Transcript Slide 1

(continuum)
VISIBILITY & CALIBRATION
Daniele Dallacasa
Astronomy Dept. University of Bologna
Istitute of Radio Astronomy, INAF, Bologna
Outline:
I.
Setting the scene
[from antenna measurements to the interferometer;
relevant parms: baseline length, frequency, A,j,
bandwidth, integration time and effects]
II. Data structure
[what is a dataset]
III. Calibration!
[amplitudes mean flux densities, phases mean position;
theory and practice]
IV. Inspection (& editing), checks
[finding problems and remedies: prevention is better than cure!]
Let's consider two identical antennas (as much as possible)
Vij' = GiGjVij
In reality we measure a set of fringe visibilities Vij which are
corrupted by atmospheric, electronic, pointing effects etc.
These all have to be determined and corrected.
[ from P.Diamond's Lecture]
= CALIBRATION
N.B. Any e.m. radiation can be detected by means of two orthogonals systems:
They can either be perpendicular linears (XY) or circulars (RL)
Monochromatic interferometer: 
0
Each antenna measures (samples) the electric vector of the incoming radiation
+ ni (R,L)(t)
+ nj (R,L)(t)
The product of these two, for a given polarisation, on the ij baseline
Vary with time (earth rotation)
Noise does not correlate!!!!
Baseline length
ni Ej + nj Ei + njni are (should be) always 0
Signal properties and corruption are dependent on
baseline-length
observing frequency
Vary with time (earth rotation)
Baseline length
It is assumed that
all the signal corruption can be determined and
corrected solving an element/antenna based system
Modern interferometers have N elements:
The 2N samples continuously flow to a black box [correlator] which returns
4 [N (N 1) /2] interferometric measurements for each integration time (2T)
For each interferometer we have
the Visibility: R
function
in the uv-plane
implying 4 products It
forsamples
each interferometer
iRj, LiLj, RiLj, and LiRj
For each visibility sample (2T) the correlator writes many things including:
a time tag
the (ij) baseline identification
the baseline length (or u,v,w components)
amplitude and phase [Re,Im / cos, sin] (one for each RR,LL,RL,LR combination)
weight (~ error)
At this stage,
amplitudes are on an arbitrary scale,
phases may wander due to various effects
Sentitive continuum observations aim at
1. large bandwidths
2. long (time) integrations
[3. wide fields (e.g. Surveys)]
effects on uvtracks: points are not points anymore!
effects on images: radial (bandwidth) & tangential (time) smearing
getting worse and worse with distance from the field center
Cure: 1. split/slice the bandwidth (IFs possibly divided into CHANnels)
each channel in each IF produces and independent visibility
2. set short integration time (also better coherence)
1 sec integration produces 60x more visibilities than 1 min integration
Effects to be considered/corrected in calibration
–
Gi contains many components (along the signal path):
F = ionospheric Faraday rotation
T = tropospheric effects
P = parallactic angle
E = antenna voltage pattern
D = polarisation leakage
J = electronic gain
B = bandpass response
K = geometric compensation
Gi = Ki Bi Ji Di Ei Pi Ti Fi
–
Each term on the right has matrix form.
–
The full matrix equation Gi is very complex, but usually only need to consider the
terms individually or in pairs, and rarely in open form
–
Existing software does the thing (... more or less) but it is software....!
Closure relations must be preserved!
Ionospheric Faraday Rotation Fi
●
The ionosphere is birefringent; one hand of circular polarisation is delayed
w.r.t. the other, introducing a phase shift:
●
Rotates the linear polarisation position angle
●
More important at longer wavelengths (2): at 20cm it could be tens of degrees
●
●
●
More important at solar maximum and at sunrise/sunset (high and variable
TEC)
Distant antennas are likely to have very different signal paths across the
ionoshpere
Direction dependent within field-of-view
i
F
RL
e
0
0
e
i
; F
XY
cos
sin
sin
cos
[example of Fi matrix]
The Tropospheric contribution Ti
●
The troposphere causes polarization-independent amplitude and phase
effects due to emission/opacity and refraction, respectively
●
Typically 2-3m excess path length at zenith compared to vacuum
●
Higher noise contribution, less signal transmission: Lower SNR
●
Most important at  > 15 GHz where water vapor absorbs/emits
●
More important at low elevations where tropospheric path length greater
●
●
●
Clouds and weather variability make phase and opacity vary on each antenna
and across the array
Water vapor radiometry? Phase transfer from low to high frequencies?
