  Optical coherence tomography (OCT) has proven to be a powerful technique for
studying tissue morphology in ophthalmology, cardiology, and endomicroscopy.
Its performance is limited by the fundamental trade-off between the imaging
sensitivity and acquisition speed -- a predicament common in virtually all
imaging systems. In this paper, we circumvent this limit by using distributed
Raman post-amplification of the reflection from the sample. We combine the
amplification with simultaneously performed dispersive Fourier transformation,
a process that maps the optical spectrum into an easily measured time-domain
waveform. The Raman amplification enables measurement of weak signals which are
otherwise buried in noise. It extends the depth range without sacrificing the
acquisition speed or causing damage to the sample. As proof of concept,
single-shot imaging with 15 dB improvement in sensitivity at an axial scan rate
of 36.6 MHz is demonstrated.
