| 1 | from __future__ import absolute_import
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| 2 |
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| 3 | import collections
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| 4 | import math
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| 5 | import numpy as np
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| 6 | import pp
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| 7 |
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| 8 | import common.commonobjects as co
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| 9 |
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| 10 | def fftshift(data, shift):
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| 11 | """Method to shift a 2d complex data array by applying the
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| 12 | given phase shift to its Fourier transform.
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| 13 | """
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| 14 | # move centre of image to array origin
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| 15 | temp = numpy.fft.fftshift(data)
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| 16 | # 2d fft
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| 17 | temp = numpy.fft.fft2(temp)
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| 18 | # apply phase shift
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| 19 | temp *= shift
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| 20 | # transform and shift back
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| 21 | temp = numpy.fft.ifft2(temp)
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| 22 | temp = numpy.fft.fftshift(temp)
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| 23 |
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| 24 | return temp
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| 25 |
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| 26 |
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| 27 | class DoubleFourier(object):
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| 28 | """Class to compute interferograms.
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| 29 | """
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| 30 |
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| 31 | def __init__(self, parameters, previous_results, job_server):
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| 32 | self.parameters = parameters
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| 33 | self.previous_results = previous_results
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| 34 | self.job_server = job_server
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| 35 |
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| 36 | self.result = collections.OrderedDict()
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| 37 |
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| 38 | def run(self):
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| 39 | print 'DoubleFourier.run'
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| 40 |
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| 41 | # convert lengths to m. Wavenumbers leave as cm-1.
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| 42 | fts = self.previous_results['fts']
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| 43 | fts_wn = fts['fts_wn']
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| 44 | fts_wn_truncated = fts['fts_wn_truncated']
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| 45 | opd_max = fts['opd_max'] / 100.0
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| 46 | fts_nsample = fts['ftsnsample']
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| 47 | vdrive = fts['vdrive'] / 100.0
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| 48 | delta_opd = fts['delta_opd']
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| 49 | delta_time = delta_opd / vdrive
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| 50 |
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| 51 | times = np.arange(int(fts_nsample), dtype=np.float)
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| 52 | times *= delta_time
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| 53 | opd_start = -((fts_nsample + 1) / 2) * delta_opd
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| 54 |
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| 55 | beamsgenerator = self.previous_results['beamsgenerator']
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| 56 |
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| 57 | uvmapgenerator = self.previous_results['uvmapgenerator']
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| 58 | bxby = uvmapgenerator['bxby']
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| 59 |
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| 60 | skygenerator = self.previous_results['skygenerator']
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| 61 | skymodel = skygenerator['sky model']
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| 62 | spatial_axis = self.result['spatial axis'] = skygenerator['spatial axis']
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| 63 | self.result['frequency axis'] = fts_wn_truncated
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| 64 |
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| 65 | # assuming nx is even then transform has 0 freq at origin and [nx/2] is
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| 66 | # Nyquist frequency. Nyq freq = 0.5 * Nyquist sampling freq.
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| 67 | # Assume further that the fft is shifted so that 0 freq is at nx/2
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| 68 | nx = len(spatial_axis)
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| 69 | spatial_freq_axis = np.arange(-nx/2, nx/2, dtype=np.float)
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| 70 | sample_freq = (180.0 * 3600.0 / np.pi) / (spatial_axis[1] - spatial_axis[0])
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| 71 | spatial_freq_axis *= (sample_freq / nx)
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| 72 | self.result['spatial frequency axis'] = spatial_freq_axis
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| 73 |
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| 74 | self.result['baseline interferograms'] = collections.OrderedDict()
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| 75 | # for baseline in bxby:
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| 76 | for baseline in bxby[:1]:
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| 77 | print 'baseline', baseline
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| 78 | measurement = np.zeros(np.shape(times))
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| 79 | opd = np.zeros(np.shape(times))
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| 80 |
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| 81 | # FTS path diff and possibly baseline itself vary with time
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| 82 | for tindex,t in enumerate(times):
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| 83 |
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| 84 | # calculate the sky that the system is observing at this
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| 85 | # moment, incorporating various errors in turn. Be explicit
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| 86 | # about the copy otherwise a reference is made instead.
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| 87 | sky_now = skymodel.copy()
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| 88 |
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| 89 | # 1. baseline should be perp to centre of field.
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| 90 | # If baseline is tilted then origin of sky map shifts.
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| 91 | # (I think effect could be corrected by changing
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| 92 | # FTS sample position to compensate.?)
