H1C IDR 2.1 is the first calibrated and LST-binned data release from H1C. The H1C observing campaign was the first science-grade HERA observing campaign with $\lesssim$100 antennas ("H" is for HERA and "1C" means $\sim$100). It started in September 2017 and continued through the beginning of April 2018.
This jupyter memo is designed to be run when logged into NRAO. In addition to the standard python libraries, it requires pyuvdata, hera_cal, and hera_qm. For more information on access, see the HERA wiki. For ongoing analysis results, see this wiki page and the #hera-analysis Slack channel.
!hostname
The day-by-day data, along with the pipeline settings file used (idr_v1.cfg), and the LST-binned data can be found in:
ls /lustre/aoc/projects/hera/H1C_IDR2/IDR2_1/
analysis_folder = '/lustre/aoc/projects/hera/H1C_IDR2/IDR2_1'
1. Finding and Loading Data¶
H1C IDR 2.1 includes 18 nearly-consecutive nights of data. All data products are sorted by JD into the following folders on the NRAO servers, which also contain softlinks to raw H1C IDR 2 data and antenna metrics released by the commissioning team. Each night has 73 raw visibility files in each of the 4 visibility polarizations. Each file has 1024 frequency channels and (usually) 60 integrations, each 10.7374 seconds.
More information about the data products produced by the analysis team are on the HERA wiki.
import glob, os
for night in sorted(glob.glob(os.path.join(analysis_folder,'245*'))):
print night, 'has', len(glob.glob(night + '/*.uv')), 'raw visibility files.'
The HERA collaboration's standard way to load in data files is using pyuvdata (for more, see pyuvdata's documentation).
We can load in a sample data file like this:
bl = (65,71,'xx')
sample_data_file = os.path.join(analysis_folder, '2458098/zen.2458098.43124.xx.HH.uv')
from pyuvdata import UVData
uvd = UVData()
uvd.read_miriad(sample_data_file)
To simplify the extraction of data and abstract away a lot of the complexity of a pyuvdata object, we can quickly get out the data and flags we're interested, along with the most useful metadata using hera_cal.io, a wrapper around pyuvdata for in-memory inspection, manipulation, and plotting of data. For keeping careful track of metadata for pipeline processes, it is often best to use pyuvdata directly.
from hera_cal import io
import numpy as np
(data, flags, antpos, ants, freqs, times, lsts, pols) = io.load_vis(uvd, return_meta=True)
# One can also load straight for a string path rather than a UVData object, e.g.:
# data, flags = io.load_vis(sample_data_file)
print np.all(uvd.get_data(bl) == data[bl])
The data and flags loaded through hera_cal.io.load_vis are stored in DataContainer objects, which act like dictionaries mapping baseline tuples in the (ant1,ant2,pol) format like (65,71,'xx') to waterfalls of shape (Ntimes, Nfreqs). DataContainers support getting data and flags via [] and normal dictionary functions like .keys(), .values(), .items(), .has_key(). It also knows to conjugate data when the reversed baseline key is provided:
print np.all(data[65,71,'xx'] == np.conj(data[71,65,'xx']))
This then allows for easy data access and plotting, such as:
from matplotlib import pyplot as plt
%matplotlib inline
plt.figure(figsize=(4,4), dpi=100)
bl = (65,71,'xx')
plt.imshow(np.angle(data[bl]) / (~flags[bl]), aspect='auto',
extent=[freqs[0]/1e6,freqs[-1]/1e6,times[-1]-2458098,times[0]-2458098])
plt.ylabel('JD - 2458098')
plt.xlabel('Frequency (MHz)')
plt.title('Raw Visibilities: ' + str(bl))
plt.colorbar(label='Phase of Uncalibrated Visibility (Radians)');
2. Array and Bad Antennas¶
The data taken for IDR2.1 began on 2458098 and ended on 2458116 with 52 antennas (~47 functional). Bad antennas, as determined by the commissioning team, are summarized in this folder:
bad_ants_folder = '/users/heramgr/hera_software/hera_opm/hera_opm/data/idr2/bad_ants'
bad_ants = np.loadtxt(os.path.join(bad_ants_folder, '2458098.txt')).astype(int)
print 'Bad antennas on 2458098:', bad_ants
We can visualize the array on 2458098 as follows:
plt.figure(figsize=(4,4), dpi=100)
plt.scatter(np.array(antpos.values())[:,0], np.array(antpos.values())[:,1],
c=[ant in bad_ants for ant in antpos.keys()], s=400, cmap='jet')
for ant,pos in antpos.items():
plt.text(pos[0],pos[1],str(ant), va='center', ha='center', color='w')
plt.xlabel("East-West [meters]", fontsize=14)
plt.ylabel("North-South [meters]", fontsize=14)
plt.title('Antenna Positions on 2458098 (Red = Flagged)');
plt.axis('equal')
plt.tight_layout()
All data in this IDR come from antennas in the Southwest sector of the split HERA core.
