I wrote a small FFT library to support an experimental game idea. (Github)
The library supports image FFT's, as well as visualising them in the canonical way. (Shifted so the largest values are in the centre and log-scaled values) It uses the Cooley-Tukey algorithm, which is not the fastest possible, but it is fast enough to sketch out most ideas, and remains simple. (Under 150 lines for the 1D function + ~100 for the 2D functions)
The API is very much fit for the specific purpose I was using it initially, but I plan on going back and generalizing it soon.
It is written in the JAI language which as of the publishing of this page the language is not openly-available. However, I must say, it is a joy to work in and I highly recommend giving it a try once it leaves closed-beta.