High-resolution Interferometric Diagnostics for Ultrashort Pulses

3.7 Signal-to-noise ratio cost of acquiring multiple shears3.7 Signal-to-noise ratio cost of acquiring multiple shearsAcquiring multiple shears will generally add complexity to the apparatus and will reduce the SNRof the acquired data for a fixed set of measurement resources, such as acquisition time and detectorpixels — simply because more information must be acquired. For multi-shear to be beneficial,this must be more than offset by the gain in SNR of the reconstruction. In this section I considerthe general properties of various experimental implementations of multi-shear and discuss theSNR reduction that they entail. The multiple shear measurements may be acquired simultaneouslyor sequentially and I shall consider each case in turn.For simultaneous acquisition of the multiple shears, the loss of SNR in the raw data comesfrom two factors: the reduction in signal power caused by additional beam splitting to create theadditional shears and the reduction in detector SNR caused by the multiplexing of the additionalsignals. I consider each in turn. One must distinguish between the detector being near saturation,with additional signal input power available, or being below saturation at full input power so thatsensitivity is limiting the precision of the measurement.Simultaneous acquisition is possible by adding additional beam splitting optics to generatemore replicas. In conventional SPIDER, the unknown arm is split L ways and each replica mixedwith a single chirped ancilla, whereas in ZAP- and SEA-SPIDER, the chirped ancillas are split. Eitherway, the energy of the signal is proportional to 1/L, so that, for example, adding a third arm toprovide three shears gives a 33% reduction in signal. If detector sensitivity, rather than saturation,is limiting the measurement, this translates into a corresponding reduction in SNR. In general,each pair of replicas can interfere, yielding M = L(L − 1)/2 shears assuming the upconversionfrequencies are chosen to give no degeneracies.Assuming that the detector is completely filled, the multiple interferograms must then be multiplexed.One potential method is to use a carrier-division multiplexing scheme, in which eachinterference term has a different carrier such as time delay or, for spatially encoded arrangements,beam convergence angle. The various terms, each corresponding to different shears, are disjointin the Fourier domain and can be isolated by appropriate filtering. The detector resolution must81