3. Day-by-Day Data Products and Access¶
3.1 Input Files¶
Raw HERA visibility for IDR2 by the commissioning team generally has the format zen.2458098.43124.xx.HH.uv which can be interpreted as:
zen: zenith pointing2458098: Julian date integer43124: first five decimal digits of the time of the first integration in the filexx: visibility polarization. Options arexx,xy,yx, andyyHH: "HERA Hex", visibilities purely between HERA core antennasuv: file extension conventionally used for miriad data files (which are technically folders)
Additionally, we inherit antenna metrics from the commissioning team. These come in json files with the format zen.2458098.43124.HH.uv.ant_metrics.json, one for all four visibility polarizations. These can be read hera_qm.ant_metrics.load_antenna_metrics:
from hera_qm.ant_metrics import load_antenna_metrics
am = load_antenna_metrics(os.path.join(analysis_folder, '2458098/zen.2458098.43124.HH.uv.ant_metrics.json'))
print 'Automatically detected bad antennas:', am['xants']
The list of bad antennas generated by ant_metrics is generally a subset of the flagged antennas, but both are ORed together on a file-by-file basis. There visibilities are still in all visibility data files, but their flag arrays are all True.
3.2 Visibility Data Files and Access¶
At each stage of the analysis, we produce new copies of the visibility data files in the same format as the raw data. Generally speaking, newly calibrated data is produced by applying calibration solutions (see below) to the raw .uv data files. Following the PAPER convention, these get a single letter suffix appended to denote what stage in the processing they represent (one can also look at their histories for more detailed analysis). They are:
zen.*.uv: Raw data files from the commissioning team.zen.*.uvO: Partially-calibrated data files using bothfirstcalandomnical. These have only the first and last 50 channels flagged. O is for Omnical.zen.*.uvOC: Calibrated data files usingfirstcal,omnical, andabscal(a sky-referenced) which as been restricted to operate in the degenerate subspace ofomnical. That means thatabscalis restricted to solving for four numbers per frequency, integration, and polarization. These have the first and last 50 channels flagged and are flagged when the sun is up in either the data or the abscal model. C is for absCal.zen.*.uvOCR: RFI-flagged, absolute calibrated datafiles. The data here are identical to the.uvOCdata, only the flags are updated (but still include the band edge and solar flagging). R is for RFI.zen.*.uvOCRS: RFI-flagged, absolute calibrated data, the calibration solutions for which have been smoothed on 30 minute timescales and then 10 MHz frequency scales. S is for Smoothed gains.zen.*.uvOCRSD: Delay-filtered versions of the.uvOCRSfiles, which have been filtered at the horizon wedge + 15 ns using a Tukey window with $\alpha = 0.5$. D is for Delay filtered.
Likely the .uvOCRS and .uvOCRSD files will be the most interesting, depending on whether you want data "with foreground" or "without foregrounds."
Note: the .uvO and .uvOC files are produced during the pipeline but then deleted to save space after they are no longer necessary. They can be straightfowardly reproduced using hera_cal.apply_cal.
Again, we can use pyuvdata or hera_cal.io to look at the data.
abscaled_datafile = os.path.join(analysis_folder, '2458098/zen.2458098.43124.xx.HH.uvOCRS')
filtered_datafile = os.path.join(analysis_folder, '2458098/zen.2458098.43124.xx.HH.uvOCRSD')
abscaled_data, abscaled_flags = io.load_vis(abscaled_datafile)
filtered_data, filtered_flags = io.load_vis(filtered_datafile)
bl = (65,71,'xx')
plt.figure(figsize=(10,4), dpi=100)
for data, flags, sub, t in zip([abscaled_data, filtered_data], [abscaled_flags, filtered_flags],
[121, 122], ['Smooth Absolute Calibrated: .uvORCS', 'Delay-Filtered: .uvORCSD']):
plt.subplot(sub)
plt.imshow(np.angle(data[bl]) / (~flags[bl]), aspect='auto',
extent=[freqs[0]/1e6,freqs[-1]/1e6,times[-1]-2458098,times[0]-2458098])
