Generally, FFT is used to obtain the spectrum in the frequency domain. What are the informations we can get from the FFT analysis of a spectrum?
Which frequency bands contain the majority energy content of the signal
There are situations where the "spectrum" might be a spatial spectrum, for example an image in the focal plane of a lens. Using an (inverse) FFT, you could obtain the light field at the plane of the lens, which tells you something about the lens aberrations. Usually you don't have the phase of the field, just its intensity, so various tricks can be used to recover the phase. See https://en.wikipedia.org/wiki/Phase_retrieval
Hello Koustav
My reply will focus on the need for the Fast part of the Fast Fourier Transform (FFT), as I assume you already know what are the uses of Optical Fourier Transform.
In general, Fourier transforming a signal is a heavy computational operation of O(N^2) complexity, where N is the size of the signal you wish to transform. The FFT method is an approach to reduce that complexity to O(N log(N)) by a clever decomposition of the signal to halves, and recursive calculation of smaller and smaller FFTs.
You can imagine the enormous improvement in calculation times for large N, which is very important in the optical domain for fast acquisition and imaging purposes.
However, one has to remember the well known differences between the straight forward Fourier transform and the various FFT algorithms which arise from different partition of the Fourier kernels. In addition, note that FFT algorithms optimally work on signal size N which equals to some power of 2 (i.e. N = 2^p).
Regards,
Nati
Perhaps you know the Fourier transform spectrometer based on Michelson?
If you want your result in real time you use FFT
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