Lecture: Fourier Transforms

I just watched the lecture Melodie posted on Fourier transforms. One thing I learned was the different kinds of telescopes - I had no idea that some telescopes used three mirrors. A thing I like about the lecture was that it didn't delve too deeply into mathematical "grunginess," keeping things simple. However, that ties into something I disliked, which was the fact that some things felt too rushed. For example, I didn't really get a clear understanding of the physical meaning of the Fourier transform in regards to telescopes, or why we use it. A better explanation of the system being discussed would have been nice, as well as a quick derivation of some Fourier transforms.