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jmeyers314/Batoid ImSim integration.ipynb

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Batoid ImSim integration
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Batoid ImSim integration.ipynb
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BatoidWCS.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-11T20:25:58.314624Z",
"start_time": "2019-10-11T20:25:53.884963Z"
}
},
"outputs": [],
"source": [
"import lsst.afw.cameraGeom as cameraGeom\n",
"from lsst.obs.lsst import LsstCamMapper\n",
"import lsst.obs.lsst.cameraTransforms as cameraTransforms\n",
"\n",
"import batoid\n",
"import galsim\n",
"\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-11T20:26:04.503467Z",
"start_time": "2019-10-11T20:25:58.316967Z"
}
},
"outputs": [],
"source": [
"camera = LsstCamMapper().camera"
]
},
{
"cell_type": "code",
"execution_count": 1028,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-11T20:26:04.520761Z",
"start_time": "2019-10-11T20:26:04.508135Z"
}
},
"outputs": [],
"source": [
"class BatoidWCS(galsim.wcs.CelestialWCS):\n",
" \"\"\"\n",
" Parameters\n",
" ----------\n",
" boresight : galsim.CelestialCoord\n",
" rotSkyPos : galsim.Angle\n",
" rotTelPos : galsim.Angle\n",
" fiducial_telescope : batoid.Optic\n",
" Telescope before application of rotator\n",
" wavelength : float\n",
" Nanometers\n",
" camera : lsst.afw.cameraGeom.camera.camera.Camera\n",
" det : lsst.afw.cameraGeom.detector.detector.Detector\n",
" \"\"\"\n",
" def __init__(self, boresight, rotSkyPos, rotTelPos, fiducial_telescope, wavelength, camera, det):\n",
" self.boresight = boresight\n",
" self.rotSkyPos = rotSkyPos\n",
" self.rotTelPos = rotTelPos\n",
" self.fiducial_telescope = fiducial_telescope\n",
" self.wavelength = wavelength\n",
" self.camera = camera\n",
" self.det = det\n",
" \n",
" # Initialize RaDec -> field\n",
" q = rotTelPos - rotSkyPos\n",
" cq, sq = np.cos(q), np.sin(q) # +q or -q here?\n",
" jac = [cq, -sq, sq, cq]\n",
" affine = galsim.AffineTransform(*jac)\n",
" self._radec2field = galsim.TanWCS(affine, boresight, units=galsim.radians)\n",
"\n",
" # Initialize field -> focal\n",
" _pz = fiducial_telescope.stopSurface.surface.sag(0.0, 0.0)\n",
" transform = batoid.CoordTransform(fiducial_telescope.stopSurface.coordSys, batoid.globalCoordSys)\n",
" _, _, self._pz = transform.applyForward(0, 0, _pz)\n",
" self._refractive_index = fiducial_telescope.inMedium.getN(wavelength*1e-9)\n",
" self._telescope = fiducial_telescope.withLocallyRotatedOptic(\"LSSTCamera\", batoid.RotZ(-self.rotTelPos))\n",
"\n",
" # Initialize focal -> pixel\n",
" lct = cameraTransforms.LsstCameraTransforms(camera)\n",
" center = 509*4 + 0.5, 2000.5\n",
" # Focal plane coords of center of CCD\n",
" _x, _y = lct.ccdPixelToFocalMm(*center, det.getName())\n",
" self._focal_x = _x*1e-3 # meters\n",
" self._focal_y = _y*1e-3 # meters\n",
" \n",
" # Also calculate field angle of CCD center\n",
" self._field_x, self._field_y = self._focalToField(self._focal_x, self._focal_y)\n",
" \n",
" # Required by galsim.BaseWCS\n",
" self._color = None\n",
