High-resolution Interferometric Diagnostics for Ultrashort Pulses

3.10 Summary, critical evaluation, and outlookconstruction done using smaller shears. I discussed the cost, in terms of measurement precision,of acquiring interferograms at several shears and then showed that even for a spectrum with nogaps, a multi-shear reconstruction yields superior precision. Finally I presented two numericalexamples, demonstrating the robustness of the preprocessing step and the performance improvementachieved by adding a second shear.There are nonetheless several limitations to the work presented in this chapter. The multipleshearalgorithm is considerably more complex than single-shear concatenation. Furthermore, itrequires the shears to be exact integer multiples of one another. In a practical situation where theshears are acquired sequentially by adjusting the apparatus, this requires the parameter (such asa delay stage position) which controls the shear to be calibrated in advance. Finally, the relativephase ambiguity, a motivation for developing the algorithm, is only resolved for spectral separationswhich are smaller than the largest continuous spectral region. For larger spectral nulls, theambiguity remains, in common with all known self-referenced method based on the second-ordernonlinearity [81].There are several immediate applications of the multi-shear algorithm. Many implementationsof SSI, such as spatially encoded arrangement SPIDER (SEA-SPIDER) [196] or methods whichprepare the ancillae using tunable spectral filters [288], allow the shear to be easily adjusted. Sequentialacquisition of multiple shears could potentially be automated in implementations basedon electro-optic modulation [289], in which the shear is proportional to the applied voltage. Finally,there are several implementations which acquire a range of shears simultaneously on a twodimensionaldetector [200, 282]. In these setups, the use of multiple shears will allow more complicatedpulses to be measured without losing precision.A possible extension to this algorithm is the ability to handle a set of shears which are not ininteger ratios. As discussed in section 3.4, expressing the phase differences (3.7) in terms of thesampled phase points {φ n } requires interpolation when the shears are not integer multiples of thesampling rate. Adhering to the assumption of finite support, the “correct” basis for interpolation91