Available Graphs ================ The QA display provides a number of key visualisations of the data. The plots are separated between multiple pages; ``Home``, which represents an at a glance view of the system, ``Visibility``, which houses the real time visualisation of incoming data, ``Calibration``, which holds the outputs of the calibration pipelines, and ``PST``, which is home to metrics from the Pulsar Timing capabilities. Home ---- Below are the descriptions of the plots on the home page of the QA display. Average Visibility Amplitude per baseline ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This n^2 plot displays the band averaged visibility amplitude for every baseline. By default the colour scale is logarihmic, but a linear scale can be selected. The lower left triangle represents the XX pol, whilst the upper right triangle represents the YY pol. The diagonal represents XX+YY. The zoomed region allows for closer inspection of baseline regions when large numbers of baselines are in use, and the raw visibilities section allows a user to select a baseline/polarisation pair and inspect the non-averaged visibilities. .. image:: /images/new/nsquared.png :width: 100% Amplitude vs UV Distance ~~~~~~~~~~~~~~~~~~~~~~~~ These plots display the variance of visibility amplitude and phase as a function of either uv Distance or baseline distance. .. image:: /images/new/uv_distance.png :width: 100% .. image:: /images/new/baseline_length.png :width: 100% Visibility ---------- Below are the descriptions of each plot in the Visibility tab and how they respond. Spectrum ~~~~~~~~ The incident flux on the telescope is distributed over a finite receiving band and is a function of frequency. The spectrum is the flux per unit bandwidth. The broad continuum spectrum of a radio source may contain a number of spectral lines, whose profiles are the subject of detailed study. However, a receiver bandpass is usually wide enough to contain one or more spectral lines, and so we sub-divide the band into a number of filter channels. A digital autocorrelation spectrometer samples the input signal at the Nyquist frequency, producing a series of binary packets representing the signal in time. The signal is then delayed by a series of identical values, or lags, such that the inputs to the multipliers are the signal itself and a series of delayed signals. Sampling of the output provides an estimate of the discrete autocorrelation function. Once noise has been accounted for, the autocorrelation function is related to the power spectrum by the Discrete Fourier Transform. The spectrum plot now combines both a line plot and a waterfall plot in a single view. The line plot shows the current mean autospectrum averaged over all channels and baselines, per polarisation. The waterfall plot above it displays the historical spectrum data, allowing users to track changes over time. The scale of the y-axis can be changed between linear, decibels, and logarithmic using the buttons in the top right corner of the plot view. .. image:: /images/spectrum_and_waterfall.png :width: 100% Power vs Phase ~~~~~~~~~~~~~~ For each baseline and polarisation a plot of the amplitude of the visibility spectrum is displayed, along with a plot of the phase of the visibility spectrum. From the plot of the amplitude it is possible to discern whether a source is resolved, along with information about its shape. The phase information allows us to determine the source's offset from the phase center. .. image:: /images/amplitude_phase.png :width: 100% The display can be toggled between amplitude/phase and real/imaginary components using the mode selector buttons positioned above the plots. When viewing amplitude, the y-axis scale can be changed between linear, decibels, and logarithmic using the scale selector buttons (logarithmic scaling is disabled when viewing real components since it is not possible to take the logarithm of a negative number). When viewing phase, the units can be changed between radians and degrees using the units selector buttons (this option is disabled when viewing imaginary components). Band Averaged Cross Correlation Power ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ For each polarisation and baseline, a plot of the band averaged cross correlation power is displayed as a time series. The scale of the y-axis can be changed between linear, decibels and logarithmic using the buttons in the top right corner of the plot view. .. image:: /images/band_average_xcorr_power.png :width: 100% Spectrogram Waterfall ~~~~~~~~~~~~~~~~~~~~~ A visibility is the correlation between two antennas over a time and frequency interval. A lag or XF correlator multiplies (X) the signals from each antenna together as a function of lag. .. image:: /images/lag_X.png :width: 400 This can be integrated for multiple time steps and is what an XF correlator outputs. However, the contributions from all the channels are mixed together, and so to extract the information about the power in each channel, we Fourier transform (F) this signal (and this is where the F in XF comes from). .. image:: /images/freq_X.png :width: 400 This is the Cross-Correlation power as a function of frequency and it is what we get from our correlator. For each baseline and polarisation, we present a waterfall plot of the phases of the visibilities as a function of frequency. A flat spectrum of phases is synonymous with zero residual delay. This is due to the 'Shift Theorem' which states that a delay in the time domain corresponds to a linear phase term in the frequency domain. .. image:: /images/spectrogram.png :width: 100% The "time" axes of the spectrogram plots represent an incoming time slice, which increases by one upon each new data point. The Spectrogram Plots page defaults to showing only the cross-correlation baselines, but this is configurable using the