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This paper describes and demonstrates a single-shot, full-field (amplitude and phase) optical waveform measurement technique that utilizes interferometry, frequency-to-time mapping, and four-quadrature coherent detection. This generalized frequency-to-time-mapping technique and associated reconstruction algorithm does not need to satisfy the usual far-field (Fraunhofer) requirement for performing an optical Fourier transform (OFT), and therefore, it provides significant improvements in fidelity and record length compared with previous OFT-based methods. Different implementations of the method demonstrate polarization-diversified, real-time, single-shot measurements with optical bandwidths in excess of 560 GHz, signal powers as small as 25 μW, and extend record lengths to more than 3 μs. Results show the measurement of complex waveforms with time-bandwidth products in excess of 1 million.