def test_fftim(self):
self.m31image = create_test_image(cellsize=0.001,
frequency=[1e8],
canonical=True)
m31_fft = fft_image(self.m31image)
m31_fft_ifft = fft_image(m31_fft, self.m31image)
numpy.testing.assert_array_almost_equal(self.m31image.data,
m31_fft_ifft.data.real, 12)
m31_fft.data = numpy.abs(m31_fft.data)
export_image_to_fits(m31_fft,
fitsfile='%s/test_m31_fft.fits' % (self.dir))
def test_tapering_Gaussian(self):
self.actualSetUp()
size_required = 0.003542
self.componentvis, _, _ = weight_visibility(self.componentvis,
self.model,
algoritm='uniform')
self.componentvis = taper_visibility_gaussian(self.componentvis,
beam=size_required)
psf, sumwt = invert_2d(self.componentvis, self.model, dopsf=True)
export_image_to_fits(
psf, '%s/test_weighting_gaussian_taper_psf.fits' % self.dir)
xfr = fft_image(psf)
xfr.data = xfr.data.real.astype('float')
export_image_to_fits(
xfr, '%s/test_weighting_gaussian_taper_xfr.fits' % self.dir)
npixel = psf.data.shape[3]
sl = slice(npixel // 2 - 7, npixel // 2 + 8)
fit = fit_2dgaussian(psf.data[0, 0, sl, sl])
if fit.x_stddev <= 0.0 or fit.y_stddev <= 0.0:
raise ValueError('Error in fitting to psf')
# fit_2dgaussian returns sqrt of variance. We need to convert that to FWHM.
# https://en.wikipedia.org/wiki/Full_width_at_half_maximum
scale_factor = numpy.sqrt(8 * numpy.log(2.0))
size = numpy.sqrt(fit.x_stddev * fit.y_stddev) * scale_factor
# Now we need to convert to radians
size *= numpy.pi * self.model.wcs.wcs.cdelt[1] / 180.0
# Very impressive! Desired 0.01 Acheived 0.0100006250829
assert numpy.abs(size - size_required) < 0.001 * size_required, \
"Fit should be %f, actually is %f" % (size_required, size)
def test_fftim_factors(self):
for i in [3, 5, 7]:
npixel = 256 * i
m31image = create_test_image(cellsize=0.001,
frequency=[1e8],
canonical=True)
padded = pad_image(m31image, [1, 1, npixel, npixel])
assert padded.shape == (1, 1, npixel, npixel)
padded_fft = fft_image(padded)
padded_fft_ifft = fft_image(padded_fft, m31image)
numpy.testing.assert_array_almost_equal(padded.data,
padded_fft_ifft.data.real,
12)
padded_fft.data = numpy.abs(padded_fft.data)
export_image_to_fits(padded_fft,
fitsfile='%s/test_m31_fft_%d.fits' %
(self.dir, npixel))
def test_convert_image_to_kernel(self):
m31image = create_test_image(cellsize=0.001,
frequency=[1e8],
canonical=True)
screen = create_w_term_like(m31image, w=20000.0, remove_shift=True)
screen_fft = fft_image(screen)
converted = convert_image_to_kernel(screen_fft, 8, 8)
assert converted.shape == (1, 1, 8, 8, 8, 8)
with self.assertRaises(AssertionError):
converted = convert_image_to_kernel(m31image, 15, 1)
with self.assertRaises(AssertionError):
converted = convert_image_to_kernel(m31image, 15, 1000)
def test_tapering_Tukey(self):
self.actualSetUp()
self.componentvis, _, _ = weight_visibility(self.componentvis,
self.model,
algoritm='uniform')
self.componentvis = taper_visibility_tukey(self.componentvis,
tukey=1.0)
psf, sumwt = invert_2d(self.componentvis, self.model, dopsf=True)
export_image_to_fits(
psf, '%s/test_weighting_tukey_taper_psf.fits' % self.dir)
xfr = fft_image(psf)
xfr.data = xfr.data.real.astype('float')
export_image_to_fits(
xfr, '%s/test_weighting_tukey_taper_xfr.fits' % self.dir)
def create_awterm_convolutionfunction(im,
make_pb=None,
nw=1,
wstep=1e15,
oversampling=8,
support=6,
use_aaf=True,
maxsupport=512):
""" Fill AW projection kernel into a GridData.
