Tools for testing

[keflavich]

We can use image_registration to make synthetic images

np.random.seed(0)
im = image_registration.tests.make_extended(imsize=256., powerlaw=1.5)

cc @baobabyoo

[keflavich]

[keflavich]

"synthetic interferometric imaging":

ygrid, xgrid = np.indices(im.shape, dtype='float')
rr = ((xgrid-im.shape[1]/2)**2+(ygrid-im.shape[0]/2)**2)**0.5
ring = (rr>=8) & (rr<=(256/3.))
pl.imshow(ring)
imfft = np.fft.fft2(im)
imfft_interferometered = imfft * np.fft.fftshift(ring)
im_interferometered = np.fft.ifft2(imfft_interferometered)

ring:

"interferometered" image:

[keflavich]

from astropy import convolution
singledish_im = convolution.convolve_fft(im, convolution.Gaussian2DKernel(40/2.35), boundary='fill', fill_value=im.mean())

[keflavich]

from uvcombine.uvcombine import feather_kernel, fftmerge

pixscale = 1
lowresfwhm = 40
nax1,nax2 = im.shape
kfft, ikfft = feather_kernel(nax2, nax1, lowresfwhm, pixscale,)


im_hi = im_interferometered.real
im_low = singledish_im
lowresscalefactor=1
replace_hires=False
highpassfilterSD = False
deconvSD = False
highresscalefactor=1
fftsum, combo = fftmerge(kfft, ikfft, im_hi*highresscalefactor,
                         im_low*lowresscalefactor,
                         replace_hires=replace_hires,
                         highpassfilterSD=highpassfilterSD,
                         deconvSD=deconvSD,
                        )

combined, real:

original - feather combined:

[keflavich]

Gaussian synthetic image:

# 20 pixel gaussian as input image
singledish_kernel = np.exp(-rr**2 / (2*(20/2.35)**2))
# "interferometrically" observe: (note fftshift!!!!)
sd_interferometered = np.fft.ifft2(np.fft.fft2(singledish_kernel) * np.fft.fftshift(ring))
# single-dish image
lowresfwhm = 40
im_low = singledish_im = convolution.convolve_fft(singledish_kernel, convolution.Gaussian2DKernel(lowresfwhm/2.35), boundary='fill', fill_value=0)
kfft, ikfft = feather_kernel(nax2, nax1, lowresfwhm, pixscale,)

im_hi = sd_interferometered.real
fftsum, combo = fftmerge(kfft, ikfft, im_hi*highresscalefactor,
                         im_low*lowresscalefactor,
                         replace_hires=replace_hires,
                         highpassfilterSD=highpassfilterSD,
                         deconvSD=deconvSD,
                        )

input:

interferometered:

combined:

[keflavich]

Creating an exponential kernel:

expkernel[rr < 8] = 1.0
expkernel[rr >= 8] = (np.exp(-rr/10.) / np.exp(-8./10.))[rr>=8]
kfft = expkernel
ikfft = 1-expkernel
fftsum, combo = fftmerge(kfft, ikfft, im_hi*highresscalefactor,
                         im_low*lowresscalefactor,
                         replace_hires=replace_hires,
                         highpassfilterSD=highpassfilterSD,
                         deconvSD=deconvSD,
                        )
expcombo = combo

lowresfwhm = 40
# note the *u.deg "hack"
kfft, ikfft = feather_kernel(nax2, nax1, lowresfwhm*u.deg, pixscale,)
fftsum, combo = fftmerge(kfft, ikfft, im_hi*highresscalefactor,
                         im_low*lowresscalefactor,
                         replace_hires=replace_hires,
                         highpassfilterSD=highpassfilterSD,
                         deconvSD=deconvSD,
                        )
feathercombo = combo

[keflavich]

Note that there has been some simulation of array combination on the ALMA memo series, specifically simulations performed in Memo 488 which were criticized in the subsequent memo. Older imaging simulations for ACA+12m were done in 368. 398 describes a complete simulation pipeline.

[keflavich]

See https://github.com/radio-astro-tools/uvcombine/blob/master/examples/test_examples.py for a written-out script version of this. Colorbar'd, nicer figures:

[keflavich]

On image deconvolution: http://scikit-image.org/docs/dev/auto_examples/plot_restoration.html

[keflavich]

Notes from workshop:
https://www.eso.org/projects/alma/arc/tw/pub/External/CombinationWorkshop2016/

[keflavich]

Another important resource:
http://esoads.eso.org/abs/2009PASJ...61..873K
These folks have done some careful analysis of various effects we were exploring here and came up with some heuristics, though they used some simplified inputs (sphere, ellipse)