Interesting topic, but one thing should be made clear for people without an engineering/applied mathematics background.

The FFT is not the same as the fourier transform. Most of the time the distinction is irrelevant, but in this case it truly does matter. The transformed signal measured with the lens is the result of a sampled continuous space fourier transform (CSFT). The FFT computed is the discrete space fourier transform. The two are not always equivalent.

I bring this up because the author uses the terms "fourier transform" and "FFT" interchangeably.