:param im: Image template
:param make_pb: Function to make the primary beam model image
:param nw: Number of w planes
:param wstep: Step in w (wavelengths)
:param oversampling: Oversampling of the convolution function in uv space
:return: griddata correction Image, griddata kernel as GridData
"""
d2r = numpy.pi / 180.0
# We only need the griddata correction function for the PSWF so we make
# it for the shape of the image
nchan, npol, ony, onx = im.data.shape
assert isinstance(im, Image)
# Calculate the template convolution kernel.
cf = create_convolutionfunction_from_image(im,
oversampling=oversampling,
support=support)
cf_shape = list(cf.data.shape)
cf_shape[2] = nw
cf.data = numpy.zeros(cf_shape).astype('complex')
cf.grid_wcs.wcs.crpix[4] = nw // 2 + 1.0
cf.grid_wcs.wcs.cdelt[4] = wstep
cf.grid_wcs.wcs.ctype[4] = 'WW'
if numpy.abs(wstep) > 0.0:
w_list = cf.grid_wcs.sub([5]).wcs_pix2world(range(nw), 0)[0]
else:
w_list = [0.0]
assert isinstance(oversampling, int)
assert oversampling > 0
nx = max(maxsupport, 2 * oversampling * support)
ny = max(maxsupport, 2 * oversampling * support)
qnx = nx // oversampling
qny = ny // oversampling
cf.data[...] = 0.0
subim = copy_image(im)
ccell = onx * numpy.abs(d2r * subim.wcs.wcs.cdelt[0]) / qnx
subim.data = numpy.zeros([nchan, npol, qny, qnx])
subim.wcs.wcs.cdelt[0] = -ccell / d2r
subim.wcs.wcs.cdelt[1] = +ccell / d2r
subim.wcs.wcs.crpix[0] = qnx // 2 + 1.0
subim.wcs.wcs.crpix[1] = qny // 2 + 1.0
if use_aaf:
this_pswf_gcf, _ = create_pswf_convolutionfunction(subim,
oversampling=1,
support=6)
norm = 1.0 / this_pswf_gcf.data
else:
norm = 1.0
if make_pb is not None:
pb = make_pb(subim)
rpb, footprint = reproject_image(pb, subim.wcs, shape=subim.shape)
rpb.data[footprint.data < 1e-6] = 0.0
norm *= rpb.data
# We might need to work with a larger image
padded_shape = [nchan, npol, ny, nx]
thisplane = copy_image(subim)
thisplane.data = numpy.zeros(thisplane.shape, dtype='complex')
for z, w in enumerate(w_list):
thisplane.data[...] = 0.0 + 0.0j
thisplane = create_w_term_like(thisplane, w, dopol=True)
thisplane.data *= norm
paddedplane = pad_image(thisplane, padded_shape)
paddedplane = fft_image(paddedplane)
ycen, xcen = ny // 2, nx // 2
for y in range(oversampling):
ybeg = y + ycen + (support * oversampling) // 2 - oversampling // 2
yend = y + ycen - (support * oversampling) // 2 - oversampling // 2
vv = range(ybeg, yend, -oversampling)
for x in range(oversampling):
xbeg = x + xcen + (support *
oversampling) // 2 - oversampling // 2
xend = x + xcen - (support *
oversampling) // 2 - oversampling // 2
uu = range(xbeg, xend, -oversampling)
for chan in range(nchan):
for pol in range(npol):
cf.data[chan, pol, z, y, x, :, :] = paddedplane.data[
chan, pol, :, :][vv, :][:, uu]
cf.data /= numpy.sum(
numpy.real(cf.data[0, 0, nw // 2, oversampling // 2,
oversampling // 2, :, :]))
cf.data = numpy.conjugate(cf.data)
if use_aaf:
pswf_gcf, _ = create_pswf_convolutionfunction(im,
oversampling=1,
support=6)
else:
pswf_gcf = create_empty_image_like(im)
pswf_gcf.data[...] = 1.0
return pswf_gcf, cf
def create_awterm_convolutionfunction(im,
make_pb=None,
nw=1,
wstep=1e15,
oversampling=8,
support=6,
use_aaf=True,
maxsupport=512,
**kwargs):
""" Fill AW projection kernel into a GridData.
