Clarifications on the 0.5 λ/NA resolution limit

Abbe’s reasoning behind his expression of the resolution limit can be seen from his 1876 letter to J. W. Stephenson. Helmholtz came up with the same resolution limit expression almost at the same time as Abbe in another way. The numerical aperture (NA ≡ n sin θ) part of the expression is a consequence of the sine condition, which must be fulfilled for aplanatic imaging.