provided legend, as shown below. .. image:: /images/spectrogramPage.png :width: 100% Cross-Correlation Power vs Time Lag ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The output of our Correlator is the Cross-Correlation power as a function of frequency (see above), and furthermore it is an FX correlator, performing the Fourier transform before the multiplication. To change this back to "Cross-Correlation power as a function lag" we need to calculate the inverse Fourier transform (iFFT) of the visibilities for each baseline. We present this calculation in the form of a Waterfall plot. For each baseline and timestep, the iFFT of the complex visibility spectrum is calculated. The y-axis represents time in UTC format (HH:MM:SS), allowing you to track the evolution of the cross-correlation pattern over time. To efficiently render the data, the plot displays the maximum value within binned sections of the lag axis for each time slice. The number of bins is automatically matched to the display's pixel resolution, ensuring that even single-point peaks in the data are preserved and visible in the visualization. This binning strategy guarantees that no signal peaks are lost due to downsampling. .. image:: /images/lag_plot.png :width: 100% Any residual delay will manifest itself as a shift of the peak of the lag plot away from zero. I.e., if the signals have been correctly delayed before their Cross-Correlation the peak power in Cross-Correlation will be at zero lag. The Lag Plots page shows only the cross correlation baselines, but the subset of these is configurable as shown below. .. image:: /images/lagplotPage.png :width: 100% Weight Distribution and UV-Coverage Plots ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ An interferometer measures components of the sky Fourier Transform through the sampling of the Visibility function V. These samples live in (u, v, w) space and are often projected into a plane, the uv-plane. We present the weight distribution W(u, v) as a time series plot, showing how the uv-plane gets filled in with the earth's rotation. .. image:: /images/uv_coverage.png :width: 100% Calibration Data ---------------- Descriptions of each plot in the Calibration Data tab and how they respond follows. Pointing Offset Calibration Data ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The pointing offset calibration pipeline fits 2D Gaussian primary beams to the visibility or gain amplitudes. Each scan is split into a number of frequency chunks, and the primary beam is fitted for each frequency chunk and dish. The weighted average of the fitted parameters for each frequency chunk is provided for each antenna. Elevation and Cross-elevation offset ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The fitted parameter representing the centre of the primary beam provides the elevation and Cross-elevation offsets, along with their standard deviations. If a calculated pointing offset exceeds a threshold percentage of the expected value, then it is discounted. These discounted pointing offsets are indicated by the red shaded regions in the graphs. A marginal histogram of the points' distribution is also available. .. image:: /images/cross-elevation.png :width: 100% Beam width ^^^^^^^^^^ The expected and fitted widths of the 2D gaussian primary beam are displayed, along with their standard deviations. .. image:: /images/beam-widths.png :width: 100% Beam height ^^^^^^^^^^^ The expected and fitted heights of the 2D gaussian primary beam are displayed, along with their standard deviations. A marginal histogram of the points' distribution is also available. .. image:: /images/beam-height.png :width: 100% Realtime Calibration Data ~~~~~~~~~~~~~~~~~~~~~~~~~ In radio telescopes, the complex receiver gains are initially unknown and need to be calibrated. Measured interferometer data is generally corrupted by instrumental and atmospheric effects, which can be corrected for through a process known as gain calibration. Gain calibration enhances the quality of astronomical images and improves the effectiveness of signal processing techniques. Gain Calibration ^^^^^^^^^^^^^^^^ Since the antenna gains are unknown prior to observing the field of interest, science scans are typically interspersed with calibrator scans of high SNR, well-modelled objects. By determining the major factors influencing the antenna gains, and applying the inverse to the target field, we can produce corrected data that can act as the starting point for self calibration. In order to assess the stability of the gain calibration solution with time, we present a time-series plot of the amplitude and phase of the complex gains, for each antenna. Currently, only the first frequency channel is displayed. .. image:: /images/gaincal.png :width: 400 Pulsar Timing ------------- Below are the descriptions of each plot in the PST tab and how they respond. Bandpass ~~~~~~~~ The bandpass message comes from the mean spectral power calculated by STAT (i.e. the MEAN_SPECTRAL_POWER record in the HDF5 file). This is the average power per channel averaged for the given sample of the complex voltages. Note power is (Re^2 + Im^2) of the complex voltage. .. image:: /images/pstbandpass.png :width: 400 Timeseries ~~~~~~~~~~ The timeseries message comes TIMESERIES record in the HDF5 file but only using the mean values, whereas that record has max, min and mean. The time series of the data for each polarisation, rebinned in time to NDAT_DS bins, averaged over all frequency channels. .. image:: /images/psttimeseries.png :width: 400 Histogram ~~~~~~~~~ The histogram message comes from the HISTOGRAM_1D_FREQ_AVG record in the HDF5 file. The two plots are separate histogram plots, one for Pol A and one for Pol B both of which have counts for the real and imaginary parts of the complex voltage. .. image:: /images/psthistogram.png :width: 400