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| 93 | # for now assume 0 error but do full calculation for timing
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| 94 | # purposes
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| 95 |
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| 96 | # perfect baseline is perpendicular to direction to 'centre'
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| 97 | # on sky. Add errors in x,y,z - z towards sky 'centre'
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| 98 | bz = 0.0
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| 99 | # convert bz to angular error
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| 100 | blength = math.sqrt(baseline[0]*baseline[0] +
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| 101 | baseline[1]*baseline[1])
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| 102 | bangle = (180.0 * 3600.0 / math.pi) * bz / blength
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| 103 | bx_error = bangle * baseline[0] / blength
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| 104 | by_error = bangle * baseline[1] / blength
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| 105 |
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| 106 | # calculate xpos, ypos in units of pixel - numpy arrays
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| 107 | # [row,col]
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| 108 | nx = len(spatial_axis)
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| 109 | colpos = float(nx-1) * bx_error / \
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| 110 | (spatial_axis[-1] - spatial_axis[0])
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| 111 | rowpos = float(nx-1) * by_error / \
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| 112 | (spatial_axis[-1] - spatial_axis[0])
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| 113 |
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| 114 | # calculate fourier phase shift to move point at [0,0] to
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| 115 | # [rowpos, colpos]
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| 116 | shiftx = np.zeros([nx], np.complex)
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| 117 | shiftx[:nx/2] = np.arange(nx/2, dtype=np.complex)
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| 118 | shiftx[nx/2:] = np.arange(-nx/2, 0, dtype=np.complex)
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| 119 | shiftx = np.exp((-2.0j * np.pi * colpos * shiftx) / float(nx))
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| 120 |
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| 121 | shifty = np.zeros([nx], np.complex)
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| 122 | shifty[:nx/2] = np.arange(nx/2, dtype=np.complex)
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| 123 | shifty[nx/2:] = np.arange(-nx/2, 0, dtype=np.complex)
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| 124 | shifty = np.exp((-2.0j * np.pi * rowpos * shifty) / float(nx))
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| 125 |
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| 126 | shift = np.ones([nx,nx], np.complex)
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| 127 | for j in range(nx):
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| 128 | shift[j,:] *= shiftx
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| 129 | for i in range(nx):
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| 130 | shift[:,i] *= shifty
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| 131 |
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| 132 | jobs = {}
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| 133 | # go through freq planes and shift them
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| 134 | for iwn,wn in enumerate(fts_wn_truncated):
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| 135 | # submit jobs
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| 136 | indata = (sky_now[:,:,iwn], shift,)
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| 137 | jobs[wn] = self.job_server.submit(fftshift,
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| 138 | indata, (), ('numpy',))
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| 139 |
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| 140 | for iwn,wn in enumerate(fts_wn_truncated):
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| 141 | # collect and store results
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| 142 | temp = jobs[wn]()
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| 143 | sky_now[:,:,iwn] = temp
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| 144 |
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| 145 | if t == times[0]:
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| 146 | # take copy of array to fix a snapshot of it now
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| 147 | self.result['sky at time 0'] = sky_now.copy()
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| 148 |
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| 149 | # 2. telescopes should be centred on centre of field
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| 150 | # Telescopes collect flux from the 'sky' and pass
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| 151 | # it to the FTS beam combiner. In doing this each
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| 152 | # telescope multiplies the sky emission by its
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| 153 | # amplitude beam response - always real but with
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| 154 | # negative areas. Is this correct? Gives right
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| 155 | # answer for 'no error' case.
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| 156 |
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| 157 | # multiply sky by amplitude beam 1 * amplitude beam 2
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| 158 | amp_beam_1 = beamsgenerator['primary amplitude beam'].data
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| 159 | amp_beam_2 = beamsgenerator['primary amplitude beam'].data
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| 160 |
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| 161 | for iwn,wn in enumerate(fts_wn):
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| 162 | # calculate shifted beams here
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| 163 | # for now assume no errors and just use beam
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| 164 | # calculated earlier
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| 165 | pass
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| 166 |
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| 167 | # multiply sky by amplitude beams of 2 antennas
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| 168 | sky_now *= amp_beam_1 * amp_beam_2
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| 169 |
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| 170 | if t == times[0]:
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| 171 | # take copy of array to fix a snapshot of it now
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| 172 | self.result['sky*beams at time 0'] = sky_now.copy()
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| 173 |
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| 174 | # 3. baseline error revisited
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| 175 | # derive baseline at this time
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| 176 | #
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| 177 | # Perhaps baseline should be a continuous function in
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| 178 | # time, which would allow baselines that intentionally
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| 179 | # smoothly vary (as in rotating tethered assembly)
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| 180 | # and errors to be handled by one description.