plt.title(t + '\n' + str(bl))
plt.ylabel('JD - 2458098')
plt.xlabel('Frequency (MHz)')
plt.colorbar(label='Visibility Phase (Radians)');
plt.tight_layout()
import matplotlib
bl = (65,71,'xx')
plt.figure(figsize=(10,4), dpi=100)
for data, flags, sub, t in zip([abscaled_data, filtered_data], [abscaled_flags, filtered_flags],
[121, 122], ['Smooth Absolute Calibrated: .uvORCS', 'Delay-Filtered: .uvORCSD']):
plt.subplot(sub)
plt.imshow(np.abs(data[bl])/(~flags[bl]), aspect='auto', norm=matplotlib.colors.LogNorm(1e-1,1e2),
extent=[freqs[0]/1e6,freqs[-1]/1e6,times[-1]-2458098,times[0]-2458098])
plt.title(t + '\n' + str(bl))
plt.ylabel('JD - 2458098')
plt.xlabel('Frequency (MHz)')
plt.colorbar(label='Visibility Amplitude (Jy)');
plt.tight_layout()
3.3 Calibration Files and Access¶
Along the pipeline, we produce and save four progressively refined calibration solutions that can be applied to raw data, meaning that they supplant previous calibrations. These are stored in the calfits format and have a form like zen.2458098.43124.xx.HH.uv.first.calfits. Calibration solutions are per-antenna, not per baseline, so xx really just means x and there are no xy or yx calfits files. They are:
zen.*.uv.first.calfits: The output offirstcal, which solves for the relative delays between antennas.zen.*.uv.omni.calfits: The output ofomnical, which uses redundancy to solve for calibrations solutions for all times and frequencies up to 4 degenerate modes per frequency, per time, and per polarization.zen.*.uv.abs.calfits: The output ofabscal, which ties the omnical solutions to the sky and picks a single reference antenna (53 for IDR2.1) to have 0 phase for all times.zen.*.uv.smooth_abs.calfits: The output ofsmooth_cal, which takes.abs.calfitscalibration solutions and smooths them on 30 minute and then 10 MHz scales. This restricts the degrees of freedom available to calibration.
Each of these calibration files also comes with its own flags. .first.calfits and .omni.calfits files generally have no flags, through bad antennas are simply not present. .abs.calfits can inherit flags from the abscal model and also flags times when the sun was up in either the data or the abscal model. .smooth_abs.calfits includes the .abs.calfits flags, but also includes flags from RFI excision that have been synthesized so that any flagged visibility that isn't with a totally-flagged antenna leads to a flag on both antenna's calibrations.
Again, one can either use pyuvdata.UVCal to load in calibration solutions, or use hera_cal.io's simple wrapper for loading calibration solutions into memory as python dictionaries.
firstcal = os.path.join(analysis_folder, '2458098/zen.2458098.43124.xx.HH.uv.first.calfits')
g_fc, f_fc = io.load_cal(firstcal)
omnical = os.path.join(analysis_folder, '2458098/zen.2458098.43124.xx.HH.uv.omni.calfits')
g_oc, f_oc, quals, total_qual, ants, freqs, times, pols = io.load_cal(omnical, return_meta=True)
abscal = os.path.join(analysis_folder, '2458098/zen.2458098.43124.xx.HH.uv.abs.calfits')
g_ac, f_ac = io.load_cal(abscal)
smoothcal = os.path.join(analysis_folder, '2458098/zen.2458098.43124.xx.HH.uv.smooth_abs.calfits')
g_sc, f_sc = io.load_cal(smoothcal)
ant = (1,'x')
phs = plt.figure(figsize=(10,8), dpi=100)
for g, f, sub, t in zip([g_fc, g_oc, g_ac, g_sc], [f_fc, f_oc, f_ac, f_sc], [221, 222, 223, 224],
['Firstcal', 'Up Through Omnical', 'Up Through Abscal', 'Up Through Flagged & Smoothed Abscal']):
plt.subplot(sub)
plt.imshow(np.angle(g[ant]) / (~f[ant]), aspect='auto',
extent=[freqs[0]/1e6,freqs[-1]/1e6,times[-1]-2458098,times[0]-2458098])
plt.title(t + ' Gains: ' + str(ant))
plt.ylabel('JD - 2458098')
plt.xlabel('Frequency (MHz)')
plt.colorbar(label='Gain Phase (Radians)');
plt.tight_layout()
Additionally, all .calfits files after firstcal inherit copies of omnical's $\chi^2$, which is an unnormalized metric of non-redundancy after calibration given by
$\chi^2(\nu,t) = \sum_{i,j}\left|V_{ij}^\text{obs}(\nu,t) - g_i(\nu,t) g_j^*(\nu,t) V_{ij}^\text{sol}(\nu,t)\right|$.
