High-resolution Interferometric Diagnostics for Ultrashort Pulses

5. COMPACT SPACE-TIME SPIDERtilt is applied in the interferometer, a lateral shear with zero tilt is what results on the detector. Inthe new design, this is not the case, because an imaging system separates the two. A lateral shearcauses both a shear and a tilt in the crystal plane, which is re-imaged onto the detector. Althoughthis hardly represents a drastic complication, I nonetheless found no analysis of the situation inthe literature. This section provides an intuitive understanding of LSI in such a configuration.The situation is depicted in Fig. 5.4(a). The MZI outputs two beams with a relative time delay,lateral shear and tilt. These pass through a lens and their interference pattern is detected by animaging spectrometer. (In fact, as with the new ST-SPIDER design, the plane may D may be reimaged,but this only results in a magnification of the interference pattern and so it suffices toanalyse the single-lens case.) In “normal” LSI, the measurement procedure is to set the device upso that the shear on the detector is zero, and thereby obtain the carrier phase which results fromthe tilt only. Then, the interferometer shear Y is adjusted to the desired setting. However, becauseof the lens, the tilt and shear of the beams in the detector plane are some linear combination of theshear and tilt leaving of the interferometer. Adjusting Y changes the tilt at the detector, as shownby the green and blue lines in Fig. 5.4(a), adding a linear spatial phase to the interferogram. Thereconstruction therefore acquires an additional quadratic term.Instead of calculating the amplitude of the quadratic term, insight is gained by observing thatthe lens is re-imaging some object plane O onto D. The position of D is given by the imagingequation. Of course, the interferometer may stand between O and D, as depicted in Fig. 5.4(a).However, by imagining that the interferometer were not there, one can find the intersections ofvirtual rays cast backwards (as in Fig. 5.4(a)) or forwards from the lens with plane O. One can alsobackpropagate the corresponding virtual fields of the two beams. The fields at D are identical (inamplitude and phase) to the virtual fields at O, except for a magnification and a quadratic spatialphase produced by the imaging. In particular, the sum of the virtual fields of the two beams atO is itself an interference pattern. The object plane and the interferometer lie in geometricallysimilar spaces — there is no lens in between. This means that the interference pattern at O maybe interpreted as a standard lateral shearing interferogram — adjustments to the interferometershear setting do not affect the tilt. For convenience, Y is defined as the separation of the beams in112