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We are inspired by mechanical gearboxes and demonstrate its analog counterpart in optics. We use nonlinear dispersion modes as "gears" to overcome the mismatch between the ultrahigh speed of optical data and the much slower sampling rate of electronic digitizers and processors. We delineate the mathematical foundations and show its utility in ultrafast optical measurements and digital image compression., Comment: Corrected affiliation

We introduce the concept of coherent temporal imaging and its combination with the anamorphic stretch transform. The new system can measure both temporal profile of fast waveforms as well as their spectrum in real time and at high-throughput. We show that the combination of coherent detection and warped time-frequency mapping also performs time-bandwidth compression. By reducing the temporal width without sacrificing spectral resolution, it addresses the Big Data problem in real time instruments. The proposed method is the first application of the recently demonstrated Anamorphic Stretch Transform to temporal imaging. Using this method narrow spectral features beyond the spectrometer resolution can be captured. At the same time the output bandwidth and hence the record length is minimized. Coherent detection allows the temporal imaging and dispersive Fourier transform systems to operate in the traditional far field as well as in near field regimes.