High-resolution Interferometric Diagnostics for Ultrashort Pulses

7.4 Data processing200x (µm)00.10.7 0.90.50.30.10.10.7 0.90.50.30.10.30.9 0.7 0.50.30.9 0.7 0.5−200−15 −10 −5 0 5 10 15z (mm)Figure 7.5: Shape of A (blue) and B (red) laser focii in the gas jet; different scales are used for the zand x directions but otherwise the drawing is to scale. Contour lines indicated the intensity. Theextreme ends of the target scan range are indicated by the black rectangles. The central axes ofbeam B for the two extreme shear stage positions are indicated by the dashed black lines.image the focal plane onto a camera and scan the shear stage in the MZI back and forth — in thegeometric focus, the beam does not move.7.4 Data processing7.4.1 Extraction of phase differencesThe phase of each interferogram was retrieved using a minor variation on the usual Fourier-domainfiltering procedure. Figure 7.6(a) shows a typical raw interferogram. As usual with beams crossingat an angle, the fringe period is proportional to the wavelength, and this is particularly evident withthe broadband harmonic spectra. To obtain the best noise rejection, I first performed a discreteFourier transform (DFT) along the x-axis, yielding the transform shown in Fig. 7.6(b). I then appliedthe filter shown by the white lines Fig. 7.6(b). This isolated the sidebands and removed noiseat high and low vertical spatial frequencies. Then, I applied a DFT along the y -axis, yielding thetransform shown in Fig. 7.6(c). A second filter, indicated by the white lines, removed noise at highhorizontal spatial frequencies. Finally, a 2D inverse DFT brought the data back to the spatial domain.Taking the complex argument yielded the fringe phase, shown in Fig. 7.6(d).167