1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
|
#from .. mappings import DEGTORAD, RADTODEG
from hstwcs.mappings import DEGTORAD, RADTODEG
import numpy
from numpy import math
from math import sin, sqrt, pow, cos, asin, atan2,pi
class MakeWCS(object):
"""
Purpose
=======
Recompute WCS keywords based on PA_V3 and distortion model.
Algorithm
=========
- update reference chip wcs
- update extension wcs
- update extension header
"""
def __init__(self, owcs, refwcs):
self.wcsobj = owcs
self.refwcs = refwcs
self.updateWCS()
self.DOMakeWCS = 'COMPLETE'
def updateWCS(self):
"""
recomputes the basic WCS kw
"""
backup_wcs = self.wcsobj.restore()
ltvoff, offshift = self.getOffsets(backup_wcs)
self.uprefwcs(ltvoff, offshift)
self.upextwcs(ltvoff, offshift)
self.updatehdr()
def upextwcs(self, loff, offsh):
"""
updates an extension wcs
"""
ltvoffx, ltvoffy = loff[0], loff[1]
offshiftx, offshifty = offsh[0], offsh[1]
backup_wcs = self.wcsobj.restore()
ltv1 = self.wcsobj.ltv1
ltv2 = self.wcsobj.ltv2
if ltv1 != 0. or ltv2 != 0.:
offsetx = backup_wcs['CRPIX1'] - ltv1 - self.wcsobj.idcmodel.refpix['XREF']
offsety = backup_wcs['CRPIX2'] - ltv2 - self.wcsobj.idcmodel.refpix['YREF']
fx,fy = self.wcsobj.idcmodel.shift(self.wcsobj.idcmodel.cx,self.wcsobj.idcmodel.cy,offsetx,offsety)
else:
fx, fy = self.wcsobj.idcmodel.cx, self.wcsobj.idcmodel.cy
ridcmodel = self.refwcs.idcmodel
v2 = self.wcsobj.idcmodel.refpix['V2REF']
v3 = self.wcsobj.idcmodel.refpix['V3REF']
v2ref = self.refwcs.idcmodel.refpix['V2REF']
v3ref = self.refwcs.idcmodel.refpix['V3REF']
R_scale = self.refwcs.idcmodel.refpix['PSCALE']/3600.0
off = sqrt((v2-v2ref)**2 + (v3-v3ref)**2)/(R_scale*3600.0)
# Here we must include the PARITY
if v3 == v3ref:
theta=0.0
else:
theta = atan2(self.wcsobj.parity[0][0]*(v2-v2ref),self.wcsobj.parity[1][1]*(v3-v3ref))
if self.refwcs.idcmodel.refpix['THETA']: theta += self.refwcs.idcmodel.refpix['THETA']*pi/180.0
dX=(off*sin(theta)) + offshiftx
dY=(off*cos(theta)) + offshifty
px = numpy.array([[dX,dY]])
newcrval = self.refwcs.pixel2world_fits(px)[0]
newcrpix = numpy.array([self.wcsobj.idcmodel.refpix['XREF'] + ltvoffx,
self.wcsobj.idcmodel.refpix['YREF'] + ltvoffy])
self.wcsobj.crval = newcrval
self.wcsobj.crpix = newcrpix
# Account for subarray offset
# Angle of chip relative to chip
if self.wcsobj.idcmodel.refpix['THETA']:
dtheta = self.wcsobj.idcmodel.refpix['THETA'] - self.refwcs.idcmodel.refpix['THETA']
else:
dtheta = 0.0
# Create a small vector, in reference image pixel scale
# There is no parity effect here ???
delXX=fx[1,1]/R_scale/3600.
delYX=fy[1,1]/R_scale/3600.
delXY=fx[1,0]/R_scale/3600.
delYY=fy[1,0]/R_scale/3600.