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| 181 | #
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| 182 | # what follows assumes zero error
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| 183 |
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| 184 | baseline_error = 0.0
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| 185 | baseline_now = baseline + baseline_error
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| 186 |
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| 187 | fft_now = np.zeros(np.shape(sky_now), np.complex)
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| 188 | spectrum = np.zeros(np.shape(fts_wn), np.complex)
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| 189 | for iwn,wn in enumerate(fts_wn_truncated):
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| 190 |
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| 191 | # derive shift needed to place baseline at one of FFT coords
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| 192 | # this depends on physical baseline and frequency
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| 193 | baseline_now_lambdas = baseline_now * wn * 100.0
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| 194 |
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| 195 | # calculate baseline position in units of pixels of FFTed
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| 196 | # sky - numpy arrays [row,col]
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| 197 | colpos = float(nx-1) * \
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| 198 | float(baseline_now_lambdas[0] - spatial_freq_axis[0]) / \
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| 199 | (spatial_freq_axis[-1] - spatial_freq_axis[0])
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| 200 | rowpos = float(nx-1) * \
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| 201 | float(baseline_now_lambdas[1] - spatial_freq_axis[0]) / \
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| 202 | (spatial_freq_axis[-1] - spatial_freq_axis[0])
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| 203 | colpos = 0.0
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| 204 | rowpos = 0.0
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| 205 |
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| 206 | # calculate fourier phase shift to move point at [rowpos,colpos] to
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| 207 | # [0,0]
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| 208 | shiftx = np.zeros([nx], np.complex)
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| 209 | shiftx[:nx/2] = np.arange(nx/2, dtype=np.complex)
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| 210 | shiftx[nx/2:] = np.arange(-nx/2, 0, dtype=np.complex)
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| 211 | shiftx = np.exp((-2.0j * np.pi * colpos * shiftx) / \
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| 212 | float(nx))
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| 213 |
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| 214 | shifty = np.zeros([nx], np.complex)
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| 215 | shifty[:nx/2] = np.arange(nx/2, dtype=np.complex)
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| 216 | shifty[nx/2:] = np.arange(-nx/2, 0, dtype=np.complex)
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| 217 | shifty = np.exp((-2.0j * np.pi * rowpos * shifty) / float(nx))
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| 218 |
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| 219 | shift = np.ones([nx,nx], np.complex)
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| 220 | for j in range(nx):
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| 221 | shift[j,:] *= shiftx
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| 222 | for i in range(nx):
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| 223 | shift[:,i] *= shifty
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| 224 |
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| 225 | # move centre of sky image to origin
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| 226 | temp = np.fft.fftshift(sky_now[:,:,iwn])
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| 227 | # apply phase shift
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| 228 | temp *= shift
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| 229 | # 2d fft
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| 230 | temp = np.fft.fft2(temp)
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| 231 | fft_now[:,:,iwn] = temp
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| 232 |
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| 233 | # set amp/phase at this frequency
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| 234 | spectrum[wn==fts_wn] = temp[0,0]
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| 235 |
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| 236 | if t == times[0]:
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| 237 | self.result['skyfft at time 0'] = fft_now.copy()
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| 238 |
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| 239 | axis = co.Axis(data=fts_wn, title='wavenumber',
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| 240 | units='cm-1')
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| 241 | temp = co.Spectrum(data=spectrum, axis=axis,
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| 242 | title='Detected spectrum', units='W sr-1 m-2 Hz-1')
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| 243 | self.result['skyfft spectrum at time 0'] = temp
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| 244 |
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| 245 | # 3. FTS sampling should be accurate
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| 246 | # derive lag due to FTS path difference
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| 247 | # 0 error for now
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| 248 |
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| 249 | if t == times[0]:
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| 250 | # test interferogram
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| 251 | # inverse fft of emission spectrum at this point
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| 252 | reflected_spectrum = np.zeros([2*(len(spectrum)-1)],
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| 253 | np.complex)
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| 254 | reflected_spectrum[:len(spectrum)].real = spectrum
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| 255 | reflected_spectrum[len(spectrum):].real = spectrum[-2:0:-1]
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| 256 |
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| 257 | temp = np.fft.ifft(reflected_spectrum)
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| 258 | pos = np.fft.fftfreq(len(reflected_spectrum), d=fts_wn[1]-fts_wn[0])
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| 259 |
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| 260 | # move 0 frequency to centre of array
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| 261 | temp = np.fft.fftshift(temp)
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| 262 | pos = np.fft.fftshift(pos)
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| 263 |
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| 264 | axis = co.Axis(data=pos, title='path difference',
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| 265 | units='cm')
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| 266 | temp = co.Spectrum(data=temp, axis=axis,
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| 267 | title='Detected interferogram', units='')
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| 268 |
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| 269 | self.result['test FTS at time 0'] = temp
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| 270 |
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| 271 | mirror_error = 0.0
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| 272 | opd[tindex] = opd_start + (vdrive * t + mirror_error)
