The optimum aperture of a lens, i.e. the aperture at which it is sharpest, varies from lens to lens, but as a general rule it's between 1 and 3 stops down from the maximum aperture for the center of the field. Why is this?
First you have to understand that no lens is perfect. They all have aberrations which reduce their performance. Classically there are five so called "Seidel" aberrations. They are sometimes called third order aberrations based on the mathematics used to model them. They are:
- Spherical aberration
- Coma
- Astigmatism
- Field curvature
- Distortion
All lenses have these aberrations and they are worse in fast lenses. Stopping down a lens greatly reduces Spherical aberration and to a lesser extent reduced the effects of Coma, Astigmatism and Field curvature on image sharpness. Distortion is unaffected by aperture. A 6th aberration, Chromatic aberration, is to a first approximation unaffected by aperture too.