Get position of different frequencies in sound signal
I don't understand the interferometer setup but have a look at:

Eric Jacobsen &amp; Richard Lyons. DSP Tips &amp; Tricks: The Sliding DFT. IEEE Signal Processing Magazine, March 2003, pp 74–80.

Eric Jacobsen &amp; Richard Lyons. DSP Tips &amp; Tricks: An Update to the Sliding DFT. IEEE Signal Processing Magazine, January 2004, pp 110–111.

You can use the sliding DFT (discrete Fourier transform) to calculate a windowed DFT starting at the time of each sample, not for all frequencies but for just the frequency you are interested about. See the subsections about generalized cosine windows in Wikipedia for the kind of windows that work with sliding DFT. Perhaps you can then use the magnitude and phase information from sliding DFT for your task.