Crate zernike[−][src]
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Zernike polynomials
Computes the Zernike polynomials according to Noll ordering:
| j | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | … |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| n | 0 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | … |
| m | 0 | 1 | 1 | 0 | 2 | 2 | 1 | 1 | 3 | 3 | 0 | 2 | 2 | 4 | 4 | 1 | 1 | 3 | 3 | 5 | 5 | … |
where n, m, and j are the radial order, the azimuthal order and the polynomial index, respectively
Functions
Surface filtering
Gram-schmidt ortho-normalization
Gram-schmidt ortho-normalization with dot product function
Returns the Zernike indices (j,n,m) for the first n_radial_orders
Orthonormal Zernike set
Orthonormal Zernike set
Zernike mode on a regular grid n_xy X n_xy
Zernike polynomial set
Surface decomposition
Surface decomposition
Returns the Zernike polynomial (j,n,m) value at the polar coordinates (o,r)