This is stored in the total_quality_array attribute of a calfits object and is accessible via hera_cal.io using the return_meta keyword argument (see above). This also useful for flagging. It looks like:
plt.figure(figsize=(4,4), dpi=100)
plt.imshow(total_qual['x'], aspect='auto', norm=matplotlib.colors.LogNorm(1e-3,1e1), cmap='inferno',
extent=[freqs[0]/1e6,freqs[-1]/1e6,times[-1]-2458098,times[0]-2458098])
plt.ylabel('JD - 2458098')
plt.xlabel('Frequency (MHz)')
plt.title('Unnormalized Omnical $\chi^2$')
plt.colorbar();
Additionally omnical produces a couple of other data productions:
zen.*.uv.vis.uvfits: These are the omnical visibility solutions stored in the uvfits format (not miriad, like the other visibilities in IDR 2.1. Omnical produces one visibility. This are used in finding RFI, but are not further calibrated right now.zen.*.uv.xtalk.uvfits: These are omnical's estimates of the crosstalk between the antennas in the baseline (i.e. correlated noise) obtained by averaging over the data file. As such, they only contain a single "integration." They are not currently used for anything.
3.4 Quality Metrics and Flagging Metadata¶
The parts of the pipeline that fall under the aegis of hera_qm produce a number of useful intermediate and summary data products that can help assess the quality of calibration solutions and the results of the iterative RFI flagging routines used.
3.4.1 Quality Metrics¶
Combined with the RTP output from the commissioning team, we produce and store 3 different .json files that assess the quality of the array. These are:
zen.*.uv.ant_metrics.json: These include a list of antennas that are suspected of being dead or cross-polarized, along with a variety of intermediate results summarizing the extent to which each antenna is an outlier. See this example notebook for more details about the creation and interpretation of these metrics.zen.*.uv.first.calfits.firstcal_metrics.json: These includes a variety of metrics assessing the stability offirstcalsolutions as a function of time. They also include information about antennas that are believed to be 180 degrees rotated, meaning that their delay intersects $\pi$ instead of 0. These files are not currently used in the pipeline. See this example notebook for more details about the creation and interpretation of these metrics.zen.*.uv.omni.calfits.omnical_metrics.json: These include metrics that assess whether any antenna appears to be performing particularly poorly in omnical, either in its contribution to $\chi^2$ or the standard deviation of its gain phase across frequency. These files are not currently used in the pipeline. See this example notebook for more details about the creation and interpretation of these metrics.
3.4.2. Flagging Files¶
Additionally, there are a number of .npz files that contain flags and flagging metadata that can help reconstruct the decisions made by the RFI flagging algorithm. These can all be opened with a standard np.load().
zen.*.uv.vis.uvfits.flags.npz: flags and flagging metadata produced using theomnicalunique baseline visibility solutions.zen.*.uv.abs.calfits.g.flags.npz: flags and flagging metadata produced usingabscalgain solutions.zen.*.uv.abs.calfits.x.flags.npz: flags and flagging metadata produced usingomnical$\chi^2$.zen.*.uvOC.flags.npz: flags and flagging metadata produced from delay-filtered data that has been pre-flagged with flags based on calibration data products above.zen.*.uvOC.xrfi_summary.npz: flagging metadata and summary produced using this function.zen.*.uvOCR.flags.applied.npz: summary of all flags applied to data
The zen.*.uvOC.flags.npz and zen.*.uvOCR.flags.applied.npz can be converted into DataContainers of flags using:
applied_flags = io.load_npz_flags(os.path.join(analysis_folder,
'2458098/zen.2458098.43124.xx.HH.uvOCR.flags.applied.npz'))
bl = (65,71,'xx')
plt.figure(figsize=(4,4), dpi=100)
plt.imshow(applied_flags[bl], aspect='auto', cmap='gray',
extent=[freqs[0]/1e6,freqs[-1]/1e6,times[-1]-2458098,times[0]-2458098])
plt.ylabel('JD - 2458098')
plt.xlabel('Frequency (MHz)')
plt.title('Flags');
4. LST-Binned Data Products¶
LST-binned HERA visibility data generally has the format zen.grp1.of2.xx.LST.1.28828.uvOCRSL which can be interpreted as:
zen: zenith pointinggrp1: 1-indexed group of nights that the LST binned data products are divided intoof2: number of groups of nights that the data was divided into before separately LST-binning each group togetherLST: LST-binned data. The other alternative isSTD, which encodes the standard deviation of the real and imaginary parts (separately) of the binned data in its real and imaginary data array1.28828: starting LST of the data in radiansuvOCRSL: extension for calibrated, RFI-flagged, LST-binned data, but not delay-filtered. The LST-binned results also includeuvOCRSDLfiles, which have been delay-filtered. L is for LST-binning.
In general, LST-binned data files are also 60 integrations, but each integration is 21.475 seconds, double the integration time of the raw data files.
The data can be found in /lustre/aoc/projects/hera/H1C_IDR2/IDR2_1/{one/two/three}_group/grp{N}/.
