Hi Zemax engineer,
I’m studying the KA-01675 about tolerance analysis. I’m confused about the following explanaiton.
It’s difficult to understand the word “degenerate”.
Best answer by Mark.Nicholson
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Userlevel 7
+3
‘Degenerate’ in this context means ‘indistinguishable’. I hate the use of this word in scientific contexts, as it’s never used in non-scientific contexts to mean this. You’ll find it in Degenerate Four-Wave Mixing, for example.
Hope I didn’t write that KB article 
Hi Mark,
Does it mean either “tilt”or “decenter”is sufficient for the surface tolerances?
Userlevel 7
+3
Yes. The bottom line is, for a spherical surface, use either tilt or decenters, but not both.
For a parabola, there is a single axis of rotation that you can separately decenter and tilt, and that’s generally true for rotationally-symmetric aspheres. But you can draw an many axes as you like through a sphere: there’s no single axis of rotation. Hence tilts and decenters are degenerate, indistinguishable, for a sphere.
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