Theory of amplified dispersive Fourier transformation

Amplified dispersive Fourier transformation (ADFT) is a powerful technique that maps the spectrum of an optical pulse into a time-domain waveform using group-velocity dispersion (GVD) and simultaneously amplifies it in the optical domain. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector, greatly simplifying the system and, more importantly, enabling ultrafast real-time spectroscopic measurements. Here we present a theory of ADFT by deriving the general equation and spectral resolution for ADFT and studying the evolution of the pulse spectrum into time, the effect of GVD coefficients on ADFT, and the requirement for dispersion. This theory is expected to lend valuable insights into the process and implementation of ADFT.