For the nights split into two groups, we have:
- grp1: 2458098, 2458101, 2458103, 2458105, 2458107, 2458109, 2458111, 2458113, 2458115
- grp2: 2458099, 2458102, 2458104, 2458106, 2458108, 2458110, 2458112, 2458114, 2458116
For the nights split into three groups, we have:
- grp1: 2458098, 2458102, 2458105, 2458108, 2458111, 2458114
- grp2: 2458099, 2458103, 2458106, 2458109, 2458112, 2458115
- grp3: 2458101, 2458104, 2458107, 2458110, 2458113, 2458116
The LST-binned data are also stored in the miriad format and accessible via pyuvdata or hera_cal.io:
lstbinned = os.path.join(analysis_folder,'LSTBIN/two_group/grp1/zen.grp1.of2.xx.LST.1.28828.uvOCRSL')
l_uvd = UVData()
l_uvd.read_miriad(lstbinned)
(l_data, l_flags, l_antpos, l_ants, l_freqs, l_times, l_lsts, l_pols) = io.load_vis(l_uvd, return_meta=True)
bl = (65,71,'xx')
plt.figure(figsize=(10,4), dpi=100)
for d, f, sub, l, t in zip([abscaled_data, l_data], [abscaled_flags, l_flags],
[121, 122], [lsts, l_lsts],
['2458098 Absolute Calibrated: .uvORCS', 'LST-Binned Group 1 of 2: .uvORCSL']):
plt.subplot(sub)
plt.imshow(np.angle(d[bl]) / (~f[bl]), aspect='auto',
extent=[freqs[0]/1e6,freqs[-1]/1e6,l[-1],l[0]])
plt.title(t + '\n' + str(bl))
plt.ylabel('LST (Radians)')
plt.xlabel('Frequency (MHz)')
plt.colorbar(label='Visibility Phase (Radians)');
plt.ylim([l_lsts[-1],l_lsts[0]])
plt.tight_layout()
Note that a single LST-binned data file covers twice as much time as a single data file because the integrations are twice as long. Note also that the LST-binned data will in general have fewer flags than the observation on a single night because LST-binned data is only flagged when all the input data is flagged. However, the statistics of the data are available in two places. The first is the standard deviations of the data that go into each LST bin. The standard deviations of the real and imaginary parts are computed separately and stored as the real and imaginary parts of the visibility data in the zen.*.STD.* files. Second is the nsample_array which is accessible through pyuvdata using get_nsamples().
lst_stds, _ = io.load_vis(os.path.join(analysis_folder,'LSTBIN/two_group/grp1/zen.grp1.of2.xx.STD.1.28828.uvOCRSL'))
bl = (65,71,'xx')
nSamples = l_uvd.get_nsamples(bl)
plt.figure(figsize=(10,4), dpi=100)
plt.subplot(121)
plt.imshow(np.abs(lst_stds[bl]) / (~l_flags[bl]), aspect='auto',
extent=[freqs[0]/1e6, freqs[-1]/1e6, l_lsts[-1], l_lsts[0]])
plt.colorbar(label='Visibility $|\sigma|$ (Jy)');
plt.ylabel('LST (Radians)')
plt.xlabel('Frequency (MHz)')
plt.title('$|\sigma|$ of Binned Visibilities\n' + str(bl))
plt.clim([0,15])
plt.subplot(122)
plt.imshow(l_uvd.get_nsamples(bl) , aspect='auto', cmap='inferno',
extent=[freqs[0]/1e6, freqs[-1]/1e6, l_lsts[-1], l_lsts[0]])
plt.colorbar(label='Bin Counts');
plt.ylabel('LST (Radians)')
plt.xlabel('Frequency (MHz)')
plt.title('LST-Binned Visibility Count\n' + str(bl))
plt.tight_layout()
5. Analysis Steps and Pipeline¶
The data products are produced by a pipeline managed by Makeflow. The pipeline is built using the tools in hera_opm repo and using shell scripts and settings for them. These thin bash scripts use one of the scripts in hera_cal or hera_qm, which themselves use various unittested modules in those repositories.
A broad overview of the interdependencies of the processing can be cleaned from this flowchart:
In yellow ovals, we see the data products described above and how they were created. Red and magenta diamonds represent the various discrete steps in the pipeline. We will now review the methods in broad terms, highlighting some of the analysis choices made.
5.1 Redundant Calibration¶
Redundant-baseline calibration takes place in two steps. The first is firstcal, which uses redundancy to solve for the relative delays between antennas. It cannot solve for an overall delay, delay gradients across the array, or the relative delay between x and y polarizations. Also, if an antenna drops out between files, there may be a jump in the firstcal solution for a specific antenna. All of theses issues are resolved in abscal.
