class openmc.ZernikeRadialFilter(order, x=0.0, y=0.0, r=1.0, filter_id=None)[source]

Score the $$m = 0$$ (radial variation only) Zernike moments up to specified order.

The Zernike polynomials are defined the same as in ZernikeFilter.

$Z_n^{0}(\rho, \theta) = R_n^{0}(\rho)$

$R_n^{0}(\rho) = \sum\limits_{k=0}^{n/2} \frac{(-1)^k (n-k)!}{k! (( \frac{n}{2} - k)!)^{2}} \rho^{n-2k}.$

With this definition, the integral of $$(Z_n^0)^2$$ over the unit disk is $$\frac{\pi}{n+1}$$.

If there is only radial dependency, the polynomials are integrated over the azimuthal angles. The only terms left are $$Z_n^{0}(\rho, \theta) = R_n^{0}(\rho)$$. Note that $$n$$ could only be even orders. Therefore, for a radial Zernike polynomials up to order of $$n$$, there are $$\frac{n}{2} + 1$$ terms in total. The indexing is from the lowest even order (0) to highest even order.

Parameters: order (int) – Maximum radial Zernike polynomial order x (float) – x-coordinate of center of circle for normalization y (float) – y-coordinate of center of circle for normalization r (int or None) – Radius of circle for normalization order (int) – Maximum radial Zernike polynomial order x (float) – x-coordinate of center of circle for normalization y (float) – y-coordinate of center of circle for normalization r (int or None) – Radius of circle for normalization id (int) – Unique identifier for the filter num_bins (int) – The number of filter bins