Antenna located at large distances are likely to have a very different signal path
across the troposhpere
The Parallactic angle  = Pi
–
Orientation of sky in the field of view of each telescope
–
It is constant for equatorial telescopes
–
It varies for alt-az-mounted telescopes:
–
Rotates the position angle of linearly polarised radiation (c.f. F)
–
Analytically known, and its variation provides the key to derive instrumental
polarisation
–
May be very different in antenna located in distant sites
The antenna voltage pattern Ei
●
Antennas of all designs have direction-dependent gain
●
●
●
Important when region of interest on sky comparable to or
larger than /D
Important at lower frequencies where radio source surface
density is greater and wide-field imaging techniques required
For convenience, direction dependence of polarisation leakage
(D) may be included in E (off-diagonal terms then non-zero)
The polarisation leakage Di
●
Polarisers are not ideal, so orthogonal polarisations are not
perfectly isolated and mix.
●
Well-designed feeds have d ~ a few percent or less
●
A geometric property of the feed design, so frequency dependent
●
●
For R,L systems, total-intensity imaging affected as ~dQ, dU, so only
important at high dynamic range (Q,U~d~few %, typically)
For R,L systems, linear polarisation imaging affected as ~dI, so
almost always important
The electronic antenna GAIN, Ji
●
Catch-all for most amplitude and phase effects introduced by
antenna electronics (amplifiers, mixers, quantizers, digitizers)
and characteristics (collecting area, efficiency,....)
●
●
●
●
●
Most commonly treated calibration component
Dominates other effects for standard interferometric ( WSRT,
VLA, MERLIN, GMRT, ATCA) observations
Includes scaling from engineering (correlation coefficient) to radio
astronomy units (Jy), by scaling solution amplitudes according to
observations of a flux density calibrator
Often also includes ionospheric and tropospheric effects which are
typically difficult to separate unto themselves
Excludes frequency dependent effects (see B)
The bandpass efficiency Bi
●
Similar to the Ji component, Bi represents the frequencydependence of antenna electronics, etc.
●
Filters used to select frequency passband not square
●
Optical and electronic reflections introduce ripples across band
●
Often assumed time-independent, but not necessarily so
●
Typically (but not necessarily) normalised
The geometric compensation Ki
●
●
The geometric model (antenna i, antenna j, source
position) must be (ideally) perfect so that Synthesis
Fourier Transform relation can work in real time;
residual errors here require Fringe-fitting
●
●
Antenna positions (geodesy)
Source directions (time-dependent in topocenter!)
(astrometry)
●
Clocks & Local Oscillators
●
Electronic pathlengths
●
Scales with frequency and baseline length
●
In general not relevant for conventional interferometers
(MERLIN, WSRT, VLA, GMRT, ATCA)
Wait for Richard Porcas' lecture on VLBI
Practical calibration I (a)
●
T, J, (K):
●
●
Strong and point-like sources at the field center have
amplitudes constant with baselinelength and phase always 0.
–
Compare with correlated ''raw'' amplitudes and phases
–
Derive ''antenna based'' solutions (for each polarisation, IF)
–
J means find the AMPLITUDES
–
T means find the PHASES [corrupted by the atmosphere
(troposphere + ionosphere)]
Track phase and amplitude variations on timescales shorter
than the coherence time: J variations should be smooth
(within a few percent) with time.
–
observe calibration sources every 10s of minutes at low frequencies
(but beware of ionosphere!), or as short as every minute or less at
high frequencies
Practical calibration I (b)
●
T, J, (K): (contd)
●
●
Observe at least one calibrator of known flux density at least
once allows the conversion from arbitrary ''correlator units'' to
Jy. If not possible, measure antenna total power (Tsys) to be
converted to flux densities (VLBI)
Choose reference antenna wisely (ever-present, stable
response)
Feed a computer with a few (obscure) parameters and
software does the work for you...
Always
CHECK RESULTS
Be able to understand what is good and what is bad (and do something about it!)
