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cdtools/CDTools/tools/propagators.py
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"""This module contains various propagators for light fields
All the functions here are designed for use in an automatic differentiation
ptychography model. Each function implements a different propagator.
"""
from __future__ import division, print_function, absolute_import
from CDTools.tools.cmath import *
import torch as t
from scipy import fftpack
import numpy as np
__all__ = ['far_field', 'near_field',
'generate_angular_spectrum_propagator',
'inverse_far_field', 'inverse_near_field']
def far_field(wavefront):
"""Implements a far-field propagator in torch
This accepts a torch tensor, where the last dimension
represents the real and imaginary components of the wavefield,
and returns the far-field propagated version of it assuming it matches the
detector dimensions. It assumes that the
propagation is purely far-field, without checking that the geometry
is consistent with that assumption.
It also assumes that the real space wavefront is stored in an array
[i,j] where i corresponds to the y-axis and j corresponds to the
x-axis, with the origin following the CS standard of being in the
upper right. The zero frequency component of the propagated wavefield is
shifted to the center of the array.
Parameters
----------
wavefront : torch.Tensor
The JxNxMx2 stack of complex wavefronts to be propagated
Returns
-------
propagated : torch.Tensor
The JxNxMx2 propagated wavefield
"""
return fftshift(t.fft(ifftshift(wavefront), 2, normalized=True))
def inverse_far_field(wavefront):
"""Implements the inverse of the far-field propagator in torch
This accepts a torch tensor, where the last dimension
represents the real and imaginary components of the propagated wavefield,
and returns the un-propagated array.
It assumes that the real space wavefront is stored in an array
[i,j] where i corresponds to the y-axis and j corresponds to the
x-axis, with the origin following the CS standard of being in the
upper right. The zero frequency component of the propagated wavefield is
assumed to be the center of the array.
Parameters
----------
wavefront : torch.Tensor
The JxNxMx2 stack of complex wavefronts propagated to the far-field
Returns
-------
propagated : torch.Tensor
The JxNxMx2 exit wavefield
"""
return fftshift(t.ifft(ifftshift(wavefront), 2, normalized=True))
def generate_angular_spectrum_propagator(shape, spacing, wavelength, z, *args, **kwargs):
"""Generates an angular-spectrum based near-field propagator from experimental quantities
This function generates an angular-spectrum based near field
propagator that will work on torch Tensors. The function is structured
this way - to generate the propagator first - because the
generation of the propagation mask is a bit expensive and if this
propagator is used in a reconstruction program, then it will be best
to calculate this mask once and close over it.
Formally, this propagator is the complex conjugate of the fourier
transform of the convolution kernel for light propagation in free
space
Parameters
----------
shape : array
The shape of the arrays to be propagated
spacing : array
The pixel size in each dimension of the arrays to be propagated
wavelength : float
The wavelength of light to simulate propagation of
z : float
The distance to simulate propagation over
Returns
-------
propagator : torch.Tensor
A phase mask which accounts for the phase change that each plane wave will undergo.
"""
ki = 2 * np.pi * fftpack.fftfreq(shape[0],spacing[0])
kj = 2 * np.pi * fftpack.fftfreq(shape[1],spacing[1])
Kj, Ki = np.meshgrid(kj,ki)
# Define this as complex so the square root properly gives
# k>k0 components imaginary frequencies
k0 = np.complex128((2*np.pi/wavelength))
propagator = np.exp(1j*np.sqrt(k0**2 - Ki**2 - Kj**2) * z)
# Take the conjugate explicitly here instead of negating
# the previous expression to ensure that complex frequencies
# get mapped to values <1 instead of >1
propagator = complex_to_torch(np.conj(propagator))
return propagator.to(*args, **kwargs)
def generate_generalized_angular_spectrum_propagator(shape, basis, wavelength, propagation_vector, *args, **kwargs):
"""Generates an angular-spectrum based near-field propagator from experimental quantities
This function generates an angular-spectrum based near field
propagator that will work on torch Tensors. The function is structured
this way - to generate the propagator first - because the
generation of the propagation mask is a bit expensive and if this
propagator is used in a reconstruction program, then it will be best
to calculate this mask once and close over it.
Formally, this propagator is the complex conjugate of the fourier
transform of the convolution kernel for light propagation in free
space
This function is written to work on any wavefield defined on any
array of parallelograms. In addition, there is an assumed phase ramp
applied to the wavefield before propagation, defined such that a feature
with uniform phase will propagate along the direction of the
defined propagation vector. This helps simplify
Parameters
----------
shape : array
The shape of the arrays to be propagated
spacing : array
The (2x3) set of basis vectors describing the array to be propagated
wavelength : float
The wavelength of light to simulate propagation of
propagation_vector : array
The displacement to propagate the wavefield along.
tilt : float
The tilt, in radians, of the plane that the wavefield is defined on
Returns
-------
propagator : torch.Tensor
A phase mask which accounts for the phase change that each plane wave will undergo.
"""
ki = 2 * np.pi * fftpack.fftfreq(shape[0],spacing[0])
kj = 2 * np.pi * fftpack.fftfreq(shape[1],spacing[1])
Kj, Ki = np.meshgrid(kj,ki)
# Define this as complex so the square root properly gives
# k>k0 components imaginary frequencies
k0 = np.complex128((2*np.pi/wavelength))
propagator = np.exp(1j*np.sqrt(k0**2 - Ki**2 - Kj**2) * z)
# Take the conjugate explicitly here instead of negating
# the previous expression to ensure that complex frequencies
# get mapped to values <1 instead of >1
propagator = complex_to_torch(np.conj(propagator))
return propagator.to(**kwargs)
def near_field(wavefront, angular_spectrum_propagator):
""" Propagates a wavefront via the angular spectrum method
This function accepts an 3D torch tensor, where the last dimension
represents the real and imaginary components of the wavefield, and
returns the near-field propagated version of it. It does this
using the supplied angular spectrum propagator, which is a premade
phase mask.
Parameters
----------
wavefront : torch.Tensor
The JxNxMx2 stack of complex wavefronts to be propagated
angular_spectrum_propagator : torch.Tensor
The NxM phase mask to be applied during propagation
Returns
-------
propagated : torch.Tensor
The propagated wavefront
"""
return t.ifft(cmult(angular_spectrum_propagator,t.fft(wavefront,2)), 2)
def inverse_near_field(wavefront, angular_spectrum_propagator):
""" Inverse propagates a wavefront via the angular spectrum method
This function accepts an 3D torch tensor, where the last dimension
represents the real and imaginary components of the wavefield, and
returns the near-field propagated version of it. It does this
using the supplied angular spectrum propagator, which is a premade
phase mask.
It propagates the wave using the conjugate of the supplied phase mask,
which corresponds to the inverse propagation problem.
Parameters
----------
wavefront : torch.Tensor
The JxNxMx2 stack of complex wavefronts to be propagated
angular_spectrum_propagator : torch.Tensor
The NxM phase mask to be applied during propagation
Returns
-------
propagated : torch.Tensor
The inverse propagated wavefront
"""
return t.ifft(cmult(t.fft(wavefront,2), cconj(angular_spectrum_propagator)), 2)
# I think it would be worthwhile to implement an FFT-DI based strategy as
# well, especially for probe initialization where the propagation distance
# can be large relative to what the angular spectrum method can reliably handle