High-resolution Interferometric Diagnostics for Ultrashort Pulses

5.6 Effect of miscalibrationy (pix)1000−100(a)y (pix)1000−100(b)ky (rad/pix)0.20.10−0.1(c)−0.2−200−2002.3 2.4−1000 0 10002.3 2.4ω (rad/fs)t (fs)ω (rad/fs)Figure 5.8: Angularly dispersed pulse reconstructed using ST-SPIDER. (a) Spatio-spectralphase, colour scale wrapped to [−π,π]. (b) Spatio-temporal intensity, linear colour scale. (c)Wavenumber-spectral intensity, linear colour scale.delay error τ produces an erroneous quadratic phase. Analogously, in spatial shearing interferometry,an incorrectly calibrated tilt δ produces an erroneous quadratic phase. In the compactST-SPIDER, one must distinguish between carrier errors that are common to the fundamental andupconverted interferogram, and errors that are different.If a time-delay error is common to the fundamental and upconverted interferograms, as is alwaysthe case when the two are acquired simultaneously, then the subtraction step (5.5) removesthe time-delay error from the upconverted interferogram. This mode of time-delay error thereforedoes not produce an erroneous quadratic phase. However it does affect the spatial phase reconstructionin a subtle way. The introduced linear spectral phase is Γ y (ω,y )=τω + n2π, where anunknown integer multiple of 2π is included because the phase is only obtained modulo 2π. Spatialconcatenation of this erroneous term givesφ(ω,y )= τωyY+ n2πyY. (5.12)The first term corresponds to a beam tilt — purely a rotation of the co-ordinate system. Thismay or may not be important but is not normally considered a distortion. In particular it does121