" self.origin = galsim.PositionD(0, 0)\n",
"\n",
" def _fieldToFocal(self, field_x, field_y):\n",
" ray = batoid.Ray.fromStop(\n",
" 0.0, 0.0,\n",
" optic=self._telescope,\n",
" wavelength=self.wavelength*1e-9,\n",
" theta_x=field_x, theta_y=field_y, projection='gnomonic' \n",
" )\n",
" self._telescope.traceInPlace(ray)\n",
" return ray.x, ray.y\n",
" \n",
" def _fieldToFocalMany(self, field_x, field_y):\n",
" # Setup rays to trace with batoid. For each input coordinate, we'll \n",
" # trace exactly 1 ray, the chief ray. Any displacements between the \n",
" # mean optics/atmosphere and the chief ray can then be considered \n",
" # part of the PSF.\n",
" n = len(field_x)\n",
" dirCos = np.array(batoid.utils.fieldToDirCos(field_x, field_y, projection='gnomonic'))\n",
" w = np.empty(n); w.fill(self.wavelength*1e-9)\n",
" pz = np.empty(n); pz.fill(self._pz)\n",
" rays = batoid.RayVector.fromArrays(\n",
" np.zeros(n), np.zeros(n), pz, # Chief ray -> start at center of the entrance pupil.\n",
" *(dirCos/self._refractive_index), # velocity = dirCos adjusted for refractive index\n",
" np.zeros(n), # doesn't matter what we set time to, so just use 0.0\n",
" w # wavelength\n",
" )\n",
" self._telescope.traceInPlace(rays)\n",
" return rays.x, rays.y\n",
" \n",
" def _focalToField(self, x, y):\n",
" from scipy.optimize import least_squares\n",
"\n",
" def _resid(args):\n",
" fx1, fy1 = args\n",
" x1, y1 = self._fieldToFocal(fx1, fy1)\n",
" return np.array([x1-x, y1-y])\n",
"\n",
" result = least_squares(_resid, np.array([0.0, 0.0]))\n",
" return result.x[0], result.x[1]\n",
"\n",
" def _focalToFieldMany(self, x, y):\n",
" if not hasattr(self, '_xinterp'):\n",
" from scipy.interpolate import RectBivariateSpline\n",
" # radius of circle circumscribing CCD, plus some fudge\n",
" half_length = 2000*10e-6*np.sqrt(2)*1.2\n",
" N = 4 # seems to be sufficient, kinda surprising...\n",
" focal_xs = self._focal_x + half_length*np.linspace(-1,1,N)\n",
" focal_ys = self._focal_y + half_length*np.linspace(-1,1,N)\n",
" field_xs = np.empty((N, N), dtype=float)\n",
" field_ys = np.empty((N, N), dtype=float)\n",
" for i in range(N):\n",
" for j in range(N):\n",
" field_xs[i,j], field_ys[i,j] = self._focalToField(focal_xs[i], focal_ys[j])\n",
" self._xinterp = RectBivariateSpline(focal_xs, focal_ys, field_xs)\n",
" self._yinterp = RectBivariateSpline(focal_xs, focal_ys, field_ys)\n",
" return self._xinterp(x, y, grid=False), self._yinterp(x, y, grid=False)\n",
" \n",
" def _xy(self, ra, dec, color=None):\n",
" \"\"\"\n",
" Parameters\n",
" ----------\n",
" ra : array_like\n",
" Right ascension in radians\n",
" dec : array_like\n",
" Declination in radians\n",
" \n",
" Returns\n",
" -------\n",
" xpix, ypix : array_like\n",
" \"\"\"\n",
" # Abuse GalSim's TanWCS to convert ra/dec into field angles \n",
" # centered at ra/dec and aligned with alt/az.\n",
" field_x, field_y = self._radec2field.radecToxy(ra, dec, 'rad')\n",
"\n",
" # Field -> Focal via batoid.\n",
" focal_x, focal_y = self._fieldToFocalMany(field_x, field_y)\n",
" \n",
" # For the moment, focal -> pixel is just an offset and a scaling by the pixel size.\n",
