That's a very informative article JerryLove thank you for sharing. I'm thinking of investing in a new camera some time in April hopefully, articles like these get me pretty excited I look forward to actually experiencing these things. In the mean time, I'm just trying to absorb what I can through what I read and pictures taken by others.
When I click on the link now, a month after it was posted, they seem to have removed the associated images from the article. I don't see the images referenced by JerryLove in the section on Distortion and Aberration, so I've no idea what he was referencing. But Distortion and Aberration, as discussed in the article, isn't really related to lens flare.
The part of that article that is related to flare has to do with lens coatings. Notice they point out that each surface can reflect at much as 5% of the light, and in a multi-element lens that doesn't have appropriate coating on each surface there might be nearly 50% of the light that enters the front element that is reflected off in the wrong direction and never makes it to the sensor! At exactly 50% would make an f/2.8 lens pass the same light as a perfect f/4 lens. But the bad part actually is what happens to the light that is reflected. Most of it hopefully lands on a black surfaced wall in the lens (a baffle) where it is absorbed.
But when it it reaches the sensor: Flare!
Most of such flare is spread out evenly, and will only be obvious as a lack of contrast. Light from the such reflections is cast into every shadow. So the lens will not only be darker than expected, it will exhibit low contrast.
And in certain circumstances the reflected light will bunch up in one place on the sensor, causing a more specific and visible flare. The most commonly seen examples are reflections that show the shape of the aperture. That happens with very bright light (the sun is directly in the frame, for example), and it is sometimes possible to actually count how many glass surfaces there are in a lens, because the shape of the aperture will reflect from each and every one of them!
With digital sensors we get another common type of flare that didn't exist with film. The sensor itself can reflect light back at the lens, and if the rear element of the lens is not properly coat it will in turn reflect it back at the sensor. With a bright scene (daytime sky for example) that might result if a rather large roundish blob of light near the center of an image. Several older lenses from the film era are relatively poor in this way.
Something to keep in mind then, is that not all flare is visible as a shape in an image. Flare usually manifests as lower contrast.