Newer
Older
# Copyright 2014 by Forschungszentrum Juelich GmbH
# Author: J. Caron
#
"""This module provides the :class:`~.Kernel` class, representing the phase contribution of one
single magnetized pixel."""
from pyramid import fft
__all__ = ['Kernel']
PHI_0 = 2067.83 # magnetic flux in T*nm²
class Kernel(object):
'''Class for calculating kernel matrices for the phase calculation.
Represents the phase of a single magnetized pixel for two orthogonal directions (`u` and `v`),
which can be accessed via the corresponding attributes. The default elementary geometry is
`disc`, but can also be specified as the phase of a `slab` representation of a single
magnetized pixel. During the construction, a few attributes are calculated that are used in
the convolution during phase calculation in the different :class:`~Phasemapper` classes.
An instance of the :class:`~.Kernel` class can be called as a function with a `vector`,
which represents the projected magnetization onto a 2-dimensional grid.
Attributes
----------
a : float
The grid spacing in nm.
Dimensions of the 2-dimensional projected magnetization grid from which the phase should
be calculated.
dim_kern : tuple of int (N=2)
Dimensions of the kernel, which is ``2N-1`` for both axes compared to `dim_uv`.
dim_pad : tuple of int (N=2)
Dimensions of the padded FOV, which is ``2N`` (if FFTW is used) or the next highest power
of 2 (for numpy-FFT).
dim_fft : tuple of int (N=2)
Dimensions of the grid, which is used for the FFT, taking into account that a RFFT should
be used (one axis is halved in comparison to `dim_pad`).
b_0 : float, optional
Saturation magnetization in Tesla, which is used for the phase calculation. Default is 1.
geometry : {'disc', 'slab'}, optional
The elementary geometry of the single magnetized pixel.
u : :class:`~numpy.ndarray` (N=3)
The phase contribution of one pixel magnetized in u-direction.
v : :class:`~numpy.ndarray` (N=3)
The phase contribution of one pixel magnetized in v-direction.
u_fft : :class:`~numpy.ndarray` (N=3)
The real FFT of the phase contribution of one pixel magnetized in u-direction.
v_fft : :class:`~numpy.ndarray` (N=3)
The real FFT of the phase contribution of one pixel magnetized in v-direction.
slice_phase : tuple (N=2) of :class:`slice`
A tuple of :class:`slice` objects to extract the original FOV from the increased one with
size `dim_pad` for the elementary kernel phase. The kernel is shifted, thus the center is
not at (0, 0), which also shifts the slicing compared to `slice_mag`.
slice_mag : tuple (N=2) of :class:`slice`
A tuple of :class:`slice` objects to extract the original FOV from the increased one with
size `dim_pad` for the projected magnetization distribution.
def __init__(self, a, dim_uv, b_0=1., geometry='disc'):
self.dim_uv = dim_uv # Dimensions of the FOV
self.dim_kern = tuple(2*np.array(dim_uv)-1) # Dimensions of the kernel
self.a = a
self.geometry = geometry
if fft.BACKEND == 'pyfftw':
self.dim_pad = tuple(2*np.array(dim_uv)) # is at least even (not nec. power of 2)
elif fft.BACKEND == 'numpy':
self.dim_pad = tuple(2**np.ceil(np.log2(2*np.array(dim_uv))).astype(int)) # pow(2)
self.dim_fft = (self.dim_pad[0], self.dim_pad[1]//2+1) # last axis is real
self.slice_phase = (slice(dim_uv[0]-1, self.dim_kern[0]), # Shift because kernel center
slice(dim_uv[1]-1, self.dim_kern[1])) # is not at (0, 0)!
self.slice_mag = (slice(0, dim_uv[0]), # Magnetization is padded on the far end!
slice(0, dim_uv[1])) # (Phase cutout is shifted as listed above)
# Calculate kernel (single pixel phase):
coeff = b_0 * a**2 / (2*PHI_0) # Minus is gone because of negative z-direction
u = np.linspace(-(u_dim-1), u_dim-1, num=2*u_dim-1)
v = np.linspace(-(v_dim-1), v_dim-1, num=2*v_dim-1)
uu, vv = np.meshgrid(u, v)
self.u = fft.empty(self.dim_kern, fft.FLOAT)
self.v = fft.empty(self.dim_kern, fft.FLOAT)
self.u[...] = coeff * self._get_elementary_phase(geometry, uu, vv, a)
self.v[...] = coeff * self._get_elementary_phase(geometry, vv, uu, a)
# Calculate Fourier trafo of kernel components:
self.u_fft = fft.rfftn(self.u, self.dim_pad)
self.v_fft = fft.rfftn(self.v, self.dim_pad)
self._log.debug('Calling __repr__')
return '%s(a=%r, dim_uv=%r, geometry=%r)' % \
(self.__class__, self.a, self.dim_uv, self.geometry)
self._log.debug('Calling __str__')
return 'Kernel(a=%s, dim_uv=%s, geometry=%s)' % \
(self.a, self.dim_uv, self.geometry)
def _get_elementary_phase(self, geometry, n, m, a):
self._log.debug('Calling _get_elementary_phase')
if geometry == 'disc':
in_or_out = np.logical_not(np.logical_and(n == 0, m == 0))
return m / (n**2 + m**2 + 1E-30) * in_or_out
elif geometry == 'slab':
def F_a(n, m):
A = np.log(a**2 * (n**2 + m**2))
B = np.arctan(n / m)
return n*A - 2*n + 2*m*B
return 0.5 * (F_a(n-0.5, m-0.5) - F_a(n+0.5, m-0.5)
- F_a(n-0.5, m+0.5) + F_a(n+0.5, m+0.5))
def print_info(self):
'''Print information about the kernel.
Parameters
----------
None
Returns
-------
None
'''
self._log.debug('Calling print_info')
print 'Shape of the FOV :', self.dim_uv
print 'Shape of the Kernel:', self.dim_kern
print 'Zero-padded shape :', self.dim_pad
print 'Shape of the FFT :', self.dim_fft
print 'Slice for the phase:', self.slice_phase
print 'Slice for the magn.:', self.slice_mag
print 'Grid spacing: {} nm'.format(self.a)
print 'Geometry:', self.geometry