" pixSize = 10e-6 # m\n",
" pixel_x = (focal_x - self._focal_x)/pixSize + (509*4 + 0.5)\n",
" pixel_y = (focal_y - self._focal_y)/pixSize + 2000.5\n",
" return pixel_x, pixel_y\n",
" \n",
" def _radec(self, x, y, color=None):\n",
" # reverse of _xy.\n",
"\n",
" # pixel -> focal\n",
" pixSize = 10e-6\n",
" focal_x = pixSize*(x-(509*4+0.5)) + self._focal_x\n",
" focal_y = pixSize*(y-2000.5) + self._focal_y\n",
"\n",
" # focal -> field using interpolating function derived from field->focal\n",
" field_x, field_y = self._focalToFieldMany(focal_x, focal_y)\n",
"\n",
" # field -> ra, dec using GalSim TanWCS\n",
" return self._radec2field.xyToradec(field_x, field_y, units='rad')"
]
},
{
"cell_type": "code",
"execution_count": 1038,
"metadata": {
"ExecuteTime": {
"end_time": "2019-10-11T20:26:04.610210Z",
"start_time": "2019-10-11T20:26:04.547881Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"R02_S21\n"
]
}
],
"source": [
"# Construct a WCS for some detector\n",
"det = camera[16]\n",
"print(det.getName())\n",
"\n",
"boresight = galsim.CelestialCoord(ra=30*galsim.degrees, dec=-10*galsim.degrees)\n",
"rotTelPos = 35.0*galsim.degrees\n",
"rotSkyPos = 10.0*galsim.degrees\n",
"\n",
"wcs = BatoidWCS(\n",
" boresight, rotSkyPos, rotTelPos,\n",
" batoid.Optic.fromYaml(\"LSST_r.yaml\"),\n",
" 620, # nm\n",
" camera, det\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 1039,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.4306630586632416e-05 pixel\n"
]
}
],
"source": [
"# Test focal<->field roundtrip for individual points\n",
"# Mostly probing the accuracy of the scipy least_squares inversion. \n",
"errs = []\n",
"for _ in range(1000):\n",
" xy = np.random.uniform(-0.3, 0.3, size=2)\n",
" w = np.hypot(*xy)\n",
" if w > 0.3:\n",
" continue\n",
" errs.append((wcs._fieldToFocal(*wcs._focalToField(*xy)) - xy)/10e-6)\n",
"print(np.max(errs), \"pixel\")"
]
},
{
"cell_type": "code",
"execution_count": 1041,
"metadata": {},
"outputs": [],
"source": [
"# Roundtrip field -> focal -> field for many points at once.\n",
"# This uses an interpolation trained only in the region of the particular sensor, so \n",
"# don't wander too far away from that.\n",
"fieldx = wcs._field_x + np.deg2rad(2000*0.2/3600)*np.linspace(-1, 1, 800)\n",
"fieldy = wcs._field_y + np.deg2rad(2000*0.2/3600)*np.linspace(-1, 1, 800)\n",
"fieldx, fieldy = np.meshgrid(fieldx, fieldy)\n",
"fieldx = fieldx.ravel()\n",
"fieldy = fieldy.ravel()\n",
"\n",
"focalx, focaly = wcs._fieldToFocalMany(fieldx, fieldy)\n",
"fieldx1, fieldy1 = wcs._focalToFieldMany(focalx, focaly)"
]
},
{
"cell_type": "code",
"execution_count": 1042,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-1.8315910536664856e-06 arcsec\n",
"-2.623459060261082e-06 arcsec\n",
"2.7497054732218163e-06 arcsec\n",
"3.9374238444648215e-06 arcsec\n"
]
}
],
"source": [
"print(3600*np.rad2deg(np.median(fieldx1-fieldx)), \"arcsec\")\n",
"print(3600*np.rad2deg(np.median(fieldy1-fieldy)), \"arcsec\")\n",
"\n",
"print(3600*np.rad2deg(np.median(np.abs(fieldx1-fieldx))), \"arcsec\")\n",
"print(3600*np.rad2deg(np.median(np.abs(fieldy1-fieldy))), \"arcsec\")"
]
},
{
