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And how did I correct the problem in the second image at the beginning of this page?
Firstly, don't think that it is a bug in POV-Ray. It isn't a bug, but a real problem caused be the lighting model used in the renderer engine that is quite difficult to surpass. It's not a problem in POV-Ray in particular, but a problem in raytracing in general. Every raytracer will have this same problem when using perturbed surface normals (unless there's some fix coded into it).
Perturbed surface normals are used, in fact, to simulate the perturbation of the surface itself. When calculating the lighting of the object, the surface normal perturbation will give the impression that the surface itself is perturbed (eg. in the images at the beginning of this page the sphere looks like it has a bumpy surface).
In triangle meshes the normal interpolation is used to simulate curvature of the surface (a curvature which actually isn't there).
However, since the normal vector perturbation doesn't affect the surface itself in any way, this kind of artifact will be the price to pay (another one is that although the surface looks bumpy or smooth, its silhouette will still look straight or polygonized, but this usually is not such a big problem).
This is a real problem that happens even to the best. For example, check this »IRTC winner image. Notice the straight shadow lines on the rocks (specially in the closest rock)?
However, there are certain things that can be done to alleviate the problem.
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