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fjablo wrote:
hm convex vs. concave sounds very clear to me whereas normal or reverse requires explanation. The V in convex even illustrates the shape of the DOF! 
Convex vs concave depend on the point of view (literally).
In the normal case (simple spherical lens), the lens is front-focusing at the side of the image.
This is called Petzval curvature:
https://en.wikipedia.org/wiki/Petzval_field_curvature
Most modern lenses correct this aberration to make the focus field more "planar" (hence the Zeiss definition).
However, in some circumstances, this correction may cause the FC to be reversed at the extreme borders.
Disclaimer: IANAOE (I am not an optical engineer), so feel free to correct / add.
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