High-resolution Interferometric Diagnostics for Ultrashort Pulses

7. LATERAL SHEARING INTERFEROMETRY FOR HIGH-HARMONIC GENERATION30(a)1330(b)y (mm)2010y (mm)2010025−2 −1 0 1 2x (mm)0−5 0 5Spat. freq in x (mm −1 )Spat. freq in y (mm −1 )100−10(c)Harmonic order152025(d)−5 0 5Spat. freq in x (mm −1 )−2 −1 0 1 2Divergence (mrad)Figure 7.6: Extraction of the interferogram phase. (a) Raw data, linear colour scale. The 13 th and25 th harmonics are indicated. (b) 1D-DFT along x-axis, and sideband filter (white lines). Colourscale is logarithmic in amplitude over a range of 10 3 . (c) 2D-DFT, with noise filter (white lines).Colour scale is logarithmic in amplitude over a range of 10 3 . (d) Phase of the resulting sideband.Linear colour scale over [−π,π]. The spectral and spatial calibration has been applied and thephase is only shown in regions with significant signal.One shear, for which I defined x d = 0, was taken as a common reference. The phase of thisshear was subtracted from all the others to give the phase differences. Figure 7.7(a) shows a typicalphase difference between two interferograms. The tilt on the fringes shows that they have a spectralcomponent, possibly caused by a time delay resulting from a stage translation error. I assumedthe time delay to be completely random, and did not try to infer any information from it. The resultis that the measurement did not retrieve the linear spatial phase component in the far field,or equivalently the source transverse position in the near field. This is analogous to the randomabsolute phase in a spectral phase interferometry for direct electric-field reconstruction (SPIDER)interferogram preventing the technique from retrieving the linear spectral phase, or equivalentlythe arrival time of a pulse. Instead, I set the absolute phase of every frequency, defined by an168