[0] http://en.wikipedia.org/wiki/Numerical_aperture -- Similar to f-number from photography, and describes how big the aperture of the lens is in relation to its focal length. Specifically, it's the sine of the angle from the optical axis to the ray extending from the focal point to the edge of the lens, for a single lens system.
From experience you are being overly conservative. Foremost polarization effects depend on the rigidity of your surface and the bandwidth of your light source. The correction is minimal. Most importantly oil immersion 1.4 NA is common and nobody complains.
>>Also, ignores that Fourier optics
Although there is another good point. After making the born approximation you get this kind of dish shape in the Fourier transform, but on the other hand the dish is compensated on both sides of the lense
#1: I made this more clear by saying that this holds for a lens with focal length f ... when d=f.
#2: I made the distinction between the DFT and CFT more clear. I never say they're the same thing, but that they are closely related.
#3: I added a paragraph about the complexity of the FT. Thank you for mentioning that.
#4: I didn't want to include the derivation -- I wanted to show the end result. I pointed the readers to Goodman if they want the derivation.
I also addressed the paraxial approximation in the footnotes as well.
#1. This relationship only holds at focal points
#2. Nothing to do with Fast Fourier Transform
#3. No mention of complex part of FT
#4. No derivation of why this is the case