High-resolution Interferometric Diagnostics for Ultrashort Pulses

5.4 A common-path re-imaging ST-SPIDER(a)(b)OYBAMZIθTfDθ = 0,T = 0 θ = 0,T = 0 θ = 0,T = 0yyyωωωFigure 5.4: (a) Re-imaging LSI. The reflections caused by the mirrors of the A arm of the MZIhave been applied, so that the beam traversing the A arm (red) travels in a straight line. The lensre-images object plane O onto the spatially and spatially resolving detector D. A delay T , tilt θand shear Y is applied to the B arm output (blue). Some B arm outputs for different settings ofshear and tilt (purple and green) are drawn for explanatory purposes in the text. (b) Sample fringepatterns for different interferometer settings.the object plane. The spatio-spectral intensity profile of this virtual interferogram is re-imaged toD. This leads to the general result that LSI with a lens between the interferometer and the detectorreturns the phase of the field at the plane conjugate to the detector, with a spatial magnificationfactor. This may be generalized to an arbitrary imaging system. The spatial resolution is limitedby the numerical aperture as seen from the object plane.Figure 5.4(b)–(d) shows the nature of the interferograms formed for different delays and tilts.In particular, note Fig. 5.4(b) in which no tilt is applied and the fringes are purely spectral. Thisis somewhat counterintuitive since, as the purple line in Fig. 5.4(a) shows, even with no tilt in theinterferometer the beams cross with a tilt in the detector. The paradox is resolved by consideringthe effect of the quadratic phase resulting from imaging O on D. This quadratic phase causes alinear term in the lateral shearing interferogram which exactly cancels the linear phase resultingfrom the tilt.5.4.2 Calibration phaseAs is common in SPIDER, the reference phase is recorded using the fundamental interferogram.The calibration phase should purely reflect the geometry and be independent of the unknownpulse. It therefore must be taken at zero spatial shear. If the spatial shear can be adjusted withoutchanging the time delay, then this is straightforward. A more precise method is to double-pass theinterferometer, a technique I shall now describe.113