openmc.ZernikeFilter¶
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class
openmc.
ZernikeFilter
(order, x=0.0, y=0.0, r=1.0, filter_id=None)[source]¶ Score Zernike expansion moments in space up to specified order.
This filter allows scores to be multiplied by Zernike polynomials of the particle’s position normalized to a given unit circle, up to a user-specified order. The standard Zernike polynomials follow the definition by Born and Wolf, Principles of Optics and are defined as
\[Z_n^m(\rho, \theta) = R_n^m(\rho) \cos (m\theta), \quad m > 0 Z_n^{m}(\rho, \theta) = R_n^{m}(\rho) \sin (m\theta), \quad m < 0 Z_n^{m}(\rho, \theta) = R_n^{m}(\rho), \quad m = 0\]where the radial polynomials are
\[R_n^m(\rho) = \sum\limits_{k=0}^{(n-m)/2} \frac{(-1)^k (n-k)!}{k! ( \frac{n+m}{2} - k)! (\frac{n-m}{2} - k)!} \rho^{n-2k}. \]With this definition, the integral of \((Z_n^m)^2\) over the unit disk is \(\frac{\epsilon_m\pi}{2n+2}\) for each polynomial where \(\epsilon_m\) is 2 if \(m\) equals 0 and 1 otherwise.
Specifying a filter with order N tallies moments for all \(n\) from 0 to N and each value of \(m\). The ordering of the Zernike polynomial moments follows the ANSI Z80.28 standard, where the one-dimensional index \(j\) corresponds to the \(n\) and \(m\) by
\[j = \frac{n(n + 2) + m}{2}. \]Parameters: Variables: - order (int) – Maximum 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
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classmethod
from_hdf5
(group, **kwargs)[source]¶ Construct a new Filter instance from HDF5 data.
Parameters: group (h5py.Group) – HDF5 group to read from Keyword Arguments: meshes (dict) – Dictionary mapping integer IDs to openmc.MeshBase objects. Only used for openmc.MeshFilter objects.
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to_xml_element
()[source]¶ Return XML Element representing the filter.
Returns: element – XML element containing Zernike filter data Return type: xml.etree.ElementTree.Element