| 1 | from __future__ import absolute_import
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| 2 |
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| 3 | import collections
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| 4 | import numpy as np
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| 5 |
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| 6 |
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| 7 | class Axis(object):
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| 8 | """Class to hold axis information.
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| 9 | """
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| 10 |
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| 11 | def __init__(self, data, title='', units=''):
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| 12 | self.data = data
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| 13 | self.title = title
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| 14 | self.units = units
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| 15 |
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| 16 |
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| 17 | class Image(object):
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| 18 | """Class to hold 2d image, with axes, units, title, etc.
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| 19 | """
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| 20 | def __init__(self, data, axes=[], title='', units=''):
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| 21 | self.data = data
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| 22 | self.axes = axes
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| 23 | self.title = title
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| 24 | self.units = units
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| 25 |
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| 26 |
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| 27 | class BeamsGenerator(object):
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| 28 | """Class to generate the primary beam(s) of the simulated observation.
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| 29 | """
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| 30 |
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| 31 | def __init__(self, previous_results):
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| 32 | self.previous_results = previous_results
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| 33 | self.result = collections.OrderedDict()
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| 34 |
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| 35 | def run(self):
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| 36 | print 'BeamsGenerator.run'
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| 37 |
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| 38 | uvmapgen = self.previous_results['uvmapgenerator']
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| 39 | fts = self.previous_results['fts']
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| 40 | telescope = self.previous_results['loadparameters']['substages']\
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| 41 | ['Telescope']
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| 42 |
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| 43 | # number of mirror positions sampled by FTS
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| 44 | nsample = fts['ftsnsample']
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| 45 | fts_wn = fts['fts_wn']
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| 46 | fts_lambda = fts['fts_lambda']
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| 47 |
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| 48 | # max pixel size (radians) that will fully sample the image.
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| 49 | # Sampling freq is 2 * Nyquist freq. So sampling freq = 2 * b_max / lambda_min.
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| 50 | bmax = uvmapgen['bmax']
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| 51 | self.result['max baseline [m]'] = bmax
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| 52 | max_pixsize = np.min(fts_lambda) / (2.0 * bmax)
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| 53 | self.result['max pixsize [rad]'] = max_pixsize
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| 54 |
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| 55 | # Number of pixels per beam
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| 56 | # radius of first null of Airy disk is theta=1.22lambda/d. Number of
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| 57 | # pixels is beam diameter/max_pixsize. Calculate this for the
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| 58 | # longest wavelength, largest beam
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| 59 | max_beam_radius = 1.22 * np.max(fts_lambda) /\
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| 60 | telescope['Primary mirror diameter']
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| 61 | self.result['beam diam [rad]'] = 2.0 * max_beam_radius
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| 62 |
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| 63 | # go out to radius of first null
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| 64 | rpix = int(max_beam_radius / max_pixsize)
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| 65 | # rpix = 32
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| 66 | npix = 2 * rpix
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| 67 | self.result['npix'] = npix
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| 68 |
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| 69 | # spatial axes same for all wavelengths
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| 70 | axis = np.arange(-rpix, rpix, dtype=np.float)
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| 71 | axis *= max_pixsize
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| 72 | axis *= 206264.806247
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| 73 | self.result['spatial axis [arcsec]'] = axis
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| 74 |
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| 75 | # calculate beams for each point on fts_wn
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| 76 | # oversample uv grid by mult to minimise aliasing
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| 77 | mult = 5
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| 78 | mx,my = np.meshgrid(np.arange(-mult*rpix, mult*rpix),
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| 79 | np.arange(-mult*rpix, mult*rpix))
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| 80 | self.result['primary beam'] = collections.OrderedDict()
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| 81 | self.result['primary amplitude beam'] = collections.OrderedDict()
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| 82 | self.result['dirty beam'] = collections.OrderedDict()
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| 83 |
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| 84 | for wn in fts_wn:
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| 85 | # first calculate primary beam
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| 86 | #
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| 87 | # assume uniform illumination of primary. uv goes out to
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| 88 | # +- bmax / lambda_min, fill uv plane appropriate to primary
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| 89 | # size
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| 90 | mirror = np.ones([mult*npix,mult*npix])
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| 91 | lambda_min = 1.0 / (np.max(fts_wn) * 100.0)
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| 92 | lamb = 1.0 / (wn * 100.0)
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| 93 | mirror[(np.sqrt(mx*mx + my*my) / (mult*rpix)) *
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| 94 | (bmax / lambda_min) > \
