def fit_rotoff(self, x1, y1, x2, y2):
"""
Fit rotation + offset (but not scale) for (x1,y1) -> (x2,y2)
Args:
x1,y1,x2,y2 : 1D np.arrays of coordinates in tangent plane
"""
assert((x1.shape == y1.shape)&(x2.shape == y2.shape)&(x1.shape == x2.shape))
n = len(x1)
v = np.concatenate([x2, y2])
A = np.zeros((2*n, 4))
A[0:n, 0] = x1
A[n:, 0] = y1
A[0:n, 1] = -y1
A[n:, 1] = x1
A[0:n, 2] = 1
A[n:, 2] = 0
A[0:n, 3] = 0
A[n:, 3] = 1
ATv = A.T.dot(v)
ATA = A.T.dot(A)
p = np.linalg.solve(ATA, ATv)
self.rot_deg = arctan2d(p[1], p[0])
self.dx = p[2]
self.dy = p[3]
self.sxx = 1.
self.syy = 1.
self.sxy = 0.
def hadec2altaz(ha,dec) :
"""
Convert HA,Dec to Altitude , Azimuth at Kitt Peak elevation
Args:
ha: float or 1D np.array hour angle in degrees
dec: float or 1D np.array declination in degrees
Returns: alt, az
alt: float or 1D np.array altitude in degrees
az: float or 1D np.array azimuth in degrees
"""
sha,cha = sincosd(ha)
sdec,cdec = sincosd(dec)
slat,clat = sincosd(LATITUDE)
x = - cha * cdec * slat + sdec * clat
y = - sha * cdec
z = cha * cdec * clat + sdec * slat
r = np.hypot(x, y)
az = arctan2d(y,x)
alt = arctan2d(z,r)
return alt,az
def altaz2hadec(alt,az) :
"""
Convert Altitude, Azimuth to HA, Dec at Kitt Peak elevation
Args:
alt: float or 1D np.array altitude in degrees
az: float or 1D np.array azimuth in degrees
Returns: ha, dec
ha: float or 1D np.array Hour Angle in degrees
dec: float or 1D np.array Hour Angle in degrees
"""
salt,calt = sincosd(alt)
saz,caz = sincosd(az)
slat,clat = sincosd(LATITUDE)
ha = arctan2d( -saz*calt, -caz*slat*calt+salt*clat)
dec = arcsind(slat*salt+clat*calt*caz)
return ha,dec
def xy2qs(x, y):
'''Focal tangent plane x,y -> angular q,s on curved focal surface
Args:
x, y: cartesian location on focal tangent plane in mm
Returns (q, s) where q=angle in degrees; s=focal surface radial dist [mm]
Notes: (x,y) are in the "CS5" DESI coordinate system tangent plane to
the curved focal surface. q is the radial angle measured counter-clockwise
from the x-axis; s is the radial distance along the curved focal surface;
it is *not* sqrt(x**2 + y**2). (q,s) are the preferred coordinates for
the DESI focal plane hardware engineering team.
'''
r = np.hypot(x, y)
s = r2s(r)
q = arctan2d(y, x)
return q, s
def fit(self, x1, y1, x2, y2, solid=False) :
"""
Adjust tranformation from x1,y1 to x2,y2
Args:
x1,y1,x2,y2 : 1D np.arrays of coordinates in tangent plane
Optional:
if solid, scales are forced = 1
Returns:
None
"""
if solid :
return self.fit_rotoff(x1, y1, x2, y2)
assert((x1.shape == y1.shape)&(x2.shape == y2.shape)&(x1.shape == x2.shape))
# now fit simultaneously extra offset, rotation, scale
self.nmatch=x1.size
H=np.zeros((3,self.nmatch))
H[0] = 1.