"cell_type": "code",
"execution_count": 1043,
"metadata": {},
"outputs": [],
"source": [
"# Roundtrip focal -> field -> focal\n",
"focalx = wcs._focal_x + np.linspace(-2000*10e-6, 2000*10e-6, 80)\n",
"focaly = wcs._focal_y + np.linspace(-2000*10e-6, 2000*10e-6, 80)\n",
"focalx, focaly = np.meshgrid(focalx, focaly)\n",
"focalx = focalx.ravel()\n",
"focaly = focaly.ravel()\n",
"\n",
"fieldx, fieldy = wcs._focalToFieldMany(focalx, focaly)\n",
"focalx1, focaly1 = wcs._fieldToFocalMany(fieldx, fieldy)"
]
},
{
"cell_type": "code",
"execution_count": 1044,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-2.983737389106178e-08 pixel\n",
"-9.86531689672887e-06 pixel\n",
"2.320837749411608e-07 pixel\n",
"2.4014325250565346e-05 pixel\n"
]
}
],
"source": [
"print(np.median(focalx1-focalx)/10e-6, \"pixel\")\n",
"print(np.median(focaly1-focaly)/10e-6, \"pixel\")\n",
"\n",
"print(np.median(np.abs(focalx1-focalx))/10e-6, \"pixel\")\n",
"print(np.median(np.abs(focaly1-focaly))/10e-6, \"pixel\")"
]
},
{
"cell_type": "code",
"execution_count": 1046,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"R01_S00 7.2544181594384275e-06 arcsec\n",
"R01_S01 1.433698188485654e-05 arcsec\n",
"R01_S02 1.0243720362907117e-05 arcsec\n",
"R01_S10 1.1135579939677904e-05 arcsec\n",
"R01_S11 6.403266541792628e-06 arcsec\n",
"R01_S12 4.3049784043895906e-06 arcsec\n",
"R01_S20 5.1013095839763515e-06 arcsec\n",
"R01_S21 2.938842067336334e-06 arcsec\n",
"R01_S22 2.499024072583775e-06 arcsec\n",
"R02_S00 7.734938030505143e-06 arcsec\n",
"R02_S01 6.839891060860329e-06 arcsec\n",
"R02_S02 6.315694818984418e-06 arcsec\n",
"R02_S10 3.7584564577118143e-06 arcsec\n",
"R02_S11 3.874487684417425e-06 arcsec\n",
"R02_S12 4.002426728944234e-06 arcsec\n",
"R02_S20 2.515082693170484e-06 arcsec\n",
"R02_S21 2.7497054732218163e-06 arcsec\n",
"R02_S22 2.940118920891674e-06 arcsec\n",
"R03_S00 6.270739447745473e-06 arcsec\n",
"R03_S01 4.728063033819002e-06 arcsec\n",
"R03_S02 4.066500866608575e-06 arcsec\n",
"R03_S10 3.801634932564093e-06 arcsec\n",
"R03_S11 3.450567518303577e-06 arcsec\n",
"R03_S12 3.5868656098312167e-06 arcsec\n",
"R03_S20 2.6899331798830387e-06 arcsec\n",
"R03_S21 2.8450070620697365e-06 arcsec\n",
"R03_S22 3.27941683418751e-06 arcsec\n",
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"R10_S01 1.1894259235862296e-05 arcsec\n",
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"R10_S10 1.2412012349821431e-05 arcsec\n",
"R10_S11 7.963518253623366e-06 arcsec\n",
"R10_S12 4.0037586856094305e-06 arcsec\n",
"R10_S20 1.347066975575221e-05 arcsec\n",
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"R12_S01 2.0238459828615106e-06 arcsec\n",
"R12_S02 2.1910730079972984e-06 arcsec\n",
"R12_S10 1.4105771740586084e-06 arcsec\n",
"R12_S11 1.4753980214786736e-06 arcsec\n",
"R12_S12 1.526639798802465e-06 arcsec\n",
"R12_S20 1.0214354341290098e-06 arcsec\n",
"R12_S21 9.762393893233948e-07 arcsec\n",
"R12_S22 1.051031037128247e-06 arcsec\n",
"R13_S00 2.137109351734044e-06 arcsec\n",
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"R14_S00 4.2217800436607286e-06 arcsec\n",