# Convert to radians
rr=dtheta*pi/180.0
# Rotate the vectors
dXX = cos(rr)*delXX - sin(rr)*delYX
dYX = sin(rr)*delXX + cos(rr)*delYX
dXY = cos(rr)*delXY - sin(rr)*delYY
dYY = sin(rr)*delXY + cos(rr)*delYY
px = numpy.array([[dX+dXX,dY+dYX]])
# Transform to sky coordinates
wc = self.refwcs.pixel2world_fits(px)
a = wc[0,0]
b = wc[0,1]
px = numpy.array([[dX+dXY,dY+dYY]])
wc = self.refwcs.pixel2world_fits(px)
c = wc[0,0]
d = wc[0,1]
# Calculate the new CDs and convert to degrees
cd11 = diff_angles(a,newcrval[0])*cos(newcrval[1]*pi/180.0)
cd12 = diff_angles(c,newcrval[0])*cos(newcrval[1]*pi/180.0)
cd21 = diff_angles(b,newcrval[1])
cd22 = diff_angles(d,newcrval[1])
cd = numpy.array([[cd11, cd12], [cd21, cd22]])
self.wcsobj.cd = cd
def uprefwcs(self, loff, offsh):
"""
Updates the reference chip
"""
ltvoffx, ltvoffy = loff[0], loff[1]
offshift = offsh
backup_refwcs = self.refwcs.restore()
dec = backup_refwcs['CRVAL2']
# Get an approximate reference position on the sky
rref = numpy.array([[self.refwcs.idcmodel.refpix['XREF']+ltvoffx,
self.refwcs.idcmodel.refpix['YREF']+ltvoffy]])
crval = self.refwcs.pixel2world_fits(rref)
# Convert the PA_V3 orientation to the orientation at the aperture
# This is for the reference chip only - we use this for the
# reference tangent plane definition
# It has the same orientation as the reference chip
pv = troll(self.wcsobj.pav3,dec,self.refwcs.idcmodel.refpix['V2REF'],
self.refwcs.idcmodel.refpix['V3REF'])
# Add the chip rotation angle
if self.refwcs.idcmodel.refpix['THETA']:
pv += self.refwcs.idcmodel.refpix['THETA']
# Set values for the rest of the reference WCS
self.refwcs.crval = crval[0]
self.refwcs.crpix = numpy.array([0.0,0.0])+offsh
parity = self.refwcs.parity
R_scale = self.refwcs.idcmodel.refpix['PSCALE']/3600.0
cd11 = parity[0][0] * cos(pv*pi/180.0)*R_scale
cd12 = parity[0][0] * -sin(pv*pi/180.0)*R_scale
cd21 = parity[1][1] * sin(pv*pi/180.0)*R_scale
cd22 = parity[1][1] * cos(pv*pi/180.0)*R_scale
rcd = numpy.array([[cd11, cd12], [cd21, cd22]])
self.refwcs.cd = rcd
self.refwcs.set()
def updatehdr(self):
"""
Keywords to update:
CD1_1, CD1_2, CD2_1, CD2_2, CRPIX1, CRPIX2, CRVAL1, CRVAL2
"""
self.wcsobj.hdr.update('CD1_1', self.wcsobj.cd[0,0])
self.wcsobj.hdr.update('CD1_2', self.wcsobj.cd[0,1])
self.wcsobj.hdr.update('CD2_1', self.wcsobj.cd[1,0])
self.wcsobj.hdr.update('CD2_2', self.wcsobj.cd[1,1])
self.wcsobj.hdr.update('CRVAL1', self.wcsobj.crval[0])
self.wcsobj.hdr.update('CRVAL2', self.wcsobj.crval[1])
self.wcsobj.hdr.update('CRPIX1', self.wcsobj.crpix[0])
self.wcsobj.hdr.update('CRPIX2', self.wcsobj.crpix[1])
self.wcsobj.hdr.update('ORIENTAT', self.wcsobj.orientat)
def getOffsets(self, backup_wcs):
ltv1 = self.wcsobj.ltv1
ltv2 = self.wcsobj.ltv2
offsetx = backup_wcs['CRPIX1'] - ltv1 - self.wcsobj.idcmodel.refpix['XREF']
offsety = backup_wcs['CRPIX2'] - ltv2 - self.wcsobj.idcmodel.refpix['YREF']
shiftx = self.wcsobj.idcmodel.refpix['XREF'] + ltv1
shifty = self.wcsobj.idcmodel.refpix['YREF'] + ltv2
if ltv1 != 0. or ltv2 != 0.:
ltvoffx = ltv1 + offsetx
ltvoffy = ltv2 + offsety
offshiftx = offsetx + shiftx
offshifty = offsety + shifty
else:
ltvoffx = 0.
ltvoffy = 0.
offshiftx = 0.
offshifty = 0.
ltvoff = numpy.array([ltvoffx, ltvoffy])
offshift = numpy.array([offshiftx, offshifty])
return ltvoff, offshift
def diff_angles(a,b):
"""
Perform angle subtraction a-b taking into account
small-angle differences across 360degree line.
"""
diff = a - b
if diff > 180.0:
diff -= 360.0
if diff < -180.0:
diff += 360.0
return diff
def troll(roll, dec, v2, v3):
""" Computes the roll angle at the target position based on:
the roll angle at the V1 axis(roll),
the dec of the target(dec), and
the V2/V3 position of the aperture (v2,v3) in arcseconds.
Based on the algorithm provided by Colin Cox that is used in
Generic Conversion at STScI.
"""
# Convert all angles to radians
_roll = DEGTORAD(roll)
_dec = DEGTORAD(dec)
_v2 = DEGTORAD(v2 / 3600.)
_v3 = DEGTORAD(v3 / 3600.)
# compute components
sin_rho = sqrt((pow(sin(_v2),2)+pow(sin(_v3),2)) - (pow(sin(_v2),2)*pow(sin(_v3),2)))
rho = asin(sin_rho)
beta = asin(sin(_v3)/sin_rho)
if _v2 < 0: beta = pi - beta
gamma = asin(sin(_v2)/sin_rho)
if _v3 < 0: gamma = pi - gamma
A = pi/2. + _roll - beta
B = atan2( sin(A)*cos(_dec), (sin(_dec)*sin_rho - cos(_dec)*cos(rho)*cos(A)))
# compute final value
troll = RADTODEG(pi - (gamma+B))
return troll
|
