Aperture Effect of Lens
- Practical Electron Microscopy and Database -
- An Online Book -

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In electron-optical systems, (as well as light-optical systems), lens can work as an aperture because it can constraint the incident wave front. This is more easily understood for light-optical systems because the aperture effect is due to the finite surface area of the optical lens;

Assuming the incident wave has a complex wave function just before the lens, given by,

             incident wave --------------------------- [4159a]

After the incident wave crosses the lens, the wave function becomes,

             After the incident wave crosses the lens, the wave function becomes, --------------------------- [4159b]

So that the aperture function of the lens is given by,

             Aperture function of lens ------------------- [4159c]

                    Aperture function of lens ------------------ [4159d]

where,
          D -- The diameter of the lens
          r -- The distance from the incident point to the optic axis of the lens (r = (x2+y2)1/2)

The lens behavior constraining the wave plane to r < D/2 is so-called aperture function of the lens. For electron-optical system, the absorption of the lens is zero so that a(x,y) = A2/A1 ≈ 1. Therefore, the lens function becomes pure phase function.

 

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