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"R14_S10 4.323315753256302e-06 arcsec\n",
"R14_S11 6.079756899450768e-06 arcsec\n",
"R14_S12 1.1456109720338699e-05 arcsec\n",
"R14_S20 4.307878831717484e-06 arcsec\n",
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"R20_S00 1.0828928986452875e-05 arcsec\n",
"R20_S01 5.506583653847402e-06 arcsec\n",
"R20_S02 3.7189901076206055e-06 arcsec\n",
"R20_S10 9.785994930888448e-06 arcsec\n",
"R20_S11 5.572951413732964e-06 arcsec\n",
"R20_S12 3.939686471186748e-06 arcsec\n",
"R20_S20 9.589423889598343e-06 arcsec\n",
"R20_S21 5.745308931990021e-06 arcsec\n",
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"R21_S01 1.9736783583675165e-06 arcsec\n",
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"R21_S21 2.324068836290633e-06 arcsec\n",
"R21_S22 1.5178732607820305e-06 arcsec\n",
"R22_S00 7.1918190586734e-07 arcsec\n",
"R22_S01 4.883078592584228e-07 arcsec\n",
"R22_S02 7.426067209140189e-07 arcsec\n",
"R22_S10 6.9465632569349e-07 arcsec\n",
"R22_S11 3.294776848423244e-08 arcsec\n",
"R22_S12 6.941710649870074e-07 arcsec\n",
"R22_S20 7.426626738283292e-07 arcsec\n",
"R22_S21 4.877863141380839e-07 arcsec\n",
"R22_S22 7.191050656540824e-07 arcsec\n",
"R23_S00 1.517322453316218e-06 arcsec\n",
"R23_S01 2.324434431112034e-06 arcsec\n",
"R23_S02 3.1471060601004372e-06 arcsec\n",
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"R24_S12 9.81152269887281e-06 arcsec\n",
"R24_S20 3.7215638522257794e-06 arcsec\n",
"R24_S21 5.518217566275126e-06 arcsec\n",
"R24_S22 1.0854861082451119e-05 arcsec\n",
"R30_S00 1.0017236920462652e-05 arcsec\n",
"R30_S01 5.9422669473925256e-06 arcsec\n",
"R30_S02 4.308993954067273e-06 arcsec\n",
"R30_S10 1.1476235236682728e-05 arcsec\n",
"R30_S11 6.081246293572697e-06 arcsec\n",
"R30_S12 4.3230023095924425e-06 arcsec\n",
"R30_S20 5.945557569144434e-06 arcsec\n",
"R30_S21 6.830938773476881e-06 arcsec\n",
"R30_S22 4.225583768396624e-06 arcsec\n",
"R31_S00 3.170048812388974e-06 arcsec\n",
"R31_S01 2.188900907812993e-06 arcsec\n",
"R31_S02 1.4973043254192379e-06 arcsec\n",
"R31_S10 3.0144734113947926e-06 arcsec\n",
"R31_S11 2.2670820677722642e-06 arcsec\n",
"R31_S12 1.7577331173237774e-06 arcsec\n",
"R31_S20 3.101438016010477e-06 arcsec\n",
"R31_S21 2.501484905012948e-06 arcsec\n",
"R31_S22 2.1371761284735044e-06 arcsec\n",
"R32_S00 1.0514580415030835e-06 arcsec\n",
"R32_S01 9.759213835514153e-07 arcsec\n",
"R32_S02 1.022961861834511e-06 arcsec\n",
"R32_S10 1.5278763537360677e-06 arcsec\n",
"R32_S11 1.475563599167544e-06 arcsec\n",
"R32_S12 1.4116999893750321e-06 arcsec\n",
"R32_S20 2.1930427652684625e-06 arcsec\n",
"R32_S21 2.023010669809824e-06 arcsec\n",
"R32_S22 1.881710194580054e-06 arcsec\n",
"R33_S00 1.4539624644790492e-06 arcsec\n",
"R33_S01 2.019470831720156e-06 arcsec\n",
"R33_S02 2.724100596664895e-06 arcsec\n",
"R33_S10 1.724750596310033e-06 arcsec\n",
"R33_S11 2.1714554063574315e-06 arcsec\n",
"R33_S12 2.811880208478471e-06 arcsec\n",
"R33_S20 2.036897369118429e-06 arcsec\n",
"R33_S21 2.318973229878527e-06 arcsec\n",
"R33_S22 3.051145783347603e-06 arcsec\n",
"R34_S00 3.749451035186719e-06 arcsec\n",
"R34_S01 6.1130645824845245e-06 arcsec\n",
