Thanks, I will have a look at these. I would like to understand FT, but I would need to understand it to a level where I knew the equations represent a physical reality. With ray tracing and simple addition of wavefronts, I know what I am doing because I avoid the mathematical sophistication. Whereas with FT, I can google some code and use it, but i can't check my own work yet.
For example, with my program I can compare the Airy disc of my current telescope to a larger one I am thinking of buying:
With the curve fitting however, all I am trying to do is get back to a sine curve from a minimum number of samples with least effort. At the moment, I am just getting amplitude by brute force by calculating lots of samples.