Derivatives?

[realWDC]

Thank you for your excellent works!
I searched and it seems Zernike derivatives have not yet been implemented. Any plans for that, or which part of the code could you suggest to modify for that purpose?

Thanks,
WDC

[jacopoantonello]

Hi! Yes, that'd be a useful feature. But at the moment I have no plans / time for it. There isn't support for that in the code. I guess the derivatives / integrals can themselves be expanded in Zernike coefficients. So some methods should be added that compute the vector of Zernike coefficients for the derivative out of a given vector of the coefficients of the original function to derive. Something like (zc_dx, zc_dy) = rzern.derivative(zc).

[realWDC]

Thank you for the reply! That is exactly how I ended up with.

Based on your code, I have implemented a derivative version for the real Zernike case. The idea is to have additional functions that:

• dZk_dr(): Computes the derivatives of Zk w.r.t. rho, which involves derivatives of radial() function.
• dZk_dtheta(): Computes the derivaives of Zk w.r.t. theta, which involves derivatives of angular() function.
• Combine dZk_dr and dZk_dtheta in a chain-rule sensoe to complish the full derivatives w.r.t. x and y.

I will likely submit a PR in near future when I have time to test it thoroughly ...

[sidgairo18]

@realWDC could you please share the above.
@jacopoantonello @realWDC also is there an existing implementation to compute the Curvature at a given point?

Thanks!