Example of Ji solutions
Variations should be smooth
and within a few percent
Ji from Tsys measurements
at the telescope
Example of Ji solutions (2)
Variations should be smooth
and within a few percent
Ji derived from a flux
density (primary) calibrator
and a number of secondary
(phase) calibrators.
No smoothing applied
to Ji solutions
Before calibration........
Raw amplitudes
N.B. Interferometer with
identical antennas. It is not the
case for EVN and MERLIN
Raw phases
Now calibration has
been applied!
Practical calibration II
(when spectral channels are in use)
●
B:
●
●
●
A strong pointlike source (often, T, J calibrator is ok) should
have the same amplitude (and phase 0) across the observing
bandwidth. High SNR in each channel is necessary
–
Compare with correlated ''raw'' amplitudes and phases
–
Derive ''antenna based'' solutions (for each polarisation) for each channel
Observe often enough to track variations (e.g., waveguide reflections change
with temperature and are thus a function of time-of-day)
– However an ''average'' bandpass profile is ok for experiments several
hours long.
The bandpass profile is typical of each antenna and accounts for
all filters along the signal path and for the feed performance
within its bandwith
Example of band pass profile: 128 CHANnels (may be grouped into Ifs)
Ji calibration applied, but Bi not found yet
Normalised band bass profile: a solution for each CHANnel for each antenna
Solutions have been applied
Practical calibration III
Polarisation related stuff: ....wait for Tim Cawthorne's lecture
●
D:
●
●
●
A single calibration source for full calibration is strong, polarised and
with known orientation of the polarisation vector
If polarised (or with unknown polarisation properties), observe over a
broad range of parallactic angle to disentangle Ds and source
polarisation (often a calibrator suitable for T, J is ok)
F:
●
Choose strongly polarised source and observe often enough to track
variation: increasingly (square law!) significant at  longer than ~10
cm
When A-PRIORI calibration is over.......
–
the data can now be coherently averaged in frequency and in
time [in principle! (and when useful)]
–
speeds up all the subsequent data processing (imaging and selfcalibration, further second-order editing, plotting, etc.)
–
may be dangerous, phases are likely to need further adjustment before
averaging (true for weak targets)
A priori practical calibration summary/outcome
Planning the experiment (scheduling) is extremely
important to make the calibration easy
●
●
●
●
Observe (at least) one [pointlike] calibration source for the flux
density scale
Observe (at least) one [pointlike] (phase) reference source
close to the target object often enough to track phase variations
Observe (at least) one [pointlike] source for determining
instrumental polarisation (a wide range of  if polarised or
unknown, it does not matter if it is not), if relevant
Observe (at least) one source for the orientation of the
polarisation vector, if relevant
One (may be more!) step back:
●
After observation, the initial data examination and editing is
very important. The calibration process is much more efficient
if bad data have already been flagged out!
●
Some real-time flagging occurred during observation (antennas offsource, LO out-of-lock, etc.). Any bad data left over?
– check operator's logs
Pay attention to downtime reports, weather info, reports on RFI
Directly inspect the raw data (plot / print / display): remember that
data on calibration sources should have high SNR, while data on
target sources usually have low SNR and may appear noisy
●
–
●
Amplitude and phase should be continuously (smoothly) varying: edit outliers
●
Be conservative: those antennas/timeranges bad on calibrators are
probably bad on weak target sources as well. Edit them out!
Distinguish between bad (hopeless) data and poorly-calibrated data.
Some antennas may have significantly different amplitude response
which may not be fatal; it may only need to be calibrated/readjusted
●
Residual Radio Frequency Interference (RFI) is present?
●
Example: a 2.4 Jy source
(pointlike on this baseline MC-JB)
Each IF is plotted with
a different color (4)
More outliers.....
RFI disturbances
●
RFI originates from man-made signals generated in the
antenna electronics or by external sources (e.g., satellites,
cell-phones, radio and TV stations, automobile ignitions,
microwave ovens, etc.)
●
●
●
●
Adds to total noise power in all observations, thus decreasing
sensitivity to desired natural signal, possibly pushing electronics into
non-linear regimes (saturation)
As a contribution to the ni term, can correlate between antennas if of
common origin and baseline short enough (insufficient decorrelation
via Ki)
When RFI is correlated, it obscures natural emission in spectral line
observations
Narrow-band RFI may totally compromise wide-band measurements