"""
Utilities for velocity aberration correction.
"""
import logging
import numpy as np
from gwcs.geometry import CartesianToSpherical, SphericalToCartesian
from scipy.constants import speed_of_light
# Configure logging
logger = logging.getLogger(__name__)
SPEED_OF_LIGHT = speed_of_light / 1000 # km / s
__all__ = ["compute_va_effects_vector", "compute_va_effects"]
[docs]
def compute_va_effects_vector(velocity_x, velocity_y, velocity_z, u):
"""
Compute velocity aberration effects scale factor.
Computes constant scale factor due to velocity aberration as well as
corrected ``RA`` and ``DEC`` values, in vector form.
Parameters
----------
velocity_x, velocity_y, velocity_z : float
The components of the velocity of JWST, in km / s with respect to
the Sun. These are celestial coordinates, with x toward the
vernal equinox, y toward right ascension 90 degrees and declination
0, z toward the north celestial pole.
u : numpy.array([u0, u1, u2])
The vector form of right ascension and declination of the target (or some other
point, such as the center of a detector) in the barycentric coordinate
system. The equator and equinox should be the same as the coordinate
system for the velocity.
Returns
-------
scale_factor : float
Multiply the nominal image scale (e.g., in degrees per pixel) by
this value to obtain the image scale corrected for the "aberration
of starlight" due to the velocity of JWST with respect to the Sun.
u_corr : numpy.array([ua0, ua1, ua2])
Apparent position vector in the moving telescope frame.
"""
beta = np.array([velocity_x, velocity_y, velocity_z]) / SPEED_OF_LIGHT
beta2 = np.dot(beta, beta) # |beta|^2
if beta2 == 0.0:
logger.warning("Observatory speed is zero. Setting VA scale to 1.0")
return 1.0, u
u_beta = np.dot(u, beta)
igamma = np.sqrt(1.0 - beta2) # inverse of usual gamma
scale_factor = (1.0 + u_beta) / igamma
# Algorithm below is from Colin Cox notebook.
# Also see: Instrument Science Report OSG-CAL-97-06 by Colin Cox (1997).
u_corr = (igamma * u + beta * (1.0 + (1.0 - igamma) * u_beta / beta2)) / (1.0 + u_beta)
return scale_factor, u_corr
[docs]
def compute_va_effects(velocity_x, velocity_y, velocity_z, ra, dec):
"""
Compute velocity aberration effects.
Computes constant scale factor due to velocity aberration as well as
corrected ``RA`` and ``DEC`` values.
Parameters
----------
velocity_x, velocity_y, velocity_z : float
The components of the velocity of JWST, in km / s with respect to
the Sun. These are celestial coordinates, with x toward the
vernal equinox, y toward right ascension 90 degrees and declination
0, z toward the north celestial pole.
ra, dec : float
The right ascension and declination of the target (or some other
point, such as the center of a detector) in the barycentric coordinate
system. The equator and equinox should be the same as the coordinate
system for the velocity.
Returns
-------
scale_factor : float
Multiply the nominal image scale (e.g., in degrees per pixel) by
this value to obtain the image scale corrected for the "aberration
of starlight" due to the velocity of JWST with respect to the Sun.
apparent_ra : float
Apparent star position in the moving telescope frame.
apparent_dec : float
Apparent star position in the moving telescope frame.
"""
u = np.asanyarray(SphericalToCartesian()(ra, dec))
scale_factor, u_corr = compute_va_effects_vector(velocity_x, velocity_y, velocity_z, u)
apparent_ra, apparent_dec = CartesianToSpherical()(*u_corr)
return scale_factor, apparent_ra, apparent_dec