def compute_aberration(ra_eclip, dec_eclip, mjd, magnif):
# Given target ecliptic lonlat, and JD,
# returns the fully aberrated & magnified LonLat.
speed = 0.99365E-4 # Meeus p.151 in radians
apexlon = getSunLon(mjd) - 90.
if isinstance(ra_eclip, float):
apexXYZ = getXYZ(apexlon, 0.)
else:
apexXYZ = getXYZ(apexlon * np.ones(ra_eclip.shape),
np.zeros(ra_eclip.shape))
targetXYZ = getXYZ(ra_eclip, dec_eclip)
if len(targetXYZ.shape) > 1:
VxT = np.zeros(targetXYZ.shape)
TxVxT = np.zeros(targetXYZ.shape)
for i in range(targetXYZ.shape[1]):
VxT[:, i] = np.cross(apexXYZ[:, i], targetXYZ[:, i])
TxVxT[:, i] = np.cross(targetXYZ[:, i], VxT[:, i])
else:
VxT = np.cross(apexXYZ, targetXYZ)
TxVxT = np.cross(targetXYZ, VxT)
aberXYZ = speed * TxVxT
plotXYZ = targetXYZ + magnif * aberXYZ
# DANGER with getNormalized(): use only one triplet per call.
return getLONLAT(getNormalized(plotXYZ))
def compute_polar_misalignment_rotation_matrix(me_arcsec,ma_arcsec) :
"""
compute a rotation matrix to move the polar axis to the north
vector product
"""
ha1,dec1=altaz2hadec(alt=LATITUDE-me_arcsec/3600.,az=ma_arcsec/3600.)
xyz1=getXYZ(ha1,dec1)
ha2,dec2=altaz2hadec(alt=LATITUDE,az=0.)
xyz2=getXYZ(ha2,dec2)
cross = np.cross(xyz1,xyz2)
norme = np.sqrt(np.sum(cross**2))
if norme > 0 :
polar_misalignment_rotation = rotation_matrix(cross/norme,np.arcsin(norme))
else :
polar_misalignment_rotation = np.eye(3)
return polar_misalignment_rotation
def apply_precession(ra, dec, years) :
"""
see DESI-4957
Equator and zero longitude point glide westward at 0.0139 deg/year, so..
Star ecliptic longitudes increase +0.0139 deg/year from combined lunar and solar torques on the Earth.
To precess any sta'’s {RA,DEC}:
1. Convert to ecliptic coordinates {elon, elat}
2. Add 0.0139 deg * number of years to elon
3. Convert back to {RA,DEC}
"""
deltaELON = 360.* (years / PRECESSION_PERIOD_IN_YEARS) # degrees
lon,lat=radec2eclip(ra,dec)
xyz_ecliptic = getXYZ(lon,lat)
xyz_precessed = np.dot(vecZ(deltaELON), xyz_ecliptic)
lon,lat = getLONLAT(xyz_precessed)
return eclip2radec(lon,lat)
def hadec2xy(ha,dec,tel_ha,tel_dec) :
"""
Convert HA,Dec to tangent plane x,y given a telescope pointing tel_ha, tel_dec
Args:
ha: float or 1D np.array Hour Angle in degrees
dec: float or 1D np.array Hour Angle in degrees (same size as ha)
tel_ha: float; telescope pointing Hour Angle in degrees
tel_dec: float; telescope pointing Dec in degrees
Returns: x y float or 1D np.array
"""
xyz = getXYZ(ha,dec)
sh,ch = sincosd(tel_ha)
sd,cd = sincosd(tel_dec)
rh=np.array([[ch,sh,0],[-sh,ch,0],[0,0,1]]) # rotation about HA axis
rd=np.array([[sd,0,-cd],[0,1,0],[+cd,0,sd]]) # rotation about Dec axis
tmp = rd.dot(rh.dot(xyz))
x=tmp[1]
y=-tmp[0]
return x,y
def eclip2radec(lon,lat): # same epoch
ecliptic_xyz = getXYZ(lon,lat)
equatorial_xyz = np.dot(refX(-OBLIQ), ecliptic_xyz) # roll frame counterclockwise by obliq
return getLONLAT(equatorial_xyz)
def radec2eclip(ra,dec): # same epoch
equatorial_xyz = getXYZ(ra,dec)
ecliptic_xyz = np.dot(refX(OBLIQ), equatorial_xyz) # roll frame clockwise
return getLONLAT(ecliptic_xyz)
def tan2radec(x_tan,y_tan,tel_ra,tel_dec,mjd,lst_deg,hexrot_deg, precession = True, aberration = True, polar_misalignment = True, use_astropy = False) :
"""
Convert ICRS coordinates to tangent plane coordinates
Args:
xtan: float or 1D np.array with tangent plane coordinates
ytan: float or 1D np.array with tangent plane coordinates
tel_ra: float, in degrees, telescope pointing RA
tel_dec: float, in degrees, telescope pointing Dec
mjd: float, Modified Julian Date of observation, in days
lst_deg: float, local sidereal time, in degrees
hexrot_deg: float, hexapod rotation angle, in degrees
Returns RA,Dec in ICRS system (hopefully)
Optional arguments:
aberration: boolean; compute aberration if True
polar_misalignment: boolean; compute polar misalignment if True
