I understand from the derivation in Goodman Chapter 6 that a lens Fourier transforms light from the front focal plane onto the back focal plane, ignoring aperture effects. I've also read that a lens acts as a low pass filter, effectively masking the image in the back focal plane. It seems then that for an object located in the front focal plane, the back focal plane should reveal the Fourier transform of the object multiplied by a masking function which sets the image to zero at radii outside the mask that correspond to high frequencies in the object.
Simple multiplicative masking in the back focal plane to account for aperture effects rooted in the finite size of the lens seems strange to me. It would make more sense to me that a lens operates by masking the field present at the plane of the lens. Then this masked field would be further propagated from the lens plane to the back focal plane via the Fresnel diffraction formula which yields a more complicated expression than simply the Fourier transform of the object multiplied by a mask.
Can someone help me resolve the confusion? How is masking at the objective plane equivalent to masking at the back focal plane? In essence how is it possible that a lens acts as a low pass filter between the focal planes?