The time-stretch transform slows down broadband optical signals for capture by electronic instruments, and has brought forth MHz-rate imagers, OCT systems, and spectrometers, as well as photonically-enhanced ADCs. Conventionally, sufficient dispersion is required to bring the pulse into the temporal far-field so that the spectrum can be read as the temporal waveform. The Coherent Time-Stretch Transform obviates this requirement while simultaneously enabling high-throughput acquisition of complex optical fields in single-shot measurements. Full-field spectra are recovered via temporal interferometry on waveforms dispersed in the temporal near field. Real-time absorption spectra, including both amplitude and phase information, are acquired at 37 MHz.