:param im: Image template
:param make_pb: Function to make the primary beam model image (hint: use a partial)
:param nw: Number of w planes
:param wstep: Step in w (wavelengths)
:param oversampling: Oversampling of the convolution function in uv space
:return: griddata correction Image, griddata kernel as GridData
"""
d2r = numpy.pi / 180.0
# We only need the griddata correction function for the PSWF so we make
# it for the shape of the image
nchan, npol, ony, onx = im.data.shape
assert isinstance(im, Image)
# Calculate the template convolution kernel.
cf = create_convolutionfunction_from_image(im,
oversampling=oversampling,
support=support)
cf_shape = list(cf.data.shape)
cf_shape[2] = nw
cf.data = numpy.zeros(cf_shape).astype('complex')
cf.grid_wcs.wcs.crpix[4] = nw // 2 + 1.0
cf.grid_wcs.wcs.cdelt[4] = wstep
cf.grid_wcs.wcs.ctype[4] = 'WW'
if numpy.abs(wstep) > 0.0:
w_list = cf.grid_wcs.sub([5]).wcs_pix2world(range(nw), 0)[0]
else:
w_list = [0.0]
assert isinstance(oversampling, int)
assert oversampling > 0
nx = max(maxsupport, 2 * oversampling * support)
ny = max(maxsupport, 2 * oversampling * support)
qnx = nx // oversampling
qny = ny // oversampling
cf.data[...] = 0.0
subim = copy_image(im)
ccell = onx * numpy.abs(d2r * subim.wcs.wcs.cdelt[0]) / qnx
subim.data = numpy.zeros([nchan, npol, qny, qnx])
subim.wcs.wcs.cdelt[0] = -ccell / d2r
subim.wcs.wcs.cdelt[1] = +ccell / d2r
subim.wcs.wcs.crpix[0] = qnx // 2 + 1.0
subim.wcs.wcs.crpix[1] = qny // 2 + 1.0
if use_aaf:
this_pswf_gcf, _ = create_pswf_convolutionfunction(subim,
oversampling=1,
support=6)
norm = 1.0 / this_pswf_gcf.data
else:
norm = 1.0
if make_pb is not None:
pb = make_pb(subim)
rpb, footprint = reproject_image(pb, subim.wcs, shape=subim.shape)
rpb.data[footprint.data < 1e-6] = 0.0
norm *= rpb.data
# We might need to work with a larger image
padded_shape = [nchan, npol, ny, nx]
thisplane = copy_image(subim)
thisplane.data = numpy.zeros(thisplane.shape, dtype='complex')
for z, w in enumerate(w_list):
thisplane.data[...] = 0.0 + 0.0j
thisplane = create_w_term_like(thisplane, w, dopol=True)
thisplane.data *= norm
paddedplane = pad_image(thisplane, padded_shape)
paddedplane = fft_image(paddedplane)
ycen, xcen = ny // 2, nx // 2
for y in range(oversampling):
ybeg = y + ycen + (support * oversampling) // 2 - oversampling // 2
yend = y + ycen - (support * oversampling) // 2 - oversampling // 2
# vv = range(ybeg, yend, -oversampling)
for x in range(oversampling):
xbeg = x + xcen + (support *
oversampling) // 2 - oversampling // 2
xend = x + xcen - (support *
oversampling) // 2 - oversampling // 2
# uu = range(xbeg, xend, -oversampling)
cf.data[..., z, y,
x, :, :] = paddedplane.data[...,
ybeg:yend:-oversampling,
xbeg:xend:-oversampling]
# for chan in range(nchan):
# for pol in range(npol):
# cf.data[chan, pol, z, y, x, :, :] = paddedplane.data[chan, pol, :, :][vv, :][:, uu]
cf.data /= numpy.sum(
numpy.real(cf.data[0, 0, nw // 2, oversampling // 2,
oversampling // 2, :, :]))
cf.data = numpy.conjugate(cf.data)
#====================================
#Use ASKAPSoft routine to crop the support size
crop_ASKAPSOft_like = True
if crop_ASKAPSOft_like:
#Hardcode the cellsize: 1 / FOV
#uv_cellsize = 57.3;#N=1200 pixel and pixelsize is 3 arcseconds
#uv_cellsize = 43.97;#N=1600 pixel and pixelsize is 3 arcseconds
#uv_cellsize = 114.6;#N=1800 pixel with 1 arcsecond pixelsize
#uv_cellsize = 57.3;#N=1800 pixel with 2 arcsecond pixelsize
#uv_cellsize = 1145.91509915;#N=1800 pixxel with 0.1 arcsecond pixelsize
#Get from **kwargs
if kwargs is None:
#Safe solution works for baselines up to > 100km and result in small kernels
uv_cellsize = 1145.91509915
#N=1800 pixxel with 0.1 arcsecond pixelsize
if 'UVcellsize' in kwargs.keys():
uv_cellsize = kwargs['UVcellsize']
#print(uv_cellsize);
#Cutoff param in ASKAPSoft hardcoded as well
ASKAPSoft_cutof = 0.1
wTheta_list = numpy.zeros(len(w_list))
for i in range(0, len(w_list)):
if w_list[i] == 0:
wTheta_list[i] = 0.9
#This is due to the future if statements cause if it is small, the kernel will be 3 which is a clear cutoff
else:
wTheta_list[i] = numpy.fabs(
w_list[i]) / (uv_cellsize * uv_cellsize)
kernel_size_list = []
#We rounded the kernels according to conventional rounding rules
for i in range(0, len(wTheta_list)):
#if wTheta_list[i] < 1:
if wTheta_list[i] < 1: #Change to ASKAPSoft
kernel_size_list.append(int(3.))