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| 95 | (0.5 * telescope['Primary mirror diameter'] / lamb)] = 0.0
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| 96 |
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| 97 | # fftshift mirror to be centred at [0,0],
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| 98 | # do a 2d ftt of it,
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| 99 | # fftshift transform so that 0 freq is in centre of array
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| 100 | temp = np.fft.fftshift(mirror)
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| 101 | temp = np.fft.fft2(temp)
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| 102 | temp = np.fft.fftshift(temp)
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| 103 | # convert to real, should be real anyway as FT of symmetric function
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| 104 | # square to give intensity response
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| 105 | primary_amplitude_beam = np.real(temp)
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| 106 | primary_intensity_beam = np.power(np.abs(temp), 2)
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| 107 | # and normalise
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| 108 | primary_amplitude_beam /= np.max(primary_amplitude_beam)
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| 109 | primary_intensity_beam /= np.max(primary_intensity_beam)
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| 110 |
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| 111 | # truncate primary beam pattern
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| 112 | primary_amplitude_beam = primary_amplitude_beam[
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| 113 | (mult-1)*rpix:(mult+1)*rpix,
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| 114 | (mult-1)*rpix:(mult+1)*rpix]
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| 115 | primary_intensity_beam = primary_intensity_beam[
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| 116 | (mult-1)*rpix:(mult+1)*rpix,
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| 117 | (mult-1)*rpix:(mult+1)*rpix]
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| 118 |
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| 119 | # axes
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| 120 | axis1 = Axis(data=-axis, title='RA offset', units='arcsec')
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| 121 | axis2 = Axis(data=axis, title='Dec offset', units='arcsec')
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| 122 | image = Image(data=primary_intensity_beam, axes=[axis1, axis2],
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| 123 | title='Primary Beam %06.4g cm-1' % wn)
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| 124 | self.result['primary beam'][wn] = image
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| 125 |
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| 126 | image = Image(data=primary_amplitude_beam, axes=[axis1, axis2],
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| 127 | title='Amplitude Primary Beam %06.4g cm-1' % wn)
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| 128 | self.result['primary amplitude beam'][wn] = image
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| 129 |
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| 130 | # second calculate dirty beam
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| 131 | #
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| 132 | # 1. uv plane covered by discrete points so should use a
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| 133 | # slow dft rather than fft, which requires evenly spaced
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| 134 | # samples. Perhaps a bit slow though as calcs done in Python
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| 135 | # layer.
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| 136 | # 2. Could use shift theorem to give even-spaced equivalent
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| 137 | # of each discrete point, then use ffts. Equivalent to 1
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| 138 | # in speed.
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| 139 | # 3. Oversample uv plane and accept small error in point
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| 140 | # positions. Fastest but adequate?
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| 141 |
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| 142 | uv = np.zeros([mult*npix,mult*npix])
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| 143 | maxbx = bmax / np.min(fts_lambda)
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| 144 | for bxby in uvmapgen['bxby']:
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| 145 | ibx = int(round(((bxby[0] / lamb) / maxbx) * mult * rpix))
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| 146 | if ibx < 0:
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| 147 | ibx = mult*npix + ibx
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| 148 | iby = int(round(((bxby[1] / lamb) / maxbx) * mult * rpix))
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| 149 | if iby < 0:
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| 150 | iby = mult*npix + iby
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| 151 | uv[ibx,iby] = 1.0
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| 152 |
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| 153 | temp = np.fft.fftshift(uv)
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| 154 | temp = np.fft.fft2(temp)
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| 155 | temp = np.fft.fftshift(temp)
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| 156 | temp = np.power(temp, 2)
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| 157 | # convert to real, should be real anway as FT of symmetric function
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| 158 | dirty_beam = np.abs(temp)
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| 159 | # and normalise
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| 160 | dirty_beam /= np.max(dirty_beam)
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| 161 |
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| 162 | # truncate dirty beam pattern
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| 163 | dirty_beam = dirty_beam[
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| 164 | (mult-1)*rpix:(mult+1)*rpix,
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| 165 | (mult-1)*rpix:(mult+1)*rpix]
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| 166 |
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| 167 | # axes
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| 168 | axis = np.arange(-rpix, rpix, dtype=np.float)
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| 169 | axis *= (np.min(fts_lambda) / bmax)
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| 170 | axis *= 206264.806247
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| 171 | axis1 = Axis(data=-axis, title='RA offset', units='arcsec')
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| 172 | axis2 = Axis(data=axis, title='Dec offset', units='arcsec')
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| 173 |
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| 174 | image = Image(data=dirty_beam, axes=[axis1, axis2],
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| 175 | title='Dirty Beam %06.4g cm-1' % wn)
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| 176 |
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| 177 | self.result['dirty beam'][wn] = image
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| 178 |
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| 179 | return self.result
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| 180 |
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| 181 | def __repr__(self):
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| 182 | return 'PrimaryBeamGenerator'
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| 183 |
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