Source code for caustics.lenses.func.sis
from ...backend_obj import backend
from ...utils import translate_rotate
[docs]
def reduced_deflection_angle_sis(x0, y0, Rein, x, y, s=0.0):
"""
Compute the reduced deflection angles. See the Meneghetti lecture notes equation 3.46.
Parameters
----------
x0: ArrayLike
x-coordinate of the center of the lens.
*Unit: arcsec*
y0: ArrayLike
y-coordinate of the center of the lens.
*Unit: arcsec*
Rein: ArrayLike
Einstein radius of the lens.
*Unit: arcsec*
x: ArrayLike
x-coordinates in the lens plane.
*Unit: arcsec*
y: ArrayLike
y-coordinates in the lens plane.
*Unit: arcsec*
s: float
Softening parameter to prevent numerical instabilities.
*Unit: arcsec*
Returns
-------
x_component: ArrayLike
Deflection Angle in the x-direction.
*Unit: arcsec*
y_component: ArrayLike
Deflection Angle in the y-direction.
*Unit: arcsec*
"""
x, y = translate_rotate(x, y, x0, y0)
R = backend.sqrt(x**2 + y**2) + s
ax = Rein * x / R
ay = Rein * y / R
return ax, ay
[docs]
def potential_sis(x0, y0, Rein, x, y, s=0.0):
"""
Compute the lensing potential. See the Meneghetti lecture notes equation 3.45.
Parameters
----------
x0: ArrayLike
x-coordinate of the center of the lens.
*Unit: arcsec*
y0: ArrayLike
y-coordinate of the center of the lens.
*Unit: arcsec*
Rein: ArrayLike
Einstein radius of the lens.
*Unit: arcsec*
x: ArrayLike
x-coordinates in the lens plane.
*Unit: arcsec*
y: ArrayLike
y-coordinates in the lens plane.
*Unit: arcsec*
s: float
Softening parameter to prevent numerical instabilities.
*Unit: arcsec*
Returns
-------
potential: ArrayLike
Lensing potential.
*Unit: arcsec^2*
"""
x, y = translate_rotate(x, y, x0, y0)
R = backend.sqrt(x**2 + y**2) + s
return Rein * R
[docs]
def convergence_sis(x0, y0, Rein, x, y, s=0.0):
"""
Compute the lensing convergence. See the Meneghetti lecture notes equation 3.44.
Parameters
----------
x0: ArrayLike
x-coordinate of the center of the lens.
*Unit: arcsec*
y0: ArrayLike
y-coordinate of the center of the lens.
*Unit: arcsec*
Rein: ArrayLike
Einstein radius of the lens.
*Unit: arcsec*
x: ArrayLike
x-coordinates in the lens plane.
*Unit: arcsec*
y: ArrayLike
y-coordinates in the lens plane.
*Unit: arcsec*
s: float
Softening parameter to prevent numerical instabilities.
*Unit: arcsec*
Returns
-------
convergence: ArrayLike
Lensing convergence.
*Unit: unitless*
"""
x, y = translate_rotate(x, y, x0, y0)
R = backend.sqrt(x**2 + y**2) + s
return 0.5 * Rein / R