H[1] = x1
H[2] = y1
A = H.dot(H.T)
Ai = np.linalg.inv(A)
ax = Ai.dot(np.sum(x2*H,axis=1))
x2p = ax[0] + ax[1]*x1 + ax[2]*y1 # x2p = predicted x2 from x1 (=x1 after telescope pointing offset)
ay = Ai.dot(np.sum(y2*H,axis=1))
y2p = ay[0] + ay[1]*x1 + ay[2]*y1 # y2p = predicted y2 from y1
# tangent plane coordinates are in radians
self.rms = np.sqrt( np.mean( (x2-x2p)**2 + (y2-y2p)**2 ) )
# pointing offset
self.dx = ax[0]
self.dy = ay[0]
# dilatation and rotation
# |ax1 ax2| |sxx sxy| |ca -sa|
# |ay1 ay2|=|syx syy|*|sa ca|
# ax1=sxx*ca+sxy*sa ; ax2=-sxx*sa+sxy*ca
# ay1=syx*ca+syy*sa ; ay2=-syx*sa+syy*ca
# ax1+ay2 = (sxx+syy)*ca
# ay1-ax2 = (sxx+syy)*sa
sxx_p_syy = np.hypot(ax[1]+ay[2], ay[1]-ax[2])
sa=(ay[1]-ax[2])/sxx_p_syy
ca=(ax[1]+ay[2])/sxx_p_syy
if sa != 0 :
self.rot_deg = arctan2d(sa,ca)
sxy = sa*ax[1]+ca*ay[1] - sxx_p_syy*ca*sa
sxx =(ax[1]-sxy*sa)/ca
syy = (ay[1]-sxy*ca)/sa
else :
sxx = ax[1]
syy = ay[2]
sxy = ax[2]
self.sxx = sxx
self.syy = syy
self.sxy = sxy
def fit(self, x1, y1, x2, y2):
"""
Adjust tranformation from focal plane x1,y1 to x2,y2
Args:
x1,y1,x2,y2 : 1D np.arrays of coordinates in tangent plane
Returns:
None
"""
assert ((x1.shape == y1.shape) & (x2.shape == y2.shape) &
(x1.shape == x2.shape))
# first ajust an offset using spherical coordinates
# assume fiducial pointing of telescope to convert
# tangent plane coords to angles
self.dha = 0.
self.ddec = 0.
x1t = x1 + 0.
y1t = y1 + 0.
ha, dec = xy2hadec(x1, y1, 0, 0)
for _ in range(4):
x1t, y1t = hadec2xy(ha, dec, self.dha, self.ddec)
dx = np.mean(x2 - x1t)
dy = np.mean(y2 - y1t)
self.dha -= np.rad2deg(dx)
self.ddec -= np.rad2deg(dy)
x1t, y1t = hadec2xy(ha, dec, self.dha, self.ddec)
# now fit simultaneously extra offset, rotation, scale
self.nstars = x1t.size
H = np.zeros((3, self.nstars))
H[0] = 1.
H[1] = x1t
H[2] = y1t
A = H.dot(H.T)
Ai = np.linalg.inv(A)
ax = Ai.dot(np.sum(x2 * H, axis=1))
x2p = ax[0] + ax[1] * x1t + ax[
2] * y1t # x2p = predicted x2 from x1t (=x1 after telescope pointing offset)
ay = Ai.dot(np.sum(y2 * H, axis=1))
y2p = ay[0] + ay[1] * x1t + ay[2] * y1t # y2p = predicted y2 from y1t
# tangent plane coordinates are in radians
rms = np.sqrt(np.mean((x2 - x2p)**2 + (y2 - y2p)**2))
self.rms_arcsec = np.rad2deg(rms) * 3600.
# interpret this back into telescope pointing offset, field rotation, dilatation
# pointing offset
# increasing gaia stars x means telescope is more to the left so tel_ha should be decreased
# increasing gaia stars y means telescope is more to the bottom so tel_dec should be decreased
# tangent plane coordinates are in rad
ddha = -np.rad2deg(ax[0])
dddec = -np.rad2deg(ay[0])
self.dha += ddha
self.ddec += dddec
# dilatation and rotation
# |ax1 ax2| |sxx sxy| |ca -sa|
# |ay1 ay2|=|syx syy|*|sa ca|
# ax1=sxx*ca+sxy*sa ; ax2=-sxx*sa+sxy*ca
# ay1=syx*ca+syy*sa ; ay2=-syx*sa+syy*ca
# ax1+ay2 = (sxx+syy)*ca
# ay1-ax2 = (sxx+syy)*sa
sxx_p_syy = np.hypot(ax[1] + ay[2], ay[1] - ax[2])
sa = (ay[1] - ax[2]) / sxx_p_syy
ca = (ax[1] + ay[2]) / sxx_p_syy
self.rot_deg = arctan2d(sa, ca)
sxy = sa * ax[1] + ca * ay[1] - sxx_p_syy * ca * sa
sxx = (ax[1] - sxy * sa) / ca
syy = (ay[1] - sxy * ca) / sa
self.sxx = sxx
self.syy = syy
self.sxy = sxy
def getLONLAT(xyz):
"""Convert xyz into its spherical angles"""
xyz = getNormalized(xyz) # usually unnecessary
return arctan2d(xyz[1],xyz[0]) , arcsind(xyz[2]) # degrees
def uv2xy(u, v):
s = np.hypot(u, v)
q = arctan2d(v, u)
x, y = qs2xy(q, s)
return x, y