use_astropy: boolean; use astropy coordinates for precession and aberration if True
"""
# undo hexapod rotation
shex,chex = sincosd(hexrot_deg)
x = chex*x_tan+shex*y_tan
y = -shex*x_tan+chex*y_tan
# need to apply precession ... etc to telescope pointing to interpret the x,y
if precession :
tel_ra,tel_dec = apply_precession_from_icrs(tel_ra, tel_dec, mjd, use_astropy)
if aberration :
tel_ra,tel_dec = apply_aberration(tel_ra,tel_dec,mjd, use_astropy)
tel_ha = lst_deg - tel_ra
if polar_misalignment :
polar_misalignment_matrix = compute_polar_misalignment_rotation_matrix(me_arcsec=ME_ARCSEC,ma_arcsec=MA_ARCSEC)
tel_ha,tel_dec = getLONLAT(polar_misalignment_matrix.dot(getXYZ(tel_ha,tel_dec)))
# we need to apply refraction for the telescope pointing to interpret the x,y
tel_alt,tel_az = hadec2altaz(tel_ha,tel_dec)
# apply refraction
refracted_tel_alt = apply_refraction(tel_alt)
# back to ha,dec
refracted_tel_ha,refracted_tel_dec = altaz2hadec(refracted_tel_alt,tel_az)
# now convert x,y to ha,dec
refracted_ha,refracted_dec = xy2hadec(x,y,refracted_tel_ha,refracted_tel_dec)
# alt,az
alt,az = hadec2altaz(refracted_ha,refracted_dec)
# undo refraction
alt = undo_refraction(alt)
# back to ha,dec
ha,dec = altaz2hadec(alt,az)
# now polar mis-alignment
if polar_misalignment :
# inverse matrix
polar_misalignment_matrix = compute_polar_misalignment_rotation_matrix(me_arcsec=-ME_ARCSEC,ma_arcsec=-MA_ARCSEC)
ha,dec = getLONLAT(polar_misalignment_matrix.dot(getXYZ(ha,dec)))
# ra
ra = lst_deg - ha
if aberration :
ra,dec = undo_aberration(ra,dec,mjd, use_astropy)
if precession :
ra,dec = undo_precession_from_icrs(ra, dec, mjd, use_astropy)
return ra,dec
def radec2tan(ra,dec,tel_ra,tel_dec,mjd,lst_deg,hexrot_deg, precession = True, aberration = True, polar_misalignment = True, use_astropy = False) :
"""
Convert ICRS coordinates to tangent plane coordinates
Args:
ra: float or 1D np.array with RA in degrees
dec: float or 1D np.array with RA in degrees
tel_ra: float, in degrees, telescope pointing RA
tel_dec: float, in degrees, telescope pointing Dec
mjd: float, Modified Julian Date of observation, in days
lst_deg: float, local sidereal time, in degrees
hexrot_deg: float, hexapod rotation angle, in degrees
Returns x_tan,y_tan , tangent plane coordinates:
x_tan = sin(theta)*cos(phi) : float on np.array (same shape as input ra,dec)
y_tan = sin(theta)*sin(phi) : float on np.array (same shape as input ra,dec)
where theta,phi are polar coordinates. theta=0 for along the telescope
pointing. phi=0 for a star with the same Dec as the telescope
pointing but a larger HA (or smaller RA).
Optional arguments:
aberration: boolean; compute aberration if True
polar_misalignment: boolean; compute polar misalignment if True
use_astropy: boolean; use astropy coordinates for precession and aberration if True
"""
if precession :
ra,dec = apply_precession_from_icrs(ra, dec, mjd, use_astropy)
tel_ra,tel_dec = apply_precession_from_icrs(tel_ra, tel_dec, mjd, use_astropy)
if aberration :
ra,dec = apply_aberration(ra,dec,mjd, use_astropy)
tel_ra,tel_dec = apply_aberration(tel_ra,tel_dec,mjd, use_astropy)
# ha,dec
ha = lst_deg - ra
tel_ha = lst_deg - tel_ra
if polar_misalignment :
# rotate
polar_misalignment_matrix = compute_polar_misalignment_rotation_matrix(me_arcsec=ME_ARCSEC,ma_arcsec=MA_ARCSEC)
ha,dec = getLONLAT(polar_misalignment_matrix.dot(getXYZ(ha,dec)))
tel_ha,tel_dec = getLONLAT(polar_misalignment_matrix.dot(getXYZ(tel_ha,tel_dec)))
# alt,az
alt,az = hadec2altaz(ha,dec)
tel_alt,tel_az = hadec2altaz(tel_ha,tel_dec)
# apply refraction
alt = apply_refraction(alt)
tel_alt = apply_refraction(tel_alt)
# convert back to ha,dec
ha,dec = altaz2hadec(alt,az)
tel_ha,tel_dec = altaz2hadec(tel_alt,tel_az)
# tangent plane
x,y = hadec2xy(ha,dec,tel_ha,tel_dec)
# hexapod rotation
shex,chex = sincosd(hexrot_deg)
return chex*x-shex*y , +shex*x+chex*y