The aperture function cuts off beams scattered above a certain critical angle (given by the objective pole piece for ex), thus effectively limiting the attainable resolution. However it is the envelope function E(u) which usually dampens the signal of beams scattered at high angles, and imposes a maximum to the transmitted spatial frequency.
The aperture function confines beams scattered beyond a certain threshold angle (defined by the objective pole piece for ex), thereby constraining the attainable resolution. Conversely, it is usually the envelope function E(u) that reduces the signal strength of beams scattered at high angles and sets a limit on the transmitted spatial frequency.