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”.
Solved
spheric surface tilt and decenter tolerance
Best answer by Mark.Nicholson
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.
+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 
+3Yes. 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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