Hi! I know Zemax has up to 231 Zernike terms for Zernike Standard sag value but I can’t find the Polynomial formula for terms higher than 37. Is there any way I could find what is the mathematical formula for higher order terms? thanks!
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Zernike Standard sag (terms higher than 37)
Best answer by Mark.Nicholson
Sorry, I misunderstood your question.
Go to Analyze...Wavefront...Zernike Standard Coefficients and set the maximum term to 231. The listing will give the functional form for each term, for example:
Z 226 0.00000000 : 42^(1/2) (190p^20 - 342p^18 + 153p^16) * COS (16A)
Z 227 0.00000000 : 42^(1/2) (190p^20 - 342p^18 + 153p^16) * SIN (16A)
Z 228 0.00000000 : 42^(1/2) (20p^20 - 19p^18) * COS (18A)
Z 229 0.00000000 : 42^(1/2) (20p^20 - 19p^18) * SIN (18A)
Z 230 0.00000000 : 42^(1/2) (p^20) * COS (20A)
Z 231 0.00000000 : 42^(1/2) (p^20) * SIN (20A)
+3Hi Nafiseh, try https://en.wikipedia.org/wiki/Zernike_polynomials, it gives the general convention.
Thanks but I am looking for a table with all of the terms. CodeV and Zemax have two different coefficient orders and I usually look at the formula to find which order they are using,
+3Sorry, I misunderstood your question.
Go to Analyze...Wavefront...Zernike Standard Coefficients and set the maximum term to 231. The listing will give the functional form for each term, for example:
Z 226 0.00000000 : 42^(1/2) (190p^20 - 342p^18 + 153p^16) * COS (16A)
Z 227 0.00000000 : 42^(1/2) (190p^20 - 342p^18 + 153p^16) * SIN (16A)
Z 228 0.00000000 : 42^(1/2) (20p^20 - 19p^18) * COS (18A)
Z 229 0.00000000 : 42^(1/2) (20p^20 - 19p^18) * SIN (18A)
Z 230 0.00000000 : 42^(1/2) (p^20) * COS (20A)
Z 231 0.00000000 : 42^(1/2) (p^20) * SIN (20A)
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