I just started going through this older discussion: What does diffuse or sharpen really do? - #20 by afre. I wonder if the proposed order namings are incorrect, for two reasons:
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If each order is a different mathematical function, does that map onto detail scales? Why? (I get that each subsequent derivative can refer to change on a larger scale, but if there are different types of functions at play is that still the case?)
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The presets for lens sharpening (iirc) have positive slider values for the odd orders and negative values for the even orders. That implies they are different in kind, not just for a different scale. Unless these presets are “magic” that happens to work rather than being a rational design?