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I'm reading lens reviews and I have encountered the term 'centering quality' a few times (e.g. http://www.photozone.de/sony_nex/720-sony50f18nex?start=1).

What does this term mean? What are the factors that influence the effect?

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"Centering quality" is the degree to which the lens produces symmetrical focusing performance in all radial directions from the centre.That is, focus or resolution may change as you progress along a radial line from the centre, but in a perfectly centred lens the performance along all radial paths will be equal.

There's a reasonably good discussion here - Do it yourself centering sanity check .
The questions and answers are arguably as useful as the actual article.
The site provides a very simple template which can be printed to assist testing. In each test image 4 x black & white boundaries are arranged radially and the user assesses how sharp they are relatively.

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