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| 273 | opd_ipos = opd[tindex] / delta_opd
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| 274 |
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| 275 | # calculate shift needed to move point at opd to 0
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| 276 | nfreq = len(fts_wn)
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| 277 | ndoublefreq = 2 * (nfreq - 1)
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| 278 | shift = np.zeros([ndoublefreq], dtype=np.complex)
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| 279 | shift[:nfreq] = np.arange(nfreq, dtype=np.complex)
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| 280 | shift[nfreq:] = np.arange(nfreq, dtype=np.complex)[-2:0:-1]
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| 281 | shift = np.exp((-2.0j * np.pi * opd_ipos * shift) / \
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| 282 | float(ndoublefreq))
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| 283 |
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| 284 | # reflect spectrum about 0 to give unaliased version
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| 285 | reflected_spectrum = np.zeros([2*(len(spectrum)-1)], np.complex)
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| 286 | reflected_spectrum[:len(spectrum)].real = spectrum
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| 287 | reflected_spectrum[len(spectrum):].real = spectrum[-2:0:-1]
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| 288 |
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| 289 | # apply phase shift and fft
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| 290 | reflected_spectrum *= shift
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| 291 | spectrum_fft = np.fft.ifft(reflected_spectrum)
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| 292 | measurement[tindex] = spectrum_fft[0]
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| 293 |
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| 294 | # if np.array_equal(baseline, bxby[0]):
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| 295 | # if 'skyfft check' not in self.result.keys():
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| 296 | # self.result['skyfft check'] = {}
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| 297 | # temp = co.Spectrum(data=spectrum_fft,
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| 298 | # title='Test interferogram', units='')
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| 299 | # self.result['skyfft check'][t] = temp
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| 300 |
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| 301 | axis = co.Axis(data=np.array(opd), title='path difference',
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| 302 | units='cm')
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| 303 | temp = co.Spectrum(data=measurement, axis=axis,
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| 304 | title='Detected interferogram', units='')
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| 305 | self.result['baseline interferograms'][tuple(baseline)] = \
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| 306 | temp
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| 307 |
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| 308 | return self.result
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| 309 |
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| 310 | def matlab_transform(self):
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| 311 | # readers should look at Izumi et al. 2006, Applied Optics, 45, 2576
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| 312 | # for theoretical background. Names of variables in the code correspond
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| 313 | # to that work.
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| 314 |
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| 315 | # For now, assume 2 light collectors giving one baseline at a time.
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| 316 | interferograms = {}
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| 317 |
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| 318 | for baseline in self.baselines:
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| 319 | interferogram = 0
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| 320 |
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| 321 | # baseline length (cm) and position angle
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| 322 | bu = baseline[0]
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| 323 | bv = baseline[1]
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| 324 | mod_b = np.sqrt(pow(bu,2) + pow(bv,2))
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| 325 | ang_b = np.arctan2(bv, bu)
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| 326 |
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| 327 | # loop over sky pixels covered by primary beam
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| 328 | nx = self.sky_s.shape[1]
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| 329 | ny = self.sky_s.shape[2]
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| 330 | for j in range(ny):
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| 331 | for i in range(nx):
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| 332 |
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| 333 | # inverse fft of emission spectrum at this point
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| 334 | temp = np.fft.ifft(self.sky_s[:,j,i])
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| 335 |
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| 336 | # move 0 frequency to centre of array
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| 337 | temp = np.fft.fftshift(temp)
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| 338 |
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| 339 | # length (radians) and position angle of theta vector
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| 340 | mod_theta = np.sqrt(pow(self.sky_x[i],2) + pow(self.sky_y[j],2))
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| 341 | ang_theta = np.arctan2(self.sky_y[j], self.sky_x[i])
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| 342 |
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| 343 | # calculate b.theta (the projection of b on theta)
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| 344 | # and the corresponding delay in units of wavelength at
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| 345 | # Nyquist frequency
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| 346 | delay = mod_theta * mod_b * np.cos(ang_b - ang_theta) * self.freqs[-1]
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| 347 |
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| 348 | # sampling is done at twice Nyquist freq so shift transformed
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| 349 | # spectrum by 2 * delay samples (approximated to nint)
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| 350 | # NOTE factor of 2 discrepency with matlab version! I think
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| 351 | # this is because there the variable 'Nyq' is the Nyquist
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| 352 | # sampling rate, not the Nyquist frequency.
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| 353 | temp = np.roll(temp, int(round(2.0 * delay)))
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| 354 |
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| 355 | # want only the real part of the result
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| 356 | interferogram += np.real(temp)
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| 357 |
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| 358 | def __repr__(self):
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| 359 | return 'DoubleFourier'
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| 360 |
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