Anti-Aliasing Functions in Interferometry

Setup the data problem. Will use field of view of 0.002 radian. One source withing the field of view and a 5 times stronger just outside.



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%matplotlib inline

import sys
sys.path.append('../..')

from matplotlib import pylab

pylab.rcParams['figure.figsize'] = 16, 12


import numpy
import scipy
import scipy.special

from crocodile.clean import *
from crocodile.synthesis import *
from crocodile.simulate import *


vlas=numpy.genfromtxt("../../data/configurations/VLA_A_hor_xyz.csv", delimiter=",")
vobs=xyz_to_baselines(vlas, numpy.arange(0,numpy.pi,0.04) ,  numpy.pi/4)
yyone=simulate_point(vobs/5, 0.001, 0.001)
yytwo=yyone+ simulate_point(vobs/5, 0.0025, 0.0025)*5

Simple imaging (no convolution) with single source within field of view:



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d,p,_=do_imaging(2*0.002, 2*15000, vobs/5, None, yyone, simple_imaging)
pylab.matshow(d)  ; pylab.colorbar();  pylab.show()

Simple imaging (no convolution) with both sources, shows the strong source being "aliased" back into the field of view:



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d,p,_=do_imaging(2*0.002, 2*15000, vobs/5, None, yytwo, simple_imaging)
pylab.matshow(d)  ; pylab.colorbar();  pylab.show()
print(d[40:60,40:60].std())

Anti-aliasing function

This is an example anti-aliasing function to use:



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aa=anti_aliasing_function((120,120), 0, 5)
pylab.matshow(aa)  ; pylab.colorbar();  pylab.show()

After FFT-ing and extracting the middle this is what the anti-aliasing function looks like:



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kv=kernel_oversample(aa, 120, 4, 7)
pylab.matshow(kv[0][0].real)  ; pylab.colorbar();  pylab.show()

Imaginary part is close to nil:



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pylab.matshow(kv[0][0].imag)  ; pylab.colorbar();  pylab.show()

Gridding with the anti-aliasing function:

This is the image of single source within field of view without correcting the taper . Note that the strength of the source is surpressed.



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d,p,_=do_imaging(2*0.002, 2*15000, vobs/5, None, yyone, conv_imaging, kv=kv)
pylab.matshow(d)  ; pylab.colorbar();  pylab.show()

This is the image of single source within field of view. Note that the image is divided by the anti-aliasing funciton to correct for the taper introduced by it:



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d,p,_=do_imaging(2*0.002, 2*15000, vobs/5, None, yyone, conv_imaging, kv=kv)
pylab.matshow(d/aa)  ; pylab.colorbar();  pylab.show()

This is the image with source outside of field of view also: note that is very strongly surprssed.



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d,p,_=do_imaging(2*0.002, 2*15000, vobs/5, None, yytwo, conv_imaging, kv=kv)
pylab.matshow(d/aa)  ; pylab.colorbar();  pylab.show()
print((d/aa)[40:60,40:60].std())

As above but without correcting the taper.



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d,p,_=do_imaging(2*0.002, 2*15000, vobs/5, None, yytwo, conv_imaging, kv=kv)
pylab.matshow(d)  ; pylab.colorbar();  pylab.show()
print((d)[40:60,40:60].std())