What's the limiting factor for electron microscopes' resolution?

You actually can't make a perfect optical lens either with regular matter. If you only have positive refractive indices (like all matter), it is mathematically impossible to eliminate all aberrations. This is why all non kid-toy optics use many glass elements. Each lens uses different types of glass as an additional variable to help remove the aberrations. Even then, you cannot make a perfect image, just push closer to it.

E.g.: You have a convex lens that has a lot of chromatic aberration and a little spherical. You make it focus too hard and follow it up with a concave lens of a different material. The different refractive index gives it much stronger spherical and chromatic aberration compared to the first material, allowing it to largely cancel those terms out while not completely undoing the light bending of hte first lens. However, you've now introduced 2nd order spherical and chromatic aberrations. You can use additional elements to correct for those but then you get other aberrations. It never ends. All you can do is try and minimize the issues. I messed around with teaching myself lens design several years ago and its like a game of whack-a-mole. You fix one problem and another pops up somewhere else.

This is why things like telephoto zoom lenses can have literally dozens of glass elements in them to chase down all the aberrations over a wide range of incoming light angles. I can't even begin to fathom how they design those things. A fixed focal length design is hard enough.

The only exception is the newer science of metamaterials which allow you to basically cheat a negative refractive index. this has been done extensively in microwaves since the metamaterials are actual electromagnetic resonators in arrays. Since microwaves have large wavelengths, it is possible to make the resonators small enough.

Last I heard, the tech was working into some IR wavelengths but we're a long way from being able to do this in visible wavelengths.

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