"R34_S02 1.3462606453280697e-05 arcsec\n",
"R34_S10 4.000617092722815e-06 arcsec\n",
"R34_S11 7.975109228562888e-06 arcsec\n",
"R34_S12 1.239076437597338e-05 arcsec\n",
"R34_S20 5.553458151902675e-06 arcsec\n",
"R34_S21 1.189067681809683e-05 arcsec\n",
"R34_S22 7.97652580786108e-06 arcsec\n",
"R41_S00 3.27887620201187e-06 arcsec\n",
"R41_S01 2.844243222045283e-06 arcsec\n",
"R41_S02 2.691016367475978e-06 arcsec\n",
"R41_S10 3.5872512072044937e-06 arcsec\n",
"R41_S11 3.4524245646682166e-06 arcsec\n",
"R41_S12 3.8054942971284477e-06 arcsec\n",
"R41_S20 4.067613752630853e-06 arcsec\n",
"R41_S21 4.7327789118198416e-06 arcsec\n",
"R41_S22 6.282363878144554e-06 arcsec\n",
"R42_S00 2.940192988058819e-06 arcsec\n",
"R42_S01 2.7486082414921117e-06 arcsec\n",
"R42_S02 2.5140707996985763e-06 arcsec\n",
"R42_S10 4.002620663265936e-06 arcsec\n",
"R42_S11 3.876953190771095e-06 arcsec\n",
"R42_S12 3.7531969732197456e-06 arcsec\n",
"R42_S20 6.321685493119289e-06 arcsec\n",
"R42_S21 6.846602190265953e-06 arcsec\n",
"R42_S22 7.741481345894385e-06 arcsec\n",
"R43_S00 2.500785225224768e-06 arcsec\n",
"R43_S01 2.939119014135222e-06 arcsec\n",
"R43_S02 5.119268546228302e-06 arcsec\n",
"R43_S10 4.31645631061019e-06 arcsec\n",
"R43_S11 6.415219265070235e-06 arcsec\n",
"R43_S12 1.1143159837594767e-05 arcsec\n",
"R43_S20 1.0250233264242218e-05 arcsec\n",
"R43_S21 1.4361027593873208e-05 arcsec\n",
"R43_S22 7.255121260807699e-06 arcsec\n"
]
}
],
"source": [
"# Repeat focal -> field -> focal for all detectors\n",
"for det in camera:\n",
" wcs = BatoidWCS(\n",
" boresight, rotSkyPos, rotTelPos,\n",
" batoid.Optic.fromYaml(\"LSST_r.yaml\"),\n",
" 620, # nm\n",
" camera, det\n",
" )\n",
" \n",
" fieldx = wcs._field_x + np.deg2rad(2000*0.2/3600)*np.linspace(-1, 1, 800)\n",
" fieldy = wcs._field_y + np.deg2rad(2000*0.2/3600)*np.linspace(-1, 1, 800)\n",
" fieldx, fieldy = np.meshgrid(fieldx, fieldy)\n",
" fieldx = fieldx.ravel()\n",
" fieldy = fieldy.ravel()\n",
"\n",
" focalx, focaly = wcs._fieldToFocalMany(fieldx, fieldy)\n",
" fieldx1, fieldy1 = wcs._focalToFieldMany(focalx, focaly)\n",
" \n",
" print(det.getName(), 3600*np.rad2deg(np.median(np.abs(fieldx1-fieldx))), \"arcsec\")"
]
},
{
"cell_type": "code",
"execution_count": 1049,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.2471421630143595e-05 pixel\n",
"4.088101013621781e-05 pixel\n",
"5.574985804668309e-06 arcsec\n",
"7.499402895974616e-06 arcsec\n"
]
}
],
"source": [
"# Try pixel -> radec -> pixel -> radec roundtrip\n",
"x = np.random.uniform(-50, 4050, size=100000)\n",
"y = np.random.uniform(-50, 4050, size=100000)\n",
"ra, dec = wcs.xyToradec(x, y, units='rad')\n",
"x1, y1 = wcs.radecToxy(ra, dec, units='rad')\n",
"ra1, dec1 = wcs.xyToradec(x1, y1, units='rad')\n",
"\n",
"print(np.median(np.abs(x-x1)), \"pixel\")\n",
"print(np.median(np.abs(y-y1)), \"pixel\")\n",
"print(206265*np.median(np.abs(ra-ra1)), \"arcsec\")\n",
"print(206265*np.median(np.abs(dec-dec1)), \"arcsec\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.2"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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