The second step is omnical, which implements redundant baseline calibration with full generality, treating each time and frequency completely independently and solving for gains $g_i(t,\nu)$ in the equation:
$V_{ij}^\text{obs}(t,\nu) = g_i(t,\nu) g_j^*(t,\nu) V_{ij}^\text{sol}(t,\nu)$
where $V_{ij}^\text{obs}(t,\nu)$ are the data (pre-calibrated with firstcal) and $V_{ij}^\text{sol}(t,\nu)$ are the unique baseline visibilities. Omnical operates in 1pol mode, meaning that each polarization is calculated independently and xy and yx visibilities are not used in calibration. Each time, frequency, and polarization has four degeneracies:
- Overall amplitude
- Overall phase
- North-South phase gradient
- East-West phase gradient
For a more detailed, pedagogical explanation of the degeneracies of redundant-baseline calibration, see Section 2 of this paper.
Omnical fixes the degeneracies so that (after dividing out the firstcal solution), the average gains are 1 and the average phase phases and phase slopes are set to 0 for all times and frequencies. This ensures spectral smoothness of the degenerate part of the calibration solutions, though it can create temporal discontinuities that have to be taken out by abscal.
When omnical solutions are applied to data to produce .uvO files, (and during all subsequent apply_cal steps), the first and last 50 channels are flagged by hand. These tend to be pretty deep into the instrument's bandpass and flagging them by hand makes subsequent analysis steps more robust.
5.2 Absolute Calibration¶
The next step in calibration is absolute calibration or abscal. Absolute calibration attaches the omnical gain solutions to a sky reference, allowing us to fix the degeneracies. In fact, absolute calibration is restricted to only modify the degenerate subspace of the omnical solutions; only four degrees of freedom per polarization per time per frequency are allowed to be modified.
Instead of using a point source model, abscal takes as its input a "model," which can be either simulated visibilities or, as in our case, absolutely calibrated visibilities. Nearest neighbors in LST are phased to match the data set to be calibrated and then the four omnical degeneracies are solved for by comparing the ratio of the "data" and "model" visibilities and solving a system of equations where each visibility in the data is given equal weight. For fixing the overall amplitude, this happens in a single step. For fixing the phase gradients, abscal takes an approach that iteratively refines the solutions in order to avoid issues with phase wrapping. First abscal solves for a spatial (i.e. across the array) delay slope. Next it solves for an average (across frequency) spatial phase slope. Finally, it solves for phase slopes across the whole array. Finally, the absolute phase (which is unphysical and not calibratable by reference to a sky model) is fixed by picking a reference antenna. For IDR2.1, we define antenna 53 to have zero phase in both x and y polarizations because it is never observed to die and because it is near the center of the array. Picking a reference antenna is important for later calibration smoothing.
The abscal calibration model is actually one of the days of the IDR, 2458116, calibrated in CASA independently of the above pipeline. Its calibration is determined using a handful of point sources around the 17.5 Jy source GLEAM J0200-3053 that passes near zenith. The complex gains derived from that single field are assumed to be accurate gains for the entire night and are applied to the entire day of data. More information about the making of the abscal model for IDR2.1 is available on the HERA wiki and in HERA Memo #42.
To lower the noise in the abscal reference model and interpolate over RFI, the visibilities are delay-filtered with a Tukey window with $\alpha=0.5$ and only the smooth components kept (those with delays less than the horizon delay for a baseline plus a 150 ns buffer). A few integrations are completely flagged and thus cannot be interpolated over in this way; those flags are propagated into the data.
Finally, we flag any data during which the sun is above the horizon. These cannot be absolute calibrated because the sun is in a different position in the data and in the abscal model. Likewise, we also flag any data during LSTs that correspond to times on 2458116 when the sun is up because we also expect major differences between the data and the model.
5.3 RFI Flagging¶
Our Radio Frequency Interference (RFI) flagging algorithm takes place in two steps, dubbed cal_xrfi and delay_xrfi. In the first, we look for outliers in either the omnical $\chi^2$, the abscal gain amplitudes, or the omnical unique baseline visibility solutions. In the latter, we take the output of the cal_xrfi flags, apply them to absolute-calibrated .uvOC files, delay filter the visibilities at the horizon (plus a 15 ns buffer) using a Tukey window, and again look for outliers. Our experience has shown that narrow-spectrum, low-level RFI stands out better in delay-filtered data.
In both flagging routines, each dataset undergoes outlier detection in two steps. First, each point (gain, $\chi^2$, or visibility) is converted to a number of $\sigma$s by subtracting a median-filtered version of the data (over a 17 x 17 box in frequency channels and time integrations) and comparing this residual to a median filtered residual squared (essentially, a notion of the local variance). Points above $6\sigma$ are considered flag candidates. Finally, any point neighboring a flagged point that is above $2\sigma$ is also considered a flag candidate.
