# Copyright Biomedical Imaging Group, EPFL 2025
"""
The propagator for the vectorial field in the Cartesian coordinates.
"""
import typing as tp
import torch
from .cartesian_propagator import CartesianPropagator
from ..utils.zernike import create_pupil_mesh
[docs]
class VectorialCartesianPropagator(CartesianPropagator):
r"""
Propagator for the vectorial case of the Richard's-Wolf integral in Cartesian parameterization.
In the vectorial model, the far field :math:`\boldsymbol{e}_{\infty}` depends on the vectorial incident field
:math:`\boldsymbol{e}_{\textrm{inc}} = [\boldsymbol{e}_{\textrm{inc}}^x, \boldsymbol{e}_{\textrm{inc}}^y, 0]`
as follows:
.. math::
\boldsymbol{e}_{\infty}(\theta,\phi) =
\begin{bmatrix}
(\cos\theta+1)+(\cos\theta-1)\cos2\phi \\
(\cos\theta-1)\sin2\phi \\
-2 \cos\phi \sin\theta
\end{bmatrix} \frac{\boldsymbol{e}_{\textrm{inc}}^x}{2} +
\begin{bmatrix}
(\cos\theta-1)\sin2\phi \\
(\cos\theta+1)-(\cos\theta-1)\cos2\phi \\
- 2 \sin\phi \sin\theta
\end{bmatrix} \frac{\boldsymbol{e}_{\textrm{inc}}^y}{2}.
The equation to compute the electric field is
.. math::
\mathbf{E}(\boldsymbol{\rho})
= -\frac{\mathrm{i} fk}{2\pi}\iint\limits_{s_x^2+s_y^2 \leq s_{M}^2}
\frac{\boldsymbol{e}_{\infty}(s_x, s_y) \mathrm{e}^{\mathrm{i} kz}}{s_z}
\mathrm{e}^{\mathrm{i} k(s_x x + s_y y)} ds_x ds_y.
Parameters
----------
`self.e0x` : float, optional
Initial electric field component :math:`\mathbf{e}_0^x`. Default value is `1.0`.
`self.e0y` : float, optional
Initial electric field component :math:`\mathbf{e}_0^y`. Default value is `0.0`.
Notes
-----
The vectorial propagators have two additional arguments apart from those inherited form the base propagator
to account for polarization.
"""
def __init__(self, n_pix_pupil=128, n_pix_psf=128, device='cpu',
zernike_coefficients=None,
special_phase_mask=None,
e0x=1.0, e0y=0.0,
wavelength=632, na=1.3, pix_size=10,
defocus_step=0, n_defocus=1,
apod_factor=False, envelope=None,
gibson_lanni=False, z_p=1e3, n_s=1.3,
n_g=1.5, n_g0=1.5, t_g=170e3, t_g0=170e3,
n_i=1.5, n_i0=1.5, t_i0=100e3):
super().__init__(n_pix_pupil=n_pix_pupil, n_pix_psf=n_pix_psf, device=device,
zernike_coefficients=zernike_coefficients,
special_phase_mask=special_phase_mask,
wavelength=wavelength, na=na, pix_size=pix_size,
defocus_step=defocus_step, n_defocus=n_defocus,
apod_factor=apod_factor, envelope=envelope,
gibson_lanni=gibson_lanni, z_p=z_p, n_s=n_s,
n_g=n_g, n_g0=n_g0, t_g=t_g, t_g0=t_g0,
n_i=n_i, n_i0=n_i0, t_i0=t_i0)
# electric field component ex at focal plane
# electric field component ey at focal plane
@classmethod
[docs]
def get_name(cls) -> str:
return 'vectorial_cartesian'
[docs]
def _get_args(self) -> tp.Dict:
args = super()._get_args()
args['e0x'] = str(self.e0x)
args['e0y'] = str(self.e0y)
return args