elif ASKAPSoft_cutof < 0.01:
kernel_size_list.append(int(6 + 1.14 * wTheta_list[i]))
else:
kernel_size_list.append(
int(numpy.sqrt(49 + wTheta_list[i] * wTheta_list[i])))
log.info('W-kernel w-terms:')
log.info(w_list)
log.info('Corresponding w-kernel sizes:')
log.info(kernel_size_list)
print(numpy.unique(kernel_size_list))
#print(kernel_size_list);
crop_list = []
#another rounding according to conventional rounding rules
for i in range(0, len(kernel_size_list)):
if support - kernel_size_list[i] <= 0:
crop_list.append(int(0))
else:
crop_list.append(int((support - kernel_size_list[i]) / 2))
#Crop original suppor
for i in range(0, nw):
if crop_list[i] != 0:
cf.data[0, 0, i, :, :, 0:crop_list[i], :] = 0
cf.data[0, 0, i, :, :, -crop_list[i]:, :] = 0
cf.data[0, 0, i, :, :, :, 0:crop_list[i]] = 0
cf.data[0, 0, i, :, :, :, -crop_list[i]:] = 0
else:
pass
#Plot
#import matplotlib.pyplot as plt
#cf.data[0,0,i,0,0,...][cf.data[0,0,i,0,0,...] != 0.] = 1+0.j;
#plt.imshow(numpy.real(cf.data[0,0,i,0,0,...]))
#plt.show(block=True)
#plt.close();
#====================================
if use_aaf:
pswf_gcf, _ = create_pswf_convolutionfunction(im,
oversampling=1,
support=6)
else:
pswf_gcf = create_empty_image_like(im)
pswf_gcf.data[...] = 1.0
return pswf_gcf, cf
def create_vp_generic_numeric(model,
pointingcentre=None,
diameter=15.0,
blockage=0.0,
taper='gaussian',
edge=0.03162278,
zernikes=None,
padding=4,
use_local=True,
rho=0.0,
diff=0.0):
"""
Make an image like model and fill it with an analytical model of the primary beam
The elements of the analytical model are:
- dish, optionally blocked
- Gaussian taper, default is -12dB at the edge
- Offset to pointing centre (optional)
- zernikes in a list of dictionaries. Each list element is of the form {"coeff":0.1, "noll":5}. See aotools for
more details
- Output image can be in RA, DEC coordinates or AZELGEO coordinates (the default). use_local=True means to use
AZELGEO coordinates centered on 0deg 0deg.
The dish is zero padded according to padding and FFT'ed to get the voltage pattern.
:param model:
:param pointingcentre: SkyCoord of desired pointing centre
:param diameter: Diameter of dish in metres
:param blockage: Blockage of dish in metres
:param taper: "Gaussian" or None
:param edge: Value of taper at the end of the dish (default corresponds to -12dB)
:param zernikes: Zernikes to be applied as phase across the dish (see above)
:param padding: Pad the image by this amount
:param use_local: Use local frame (AZELGEO)?
