gives the radial Zernike polynomial .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- Explicit polynomials are given when possible.
- The Zernike polynomials are orthogonal with weight over the unit interval.
- ZernikeR can be evaluated to arbitrary numerical precision.
- ZernikeR automatically threads over lists.
Examplesopen allclose all
Basic Examples (4)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number input:
Evaluate efficiently at high precision:
Specific Values (5)
Values of ZernikeR at fixed points:
Value at zero:
Find the first positive minimum of ZernikeR[7,5,x ]:
Compute the associated ZernikeR[7,3,x] polynomial:
Different ZernikeR types give different symbolic forms:
Plot the ZernikeR function for various orders:
Plot the real part of :
Plot the imaginary part of :
Plot as real parts of two parameters vary:
First derivative with respect to r:
Higher derivatives with respect to r:
Plot the absolute values of the higher derivatives with respect to r:
Function Identities and Simplifications (2)
A function to convert a radial representation to a Cartesian one:
Visualize the combined effect of -astigmatism and -coma aberrations:
Properties & Relations (2)
Obtain sequence of Zernike polynomials from a generating function:
Compare to the directly computed sequence:
Radial Zernike polynomials are orthogonal on the unit interval with weight function :