High-resolution Interferometric Diagnostics for Ultrashort Pulses

4. EXPERIMENTAL IMPLEMENTATIONS OF MULTIPLE SPECTRAL SHEARINGINTERFEROMETRY530(a)1.5(b)530(c)5201520ky (rad/pix)510500490ky (rad/pix)0.50−0.5y (pix)510500490480−1480470−1.5470450 500 550 600 650x (pix)−1 0 1k x (rad/pix)4.7 4.74 4.78ω (rad/fs)Figure 4.3: (Color online) (a) Raw SEA-SPIDER trace. (b) 2D discrete Fourier transform, showingfilter passband (black rectangle). (c) Amplitude of the sideband after filtering and inverse Fouriertransform.is contained in the spatial sidebands, lying above and below the baseband term in the Fourier domain,and one of these is isolated by applying the filter indicated by the overlaid rectangle. Thevertical stripe at k x = 0pix −1 is an artefact of the “dead rows” of the detector, which introducenoise at all vertical spatial frequencies. The Fourier filtering substantially reduces the influenceof these artefacts. After applying the filter and inverse Fourier transforming, the amplitude of theresulting interferogram is shown in Fig. 4.3(c). The SNR, defined here as the ratio of the maximumvalue of the signal to the RMS background noise level, was ≈ 50 before the filtering and ≈ 60 afterwards.For the noninterferometric images, obtained by blocking one arm and used for the shearcalibration and obtaining the unknown pulse spectrum, I performed a similar filtering procedureto isolate the baseband components and reduce noise.I performed all subsequent steps on lineouts taken at x = 0 µm, and subtracted the commonupconversion frequency of 2.380 rad/fs to produce spectra centered around 800 nm. I obtainedthe spectral intensity, shown in Fig. 4.4(a), from the spectra taken with the B arm blocked. For thefiltered interferometric phase, I subtracted the phase of the zero-shear interferogram to yield thecomplex valued {D k (ω)}, and then applied the algorithm of sections 3.5. The phase differences96