|From:||Jose Ramom Flores das Seixas|
|Subject:||A new function for the Optics package|
|Date:||Sun, 21 Jul 2019 17:38:47 +0200|
|User-agent:||Mozilla/5.0 (X11; Linux x86_64; rv:60.0) Gecko/20100101 Thunderbird/60.8.0|
I have written a function that could be incorporated to the optics package. This new function calculates the Zernike polynomials and their partial derivatives in Cartesian coordinates, using a recursive algorithm described in reference .
I'm sending an attachment with three files:
It's the first time I've sent anything, so it's possible there
was some loose end left.
The main function has been checked by comparing it with the explicit expressions of the Zernike polynomials, and their partial derivatives, and the results obtained are coherent. I.e. the differences are either zero or very small, in the order of 1e-14.I also compared my function with zernike_cartesian.m, a function of the optics package written by Andreas Weber. The differences are either zero or very small. To my disappointment, the average execution times are similar. So the main improvement that introduces my function is the calculation of partial derivatives.
 Andersen T.B., Efficient and robust recurrence relations for
the Zernike circle polynomials and their
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