:return:
"""
beam = create_empty_image_like(model)
nchan, npol, ny, nx = beam.shape
padded_shape = [nchan, npol, padding * ny, padding * nx]
padded_beam = pad_image(beam, padded_shape)
padded_beam.data = numpy.zeros(padded_beam.data.shape, dtype='complex')
_, _, pny, pnx = padded_beam.shape
xfr = fft_image(padded_beam)
cx, cy = xfr.wcs.sub(2).wcs.crpix[0] - 1, xfr.wcs.sub(2).wcs.crpix[1] - 1
for chan in range(nchan):
# The frequency axis is the second to last in the beam
frequency = xfr.wcs.sub(['spectral']).wcs_pix2world([chan], 0)[0]
wavelength = const.c.to('m s^-1').value / frequency
scalex = xfr.wcs.sub(2).wcs.cdelt[0] * wavelength
scaley = xfr.wcs.sub(2).wcs.cdelt[1] * wavelength
# xx, yy in metres
xx, yy = numpy.meshgrid(scalex * (range(pnx) - cx),
scaley * (range(pny) - cy))
# rr in metres
rr = numpy.sqrt(xx**2 + yy**2)
for pol in range(npol):
xfr.data[chan, pol, ...] = tapered_disk(rr,
diameter / 2.0,
blockage=blockage / 2.0,
edge=edge,
taper=taper)
if pointingcentre is not None:
# Correct for pointing centre
pcx, pcy = pointingcentre.to_pixel(padded_beam.wcs, origin=0)
pxx, pyy = numpy.meshgrid((range(pnx) - cx), (range(pny) - cy))
phase = 2 * numpy.pi * ((pcx - cx) * pxx / float(pnx) +
(pcy - cy) * pyy / float(pny))
for pol in range(npol):
xfr.data[chan, pol, ...] *= numpy.exp(1j * phase)
if isinstance(zernikes, collections.Iterable):
try:
import aotools
except ModuleNotFoundError:
raise ModuleNotFoundError("aotools is not installed")
ndisk = numpy.ceil(numpy.abs(diameter / scalex)).astype('int')[0]
ndisk = 2 * ((ndisk + 1) // 2)
phase = numpy.zeros([ndisk, ndisk])
for zernike in zernikes:
phase = zernike['coeff'] * aotools.functions.zernike(
zernike['noll'], ndisk)
# import matplotlib.pyplot as plt
# plt.clf()
# plt.imshow(phase)
# plt.colorbar()
# plt.show()
#
blc = pnx // 2 - ndisk // 2
trc = pnx // 2 + ndisk // 2
for pol in range(npol):
xfr.data[chan, pol, blc:trc,
blc:trc] = xfr.data[chan, pol, blc:trc,
blc:trc] * numpy.exp(1j * phase)
padded_beam = fft_image(xfr, padded_beam)
# Undo padding
beam = create_empty_image_like(model)
beam.data = padded_beam.data[...,
(pny // 2 - ny // 2):(pny // 2 + ny // 2),
(pnx // 2 - nx // 2):(pnx // 2 + nx // 2)]
for chan in range(nchan):
beam.data[chan, ...] /= numpy.max(numpy.abs(beam.data[chan, ...]))
set_pb_header(beam, use_local=use_local)
return beam
noise_channel = args.noise_channel
resolution = args.resolution
plt.clf()
show_image(im, chan=signal_channel)
plt.title('Signal image %s' % (basename))
plt.savefig('simulation_image_channel_%d.png' % signal_channel)
plt.show()
plt.clf()
show_image(im, chan=noise_channel)
plt.title('Noise image %s' % (basename))
plt.savefig('simulation_noise_channel_%d.png' % signal_channel)
plt.show()
print(im)
imfft = fft_image(im)
print(imfft)
omega = numpy.pi * resolution**2 / (4 * numpy.log(2.0))
wavelength = consts.c / numpy.average(im.frequency)
kperjy = 1e-26 * wavelength**2 / (2 * consts.k_B * omega)
im_spectrum = copy_image(imfft)
im_spectrum.data = kperjy.value * numpy.abs(imfft.data)
plt.clf()
show_image(im_spectrum,
chan=signal_channel,
vmax=0.01 * numpy.max(im_spectrum.data[signal_channel, ...]))
plt.gca().set_title("Amplitude(FFT(image)) %s" % (basename))
plt.tight_layout()
plt.savefig('power_spectrum_image_channel_%d.png' % signal_channel)
