Source code for caustics.light.func.sersic
from ...backend_obj import backend, ArrayLike
from ...utils import translate_rotate, to_elliptical
[docs]
def k_sersic(n: ArrayLike) -> ArrayLike:
"""
Computes the value of k for the Sersic profile.
Parameters
----------
n: ArrayLike
The Sersic index, which describes the degree of concentration of the source.
*Unit: unitless*
Returns
--------
k: ArrayLike
The value of k for the Sersic profile.
*Unit: unitless*
"""
# return (2 * n - 1 / 3 + 4 / (405 * n) + 46 / (25515 * n ** 2) + 131 / (1148175 * n ** 3) - 2194697 / (
# 30690717750 * n ** 4))
x = 1 / n
return (
2 * n
- 1 / 3
+ x
* (
4 / 405
+ x * (46 / 25515 + x * (131 / 1148175 - x * (2194697 / 30690717750)))
)
)
[docs]
def k_lenstronomy(n: ArrayLike) -> ArrayLike:
"""
Computes the value of k for the Sersic profile, as used in the lenstronomy package.
Parameters
----------
n: ArrayLike
The Sersic index, which describes the degree of concentration of the source.
*Unit: unitless*
Returns
--------
k: ArrayLike
The value of k for the Sersic profile.
*Unit: unitless*
"""
return 1.9992 * n - 0.3271
[docs]
def brightness_sersic(x0, y0, q, phi, n, Re, Ie, x, y, k, s=0.0):
x, y = translate_rotate(x, y, x0, y0, phi)
ex, ey = to_elliptical(x, y, q)
e = backend.sqrt(ex**2 + ey**2) + s
exponent = -k * ((e / Re) ** (1 / n) - 1)
return Ie * backend.exp(exponent)
