| Visualize the image of a single, perfect point. The waves emanating from from that point would be spherically symmetrical (think a 360deg "field of view"[0], whereas most lenses are <<90deg). Now, since optical paths are two-way, this also implies that forming a perfect point image requires perfectlu spherically symmetric wavefronts[1] converging to that point, causing all the waves to perfectly cancel out each other everywhere except at the image point. If you take away a slice of the wavefronts (i.e. block light with an aperture), the cancellations is no longer balanced, producing stray excitations at places that should be silent. (Think of it like squeezing a beer can with your hand causing it to spurt out of the sides) The large the slice of wavefronts you are missing, the greater the imbalance. The resulting artifact are oscillations on the size order relative to the waves' frequency. Basically, high NA means trying to capture as complete of the total wavefronts as possible to minimize the imbalance, and short wavelength means trying to keep the size of whatever artifact you do end up getting to be as small as possible. [0] In air quotes because FOV != NA. The main distinction is that FOV refers to the span of principal directions (i.e. how many points can you see), whereas NA means, given a point object, how complete of its total wavefronts are you capturing it, (i.e. how bright is any given one point) [1] Up to 2pi phase differential. If your signal is CW then multiples of 2pi is indistinguishable from being in phase, think Shannon Limit. This is why lenses work despite having path differential, because all that's important is that it's back in phase for the given wavelength even if shifted by multiple cycles. |
> Basically, high NA means trying to capture as complete of the total wavefronts as possible to minimize the imbalance, and short wavelength means trying to keep the size of whatever artifact you do end up getting to be as small as possible.
User "mk_stjames" pointed me to the answer which basically explains the equation for the above - https://news.ycombinator.com/item?id=40680072