High-resolution Interferometric Diagnostics for Ultrashort Pulses

3. PHASE RECONSTRUCTION ALGORITHM FOR MULTIPLE SPECTRAL SHEARINGINTERFEROMETRY|E |(a)crbc|E |(b)rcbc0 2 4 6 8ωFigure 3.3: Schematic of a two-shear reconstruction procedure for a two-lobed spectrum where(a) one of the lobes is wider than the gap and (b) both of the lobes are narrower than the gap.The spectral amplitude (black, thick lines) is sampled (black dots) at frequencies separated by thesmall shear Ω 1 = 1. The arrows represent connections between different frequencies given by theshears; only a subset of these are shown. The small shear allows concatenation between adjacentsamples (blue arrows, labelled ’c’ for concatenation). The large shear Ω 2 = 2 bridges (red arrows,labelled ’b’ for bridge) the gap between the lobes. In (a), the absolute phase of the large shear canbe registered on one of the lobes (green arrows, labelled ’r’ for register) but in (b), no sufficientlywide continuous spectral region is available.(a)|E |R 2 GC 2GC 1|E |(b)R 3 GC 30 5 10ωFigure 3.4: Reconstruction procedure for a three lobed spectrum using three shears of size Ω k =1,2,3. (a) Incorporation of the second shear; the arrows represent the connection of frequenciesby the registration R 2 and generalized concatenation GC 2 steps. One of the pairs of frequenciesconnected by the first shear is also indicated (GC 1 ). (b) Incorporation of the third shear, using thesame notation as in (a).80