to-shot fluctuations dominate the error. Therefore, in estimating the uncertaintyof the reconstructed phase, it was necessary to include χ 2 redin the variance as describedin section 7.2.2 for most calculations.7.4.3 Extraction of intensity profilesFar-field spatial profiles were obtained by subtracting the background image from the B arm images,which were taken for every shear stage setting and gas jet z -position. A typical raw imageis shown in Fig. 7.10. I averaged the profiles across each harmonic, and then averaged across the10 shots taken at each gas jet position and shear combination. I also moved each image by theopposite of its displacement x d to undo the effect of the shear. A sample set of results, taken atdifferent shears but at the same gas jet z position, are shown in Fig. 7.11.As with the phase reconstructions, there were significant shear-to-shear variations. However,unlike in the phase reconstructions, these cannot be attributed to the presence of the A beam,since it was blocked for the intensity measurements. Instead, I attribute these fluctuations to driftsin the laser power on the approximately 30 s timescale between shear measurements. Similarfluctuations were observed in the harmonics from A arm, which was also recorded at every shearposition but remained stationary throughout the measurement. For consistency with the phasemeasurements, I averaged the intensity measurements across the different shears to produce a“grand average” for each harmonic at each gas jet position. The standard error (standard deviationdivided by square root of number of samples) of the shear average was taken as the uncertainty.7.5 Comparison of results with simulationFigure 7.12 presents the entire set of amplitude and reconstructed phase profiles.To interpret these results, I shall first show that they largely agree with the results of a simulation.With the help of the simulation, a physical interpretation will then be given. The simulationdetails are described in Appendix B. Because the spectral response of the spectrometer was unknown,I applied a scaling factor to each harmonic to obtain best agreement with theory. It must171