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Odd aspheric surface

The odd aspheric surface is a surface of revolution whose sag is given by the sum of the standard conicoid sag expression plus a general polynomial in the radius r

z = { cr^2 \over
1 + \sqrt{ 1 - (1+k)c^2r^2}
}
+ a_1 r + a_2 r^2 + a_3 r^3 
+a_4 r^4 + \ldots

By setting the curvature c to zero, this surface may be used as a general power series surface of even order.

The odd aspheric surface does not permit paraxial analysis if the linear term is not zero. This is because the surface then has a "point" and the curvature at the axis is infinite. Odd aspheres are generally used in condenser applications, not imaging systems.

The polynomial coefficients are entered in the parameters section of the surface data editor.

See also