Each of the three flag arrays are subsequently broadcast to a single waterfall (i.e. frequency vs. time). First, a flag-candidate fraction waterfall is computed. If the mean flag-candidate fraction for a given integration is greater than 25%, the entire integration is flagged. Likewise, if the mean fraction for a given frequency in a file is greater than 5%, the entire frequency is flagged for the file. Finally, any "pixel" in the waterfall (i.e. a single time and frequency) is a candidate for flagging more than 10% of the time, that frequency and time and flagged for all baselines. Only these "thresholded" flags are carried forward.
These waterfalls are then ORed together before the delay_xrfi step, which then goes through another round of the watershed algorithm, flagging, and broadcasting to a single waterfall. The result is that the RFI excision per-frequency and per-time flags for all baselines. Flags can only vary from one baseline to another if they were imposed earlier in the pipeline. Calibration smoothing will subsequently broadcast any per-baseline flags to both baselines involved.
5.4 Calibration Smoothing¶
To reduce the number of degrees of freedom in the calibration solution, we rely on the presumption that the instrument does not have spectral structure on small frequency scales and that it does not evolve quickly in time. After RFI flagging (and harmonizing those flags on an antenna rather than baseline level, though they are generally identical from baseline to baseline), we smooth both the real and imaginary parts of our abscal calibration solutions and then reapply them to data to produce the .uvOCRS files.
Our smoothing algorithm loads in a whole day of calibration solutions simultaneously and put them on a time grid, leaving flagged holes for any missing files or missing time. We smooth in time using Gaussian kernel with a a 30 minute FWHM that is renormalized for each time depending on flagging. This means that times near flags might get extra weight in this smoothing. To smooth the beginning and end of the night, we mirror the dataset before smoothing to ensure continuity. Finally, we apply a delay-filter on 10 MHz (or 100 ns) scales using a Tukey window with $\alpha=.3$ (which gives a bit more weight to the band edges) and keep the smooth components. These are finally written to disk as the .smooth_abs.calfits files.
5.5 Delay Filtering¶
In addition to the .uvOCRS data files, we also run all of our data through one more delay filter before LST-binning, producing .uvOCRSD files as well where the spectrally smooth part of the data has been subtracted.(see the bifurcation at the bottom of the above flow diagram). The delay filtering is done with a Tukey window with $\alpha=0.5$ at each baseline's horizon delay (plus a 15 ns buffer) and with a $10^{-9}$ tolerance for the delay CLEANing algorithm, which is used to iteratively remove spectral components despite irregular RFI flagging.
5.6 LST-Binning¶
Both before and after delay filtering, the data is LST-binned into a single group, into two groups of interleaved nights, and into three groups of interleaved nights. During LST binning, each integration is assigned to the the nearest LST bin, but is rephased to account for the slight difference in LST between its bin center and the LST bin's center. LST bins were chosen to be twice as long as raw data bins (21.475 seconds = 0.00156597 radians of a sidreal day), so every LST bin gets two data points for every input night.
Next, the list of rephased data points that would go into any given LST and frequency bin are examined for outliers. For relatively robust outlier detection, we compute the median absoute deviation (MAD) of all the points that are to be binned together and use that to compute a modified z-score. As long as there are at least 5 data points to bin together, we then flag all data that with a modified z-score greater than 5, which corresponds to $5\sigma$ outliers if the distribution were Gaussian.
Finally, we compute the standard deviation of both the real and imaginary parts of the unflagged data and store those in the .STD. file. We also save the number of samples that went into each binned data point in both the .LST. and .STD. files. We do not further perform a cut on the number of samples or any other form of post-LST binning RFI flagging.
6. Known Issues, Future Improvements, and Open Questions¶
The goal of IDR 2.1 was to produce data that could lead to an astrophysically interesting power spectrum upper limit. The above is merely one step in a continually improving HERA analysis pipeline. There are a number of known issues which we are working to address in future data releases:
- Cable Reflections. We know that our 150 m cables exhibit reflections on the $\sim$1000 ns ($\sim$1 MHz). While abscal and omnical pick up these cable reflections in our calibration solutions, we effectively eliminate them from our calibration solutions after smoothing due to the frequency smoothing on 10 MHz scales. This means that the calibrated data should have the cable reflections in them, more or less uncorrect.
- Flagging broadcasting and thresholding. Right our our flagging algorithm is a bit ad hoc and performs broadcasting and thresholding in multiple stages. We believe this leads to overflagging, especially since since the broadcasting in time is done on a file-by-file basis. Improving this algorithm is a high priority for the next IDR (see e.g. this GitHub issue).
- Temporal structure in gains even after smoothing. Because our calibration smoothing algorithm smooths in time and frequency separately, frequency smoothing can introduce some temporal structure (and vice versa). Since frequency smoothness is far more important, we were willing to accept a small amount of temporal structure. There's a an issue out to fix this by implementing 2D smoothing in both time and frequency simultaneously.
