Off-axis Conic

Question

I'm running opticstudio 20.2.2 and don't understand the help about the off-axis conic freeform surface. Opticstudio help on this surface type says it is governed by 'equation 5', which I've transcribed below:
z_f(r) = w(r) + A_1 x^2 + A_2 y^2 + ....
The terms listed in the lens-data editor are presented as XnYn where n is an integer from 0 to whatever # of terms you like.
So, what is the relationship between the A_n coefficients in the documentation and the XnYn coefficients in the lens data editor? Note the A coefficients start at the second power of x. I.e. is the equation something like
z(r) = w(r) + X1Y0 x^2 + ...
or
z(r) = w(r) + X1Y0 x^1 y^0 + XiYj x^i y^j + ...
It would also be great if it was possible to get the same surface but as a radius instead of x/y.

Angel Morales · Accepted Answer

Hi Nick,Just wanted to quickly confirm to you that your understanding is correct: A_1 (the first polynomial term) = X1Y0, A_2 = X0Y1, and so on.Let us know if you have any further questions here. Thanks!~ Angel

Ali H · Answer

Hi Nick,I have checked with the developer that worked on the Off-axis Conic Freefrom Surface, and unfortunately, the equation reported in the Help File is incorrect; however, the column headings in the Lens Data Editor are correct:Just to be clear, the relationship between the coefficients is,z(z) = w(r) + A_1x + A_2y + A_3x^2 + A_4xy + A_5y^2 + A_6x^3 + ...I can only apologize for the erroneous equation in the Help File.I have requested a change to the Help File so that this will be corrected for future releases of OpticStudio.Best,Ali

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