# Using DSLP operand to find surface slopes, but the signs/results are confusing

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• Zemax Staff
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I'm finding the max and min slopes on a surface as reported by DSLP to be confusing. A spherical surface with high slopes is reporting a maximum of zero. And a Tilted surface, which is just a plane, is reporting two separate values for min and max. What am I seeing with this operand?

Userlevel 3
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You are seeing the mathematical, unitless slope of rise/run, or delta Z / delta R. However, notee that delta R, for the radial coordinate, is not the same as delta X or Y would be. It is radially directed outward from the center and always positive.

A positive curvature as understood in OpticStudio will also return a positive slope. The sag in Z is increasing as R increases, so for a spherical surface or other surface with all positive curvature, the lowest slope you can see is zero, at the axis. Likewise, for a negative curvature, zero is the highest you will see, also at the center (not accounting for displacements and such).

For the Tilted surface, a slope measured with respect to delta X or delta Y would have just a single slope, but again the slope is telling us what happens to the sag in Z as R increases. For a centered, non-displaced Tilted surface, this means half the surface will see increases in Z sag with R, and half will see decreases. So, the slope changes sign over part of the surface.

Once you keep this polar orientation in mind, the surface slopes should pose no confusion.