Spherical lens elements are easy and cheap to produce and test, for manufacturers. But they have one problem: light rays at the periphery of the lens come to focus closer or further than those at the center (instead of all coming to focus at exactly the same point on the axis). This is called spherical aberration.
The central rays come to focus at one point, and the outer rays further up (or down) along the axis, creating a little blob of light around the central point. So a point in the image is imaged with a hazy halo, and really small detailed are slightly blurred and a light veil is visible, which uniformly softens the global contrast.
Spherical aberration produces a veil over highlights that can be difficult to tell from misfocusing. See below, a frame made at full aperture with the Leica Summicron-R 50/2 (full frame and enlargement).
Out of focus highlights are more useful tell-tales of the presence of spherical aberration. In a lens with spherical aberration, out of focus highlights have an outer ring instead of being uniformly bright. You can see this on the enlargement of the rev counter (speedo ?) and handlebars, below.
Combination of spherical aberration and chromatic aberration produces what is known as spherochromatisicm, which is characterised by out of focus highlights with a pinkish outer ring and greenish inner disk. This happens because spherical aberration is corrected to a different degree for various colours.
So, the best way to test for spherical aberration, in its various forms, if a lens if showing blurry images, if to shoot out of focus highlights and analyse the shape of the blur patterns.
Another symptom is uniformity over the field. While sharpness naturally declines from center to corner in almost all lenses, spherical aberration is more constant all over the frame. And it disappears when you stop down.
Spherical aberration is highly desirable in some lenses, because it softens the look of the image. The Leica Summicron-R 50/2 mentioned above is loved because if its ability to produce a soft-ish image wide open and critically sharp one closed down. An artist lens. See the image below, made with the same lens at f/8 and sharp enough to cut through steel.
Not all lenses with spherical aberration manage to sharpen-up so drastically, but stopping down the lens is essentially the only way to get rid of the aberration (it blocks-out the outer rays). It is almost impossible in post-processing.
Unfortunately, spherical aberration can be responsible for focus-shift, so make sure you refocus your shot if you stop-down.
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