High-resolution Interferometric Diagnostics for Ultrashort Pulses

5.2 Role of the measurement planetral phase measurement because the data is one-dimensional, leaving another dimension free forspatial resolution if an imaging spectrometer is used. In principle, it could be combined with anyof the spatial phase methods described in Section 2.4.4. To date, however, the only demonstrationhas been that of Dorrer et al.[58, 59, 265] who combined spectral phase interferometry for directelectric-field reconstruction (SPIDER) with lateral shearing interferometry (LSI). This chapter developsthis combination.Before presenting the new apparatus, it is necessary to discuss a subtlety which arises whenspatial and temporal measurements are performed using separate devices.5.2 Role of the measurement planeIn spatio-temporal metrology, it is important to consider the object plane in which the measurementis being performed. This is because beams undergo diffraction as they propagate in freespace. For example, if a spectrally and spatially transform-limited pulse is passed through a thindiffractive element, then just after the element, the pulse possesses angular dispersion. Uponsubsequent propagation, the frequencies travel in different directions and arrive in different positions;the pulse has acquired spatial chirp. A space-time characterization occurs in some tranverseplane, and this plane must be specified, or at least kept in mind.This consideration also applies to purely temporal measurement because of the dispersion ofair. However dispersion is simply an multiplicative phase factor exp[i φ(ω)], whereas diffraction isa convolution with the spatial Fourier transform of the paraxial propagator exp(−ikT 2 z /k ), whichis frequency-dependent. In both cases, if the plane of measurement differs from the plane of interest,then numerical propagation can relate the two. However with diffraction the relation ismore complex, contravening the practical and philosophical principle that the mapping betweenexperimental data and the physical quantities should be as simple as possible.When the spatial and spectral phase profiles are being measured separately, differences betweenthe two planes of measurement warrant particular consideration. Consider the two measurementsφ(ω,x T ,z T )+f (ω) and φ(ω,x T ,z S )+g (x T ) at different planes z T (subscript T for transversespatial) and z S . To combine these measurements, they must be first specified at a common107