- $\chi^2$ is unnormalized. Right now, the $\chi^2$ that omnical calculates in unnormalized, meaning that the difference between the data and the gain-visibility solution product that should replicate it is not normalized by the noise in the data. There are a number of ways to estimate this noise, including using the autocorrelations, and we plan to improve redundant calibration to include this information. Next season, when we implement even-odd time interleaving at the sub-integration level, this will be much easier. This is an open issue too.
- Occasional abscal phase failures. We've seen evidence for a handful of integrations not converging to the same phase solution across the the band as their neighbors. This appears to be a problem with abscal and is similar to the convergence issues we saw before which were due to phase wrapping. While these don't generally affect the final solutions much (smooth_cal basically smooths over these discontinuities), we need a robust way of identifying and flagging these integrations when the absolute calibrated dataset is very discrepant from the abscal model. There's an open issue on this too.
- Limitations of the abscal model. Our absolute calibration model is rather simple, using the calibration solutions from a single field on a single day to calibrate an entire data set. This can be improved by calibrating several fields on several days and stringing together a data set that spans the full range of nighttime LSTs in the data. One can also imagine fringe-rate filtering the model (instead of just delay-filtering it) to make it less noisy and more sky-like. Alternatively, one could instead develop a model for calibration based on simulations. This requires fairly accurate beam and sky knowledge, which is a major challenge, but might be the only way to bring
abscalinto the RTP next season.
- Cross-talk. Even after the delay filter, we see clear evidence of persistent structure on short baselines. This was seen in PAPER and is likely attributable to cross-talk. We make no effort in this IDR to remove that cross-talk, but it should probably be done after LST-bining and and on timescales longer than a single file. This is tied up in the question of how to time-average and/or fringe-rate filter the data before estimating the delay power spectrum and will need to be addressed by the power spectrum pipeline.
- Problems with 2458108.51325. The pipeline got stuck on these files for
delay_xrfi. We decided to manually flag all the abscal gains for the file for both polarizations. We should revisit this to see why the delay filter wouldn't converge.
- Fringe structure in STD files. The real and imaginary components of the STD files appear to have fringe structure in them. This is likely attributable to un/mis-calibrated gain variations from day to day, though we don't know that for sure. Does this mean that data is not integrating down properly? Is it also a problem in the delay-filtered, LST-binned, data?
Over the past several months, the Analysis team has accumulated a series of research questions that we think ought to be looked into using this data set. This includes:
Temporal structure. How stable are the calibration solutions in time (per feed)? What kind of temporal structure do they exhibit and how repeatable is that structure from day to day? What is the optimal temporal smoothing scale for calibration solutions?
Spectral structure. What kind of spectral structure do our calibration solutions exhibit? How does it vary from antenna to antenna? From integration to integration? From day to day? Is the spectral structure in our calibration solutions consistent with that expected from beam modeling of spectral structure? What is the optimal spectral smoothing scale for calibration solutions? Is there some spectral form other than delay modes on which we should be filtering (e.g. Hermite polynomials? PCA/Weiner filter?).
Characterizing cable reflections. What do the cable reflections look like and how do they vary from antenna to antenna and time to time? Is there any relationship between the NRAO and Cambridge hardware?
RFI Report. What are the persistent sources of RFI? How much of the band are we losing? Are there any major transient broadband events and can they be tracked to any source (e.g. MeerKAT, as we saw in 2458109)?
Post-LST RFI. Is there any low level RFI that we are not detecting? Does the LST-binned data product show any evidence for RFI? How should we be removing RFI after LST binning?
Versus Sky-Based Calibration. How do the calibration solutions compare to those generated purely from a sky-based calibration?
Imaging. How do images look? Do source fluxes and spectra look right? What about psuedo-Stokes I, Q, U, and V images?
Noise integration. Does the noise integrate down from day to day?
LST results. Does the difference between a given day's data and the corresponding LST-binned data look noise-like? Are there some days that are worse than others?
Noise modeling. Is the noise in the data consistent with our noise model using the autocorrelations?
Redundancy. How redundant are redundant baselines? Does the noise integrate down inside redundant baseline groups?
Repeatability of calibrated data. How repeatable are redundant baselines from day to day after calibration?
Beams. Does our beam model make sense? Can we constrain it with foregrounds moving through the beam?
Delay filtering. We use delay filtering in XRFI, calibration smoothing, and the delay filtering step. Are we using the best algorithm for it? Are we using the best tapering function?
Delay spectrum. How does the delay spectrum look? Is it noise-like at k~.2 and beyond after foreground filtering on the EoR baselines? How does it depend on LST?
If you want to work on any of these questions (or already are!) or are curious about this IDR, please join our HERA analysis telecon on Tuesdays at 10am Pacific on Zoom or the #hera-analysis Slack channel.