[evla-sw-discuss] Tsys & Calibration.

Sat Nov 28 12:19:47 EST 2009

Here is a summary of various discussions, looking for comments.
Brian's and Barry's recent target lists already contain some of
these items, but not everyone has seen them.

I will be in India till the 12th.

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The total-power detectors on the station board measure P_on and P_off,
before requantization, for the noise diode states Tcal_on, Tcal_off,
correspending to Tsys_on, Tsys_off. The attached cartoon shows this.

The requantizer gain G is used to get a desired power P_rq into the
correlator chips.

What we want is:

          Calibrated correlated flux density, baseline i-j, (Jy).

                  =  (Correlation Coeff) / sqrt(SEFD_i * SEFD_j)

where each SEFD  =  (Tsys_i in Kelvin) / (Aeff/2k in K/Jy)

There are two paths to this end, call them K and B.

Path K: ----------------------------------------------

Normalize the corr.chip outputs by the power level into the chips, in
the CBE, while they are still in the lag domain, before FFT into
spectra.

Norm.Corr.output = (Raw corr.lag) / sqrt(Prq_1 * Prq_2)

Pros & Cons:

++  Val Vleck corrections are best done here, in lags.

++  TelCal gets normalized data, with power variations & RFI mitigated.

++  Frequency averaging across subbands is possible (if desired at all).

--  Requires station board power data P_rq inserted online into the CBE.

--  Also should record the (averaged) P_rq offline, in the SDM.

--  The T_sys (computed as below) recorded in the SDM.

     Correction for delay residuals could be done online in the CBE, at
     the expense of even more data sent there. Or it could be done in post-
     processing by putting the corrections in the SDM.

Path B: ----------------------------------------------

++  Do not tax the CBE with the calibration, rather send Station board
     data every integration to the SDM via MCAF, to be applied in post-
     processing.

++  Use the same scheme for all calibration data - Tcal, Tsys, A_eff
     into the SDM. Delay residuals could go here as well, when we are ready.

--  VanVleck, state counts etc. not used in this scheme.

--  TelCal would have to live without (time) normalization. Subbands are
     handled independently of each other in TELCAL, so variations between
     subbands are less of a concern for Telcal.

In my limited view: K has some advantages, and is probably more exact
and general, but it requires data from the Station Board to get be
sent in near-real-time into the CBE. Ken estimates ~2 MByte/s of
StB data into the CBE, if it is sent every 10ms.  Other StB cal data
such as P_on, P_off, and parameters such as antenna gains and Tcals
could go in the CBE, but should also be recorded in the SDM for
post-processing. Thus, B needs only a subset of K, and appears to be a
quicker solution.

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Assuming path B, here is the recipe:

1. StB accumulates P_on and P_off, for each subband:

      P_on  = (Power when Tcal_on)  / (counts when Tcal_on  valid)
      P_off = (Power when Tcal_off) / (counts when Tcal_off valid)

     The accumulation period is:

     1.1. Equal to the visibility integration period.

     Alternatively, the Station Board could average up to 1 sec. and
     let MCAF average upto the vis.integration period.

     This should be adequate for OSRO. For RSRO, the accumulation may
     me shorter (What is the official limit?), but

     1.2. No shorter than 50 millisecond = one cycle of noise diode 20Hz.

     Here are Ken's recommendations on the integration period, originally
     written for normalization in the CBE, does it make sense for St
     Board output as well? [my inserted comment.]

     "I suggest that integration interval be a multiple of the ten
     millisecond correlator tick, that they be aligned with the tick and,
     for simplicity, that the number of integration ticks evenly divide a
     day and that an integration tick occur exactly at midnight.
     Integration intervals less than ten milliseconds can be
     accomodated if IO rates allow but the normalization will always be
     based on at least ten milliseconds [50msec] of total power
     measurement."

2. Station Board calculates 2 quantities, for each subband, and sends
    them every accumulation to MCAF.

     2.1    (P_on + P_off) = P_sum
     2.2    (P_on - P_off) = P_dif

    St.Board also sends the requantizer power

     2.3    P_rq  per subband, every accumulation.

     StB also sends the current value of the re-quantizer gain

     2.4    G per subband.

     This gain is set at most once per scan (no change in subscan,
     I believe) and could be sent every integration or every scan.

That's it for the Station Board. See item 5) for how these are used.

The next 2 items needed for calibration, T_cal and A_effective,
come from a database and are also inserted into the SDM by MCAF.

I'm thinking of these as once per scan, not once per visibility.

3. Tcal is measured on the bench every 25 MHz at L & S-band; every
    50 MHz for C; and every 100 MHz for X and shorter wavelength.
    Total data ~1000 numbers x 2 pol. x 32 Rx.

    There will be 1 normalization factor averaged over each subband,
    from the StB, so one Tcal number (interpolated or averaged) per
    subband seems to be adequate.

4. The antenna gains in (Kelvin/Jy) = A_i = (A_effective_i / 2k)
    are needed, at most 1 number per polarization per subband per
    antenna 'i'.

    I think A_i should go with the receiver: when a receiver
    changes, A_i should be re-measured with the new Tcal, so it
    can have upto the same frequency spacing as Tcal.

    At the higher frequencies a quadratic or cubic gain curve may be
    needed, one per RF band, for elevation dependence. The peak gain
    is normalized to 1.0, the frequency dependence is already in the
    A_i above.

To calibrate in post-processing:

5.1. Calibration of raw correlator visibility output R_ij,
    for antennas i,j:

    S_ij (Jansky) =  R_ij * sqrt( 1 / A_i*A_j) *

                    sqrt(Tcal_i / Pdif_i) * sqrt(Tcal_j / Pdif_j)

5.2. Barry suggested a more accurate version of this, using the
      requantizer power and gain: (hope I've got this right!)

    S_ij (Jansky) =  R_ij  * sqrt( 1 / A_i*A_j ) *

                     sqrt( G_i/Prq_i * G_j/Prq_j ) *

                     sqrt(Tcal_i / Pdif_i) * sqrt(Tcal_j / Pdif_j)

5.3. Tsys is calculated as follows for antenna 'i', each subband:
    This includes a Tcal/2 contribution from the 50% duty cycle of
    the noise diode. Tsys does not appear in the calibration of data
    when done via the Tcal as in 5.1 or 5.2. However, it is useful
    in its own right, for opacity/tipping scans, receiver diagnostics,
    and perhaps flagging.

    Tsys(i)  = Tcal(i) * (P_on + P_off) / 2* (P_on - P_off)

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