We are measuring spectra using Thorlabs OSA which also provides the interferogram signal. We would like to retrieve information about the pulse in the time domain and the pulse coherence.
the interferogram measured by FTIR-based OSA provides exactly the same information as the usual spectrum. It is impossible to retrieve the pulse shape in time domain using only FTIR interferogram. Very clear and comprehensive discussion of this issue you can find in the book:
R. Trebino, "Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses" (Kluwer Academic Publishers 2000).
Particularly relevant chapter of this book you can download from: