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cdtools/CDTools/tools/polarization/polarization.py
T

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Python

import numpy as numpy
import torch as t
# Abe - again, we don't need math here. replace with torch-native functions
# in all the definitions here. We have to use torch here if we want to be
# able to calculate derivatives w.r.t. the polarizer angle, say.
import math
from math import sin
from math import cos
__all__ = ['apply_linear_polarizer',
'apply_phase_retardance',
'apply_half_wave_plate',
'apply_quarter_wave_plate',
'apply_circular_polarizer',
'apply_jones_matrix',
'generate_linear_polarizer',
'generate_birefringent_obj']
# Abe - split these into two functions
# Note for the future: this function should
def generate_linear_polarizer(pol_angle):
single_angle = False
pol_angle = t.as_tensor(pol_angle).to(dtype=t.float32)
if pol_angle.dim() == 0:
pol_angle = t.unsqueeze(pol_angle,0)
single_angle = True
pol_angle_rad = t.deg2rad(pol_angle)
a = t.cos(pol_angle_rad) ** 2
b = t.sin(pol_angle_rad) * t.cos(pol_angle_rad)
c = b
d = t.sin(pol_angle_rad) ** 2
ab = t.stack((a, b), dim=-1)
cd = t.stack((c, d), dim=-1)
jones_matrices = t.stack((ab, cd), dim=-2)
if single_angle:
return jones_matrices[0].to(dtype=t.cfloat)
else:
return jones_matrices.to(dtype=t.cfloat)
def apply_linear_polarizer(probe, polarizer, multiple_modes=True, transpose=True):
"""
Applies a linear polarizer to the probe
Parameters:
----------
probe: t.Tensor
A (N)(P)x2xMxL tensor representing the probe, MxL - the size of the probe
The angle between the fast-axis of the linear polarizer and the horizontal axis
polarizer: t.Tensor
A 1D tensor (N) representing the polarizer angles for each of the patterns (or a single tensor of shape (1))
Returns:
--------
linearly polarized probe: t.Tensor
(N)(P)x2x1xMxL
"""
jones_matrices = generate_linear_polarizer(polarizer)
return apply_jones_matrix(probe, jones_matrices, transpose=transpose, multiple_modes=multiple_modes)
def apply_jones_matrix(probe, jones_matrix, transpose=True, multiple_modes=True):
# print('probe', probe.shape, 'jones matrix', jones_matrix.shape)
# if jones_matrix.shape == t.Size([5, 2, 2, 2, 2]):
# print('probe', probe.shape, 'jones', jones_matrix.shape)
# print('JONES', jones_matrix)
"""
Applies a given Jones matrix to the probe
Parameters:
----------
probe: t.Tensor
A (N)(P)x2xMxL tensor representing the probe
jones_matrix: t.tensor
(N)x2x2x(M)x(L)
Returns:
--------
a probe with the jones matrix applied: t.Tensor
(N)(P)x2xMxL
"""
if transpose:
if jones_matrix.dim() < 4:
jones_matrix = jones_matrix[..., None, None]
if multiple_modes:
jones_matrix = jones_matrix.unsqueeze(-5)
probe = probe[..., None, :, :]
# if jones matrices do not differ from pattern to pattern
if probe.dim() > jones_matrix.dim():
jones_matrix = jones_matrix.unsqueeze(0)
# vice versa
elif jones_matrix.dim() > probe.dim():
probe = probe.unsqueeze(0)
# print('apply jonesmatrix: probe', probe.shape, 'matrix:', jones_matrix)
jones_matrix = jones_matrix.transpose(-1, -3).transpose(-2, -4)
probe = probe.transpose(-1, -3).transpose(-2, -4)
output = t.matmul(jones_matrix, probe).transpose(-2, -4).transpose(-1, -3).squeeze(-3)
else:
raise NotImplementedError
return output
def apply_phase_retardance(probe, phase_shift, multiple_modes=True):
"""
Shifts the y-component of the field wrt the x-component by a given phase shift
Parameters:
----------
probe: t.Tensor
A (...)x2x1xMxL tensor representing the probe
phase_shift: float
phase shift in degrees
Returns:
--------
probe: t.Tensor
(...)x2x1xMxL
"""
theta = t.as_tensor(phase_shift, dtype=t.float32)
theta = t.deg2rad(theta)
probe = probe.to(dtype=t.cfloat)
jones_matrix = t.tensor([[1, 0], [0, t.exp(phase_shift)]]).to(dtype=t.cfloat)
polarized = apply_jones_matrix(probe, jones_matrix, multiple_modes=multiple_modes)
return polarized
def apply_circular_polarizer(probe, left_polarized=True, multiple_modes=True):
"""
Applies a circular polarizer to the probe
Parameters:
----------
probe: t.Tensor
A (...)x2xMxL tensor representing the probe
left_polarizd: bool
True for the left-polarization, False for the right
Returns:
--------
circularly polarized probe: t.Tensor
(...)x2xMxL
"""
probe = probe.to(dtype=t.cfloat)
if left_polarized:
jones_matrix = (1/2 * t.tensor([[1, -1j], [1j, 1]])).to(dtype=t.cfloat)
else:
jones_matrix = 1/2 * t.tensor([[1, 1j], [-1j, 1]]).to(dtype=t.cfloat)
polarized = apply_jones_matrix(probe, jones_matrix, multiple_modes=multiple_modes)
return polarized
def apply_quarter_wave_plate(probe, fast_axis_angle, multiple_modes=True):
"""
Parameters:
----------
probe: t.Tensor
A (...)x2x1xMxL tensor representing the probe, MxL - the size of the probe
fast_axis_angle: float
The angle between the fast-axis of the polarizer and the horizontal axis
Returns:
--------
polarized probe: t.Tensor
(...)x2x1xMxL
"""
probe = probe.to(dtype=t.cfloat)
theta = math.radians(fast_axis_angle)
exponent = t.exp(-1j * math.pi / 4 * t.ones(2, 2))
jones_matrix = exponent* t.tensor([[(cos(theta))**2 + 1j * (sin(theta))**2, (1 - 1j) * sin(theta) * cos(theta)], [(1 - 1j) * sin(theta) * cos(theta), (sin(theta))**2 + 1j * (cos(theta))**2]]).to(dtype=t.cfloat)
out = apply_jones_matrix(probe, jones_matrix, multiple_modes=multiple_modes)
return out
def apply_half_wave_plate(probe, fast_axis_angle, multiple_modes=True):
"""
Parameters:
----------
probe: t.Tensor
A (...)x2x1xMxL tensor representing the probe, MxL - the size of the probe
fast_axis_angle: float
The angle between the fast-axis of the polarizer and the horizontal axis
Returns:
--------
polarized probe: t.Tensor
(...)x2x1xMxL
"""
probe = probe.to(dtype=t.cfloat)
theta = math.radians(fast_axis_angle)
exponent = t.exp(-1j * math.pi / 2 * t.ones(2, 2))
jones_matrix = exponent * t.tensor([[(cos(theta))**2 - (sin(theta))**2, 2 * sin(theta) * cos(theta)], [2 * sin(theta) * cos(theta), (sin(theta))**2 - (cos(theta))**2]]).to(dtype=t.cfloat)
out = apply_jones_matrix(probe, jones_matrix, multiple_modes=multiple_modes)
return out
def generate_birefringent_obj(fast_axis=90, phase_ret=10, atten_fast=1, atten_ret=1, global_phase=0):
def to_rad(angle):
angle = t.as_tensor(angle, dtype=t.float32)
angle = t.deg2rad(angle)
return angle
fast_axis = to_rad(fast_axis)
phase_ret = to_rad(phase_ret)
global_phase = to_rad(global_phase)
def coord_rot(angle):
a = t.stack((t.cos(angle), t.sin(angle)), dim=-1)
b = t.stack((-t.sin(angle), t.cos(angle)), dim=-1)
return t.stack((a, b), dim=-2).to(dtype=t.cfloat)
r1 = coord_rot(-fast_axis)
r2 = coord_rot(fast_axis)
p = t.exp(global_phase * 1j) * t.as_tensor([[atten_fast, 0], [0, atten_ret * t.exp(phase_ret*1j)]], dtype=t.cfloat)
return t.matmul(r1, t.matmul(p, r2))