There is also a pdf version of this document.
This presentation is related to an earlier report (or out there in Torun)

The DPFU parameter plays
havoc with EVN calibration

Presented in full at TRAO Seminar, 25 Oct. 2007 and
to be briefed at TOG Meeting, Yebes, 12 Nov. 2007

Kazimierz M. Borkowski

Torun Centre for Astronomy, N. Copernicus University, Torun, Poland

  Noting that the DPFU parameter is not necessary for proper calibration of the correlated flux density, and that its presence creates confusion, it is proposed to forgo its further use.
  The simplest way to do this right away is to fix it at unity (DPFU = 1) in every rxg file of every station. This would mean expressing Tcal in units of Jansky and Tsys becoming Fsys or (almost) SEFD.

A few defining equations

The basic relationship between the amplitude of the correlation coefficient robs measured on a baseline involving two antennas to the antenna temperature TA (in Kelvins) and the system temperature Tsys (K) is described by the equation:
robs =   r


Tsys1 Tsys2

where the b-factor is due to losses inherent in the row coefficient r arising because of crude recording and simplified correlation.

For mapping purposes it is important that the final correlation coefficient does not depend on the antenna elevation angle at stations. We might account for it by dividing the amplitude by the geometric mean of Poly(Elev) at the stations. The Poly is a correction coefficient, a polynomial in the elevation angle (or in the zenith distance) normalized (e.g. at the zenith, but any other elevation can serve the porpose) to unity, reflecting the loss of received flux due to changing atmospheric attenuation and telescope efficiency with the elevation.

rcor   =   robs

Poly1 Poly2

(TA1/Poly1) (TA2/Poly2)

Tsys1 Tsys2
We see that such correction is equivalent to correcting the antenna temperatures which, however, we do not measure directly.

So obtained dimensionless quantity can be converted to the temperature scale (K):

rcor/K   =   rcor


Tsys1 Tsys2
  =   robs

Tsys1 Tsys2

Poly1 Poly2

or the flux density scale in Janskys (Jy)

rFlux/Jy   =     robs


     =   robs


DPFU1 Poly1

DPFU2 Poly2
The System Equivalent Flux Density, SEFD = Tsys / (DPFU × Poly), of each telescope is a function of time calculated from our 'continuous' monitoring of the system temperature, and the DPFU factor, Degrees Per Flux Unit (K/Jy), is a constant representing the antenna gain at the elevation where Poly = 1.

Equation (4) is the one used in practice. It requires the use of three different quantities to correct the correlation coefficient. This document aims to reduce the number to two independent quantities. Namely, in terms of the equivalent flux density we would have:

rFlux  =  robs  

    (Fsys2 /Poly2)

where Fsys = Tsys/DPFU is the total system noise power as measured by direct comparison with a nearby sky source (in this measurement the source flux density is not scaled by Poly), or with previously calibrated diode signal, Fcal (Poly-scaled). In any case, to determine Fsys no knowledge of the DPFU is required.

The above tells us that in principle we would satisfy the final users by providing the Fsys or the total system noise power expressed in Janskys and the polynomial, Poly.
Also, it seems there aren't good reasons why not to give the user the antabfs files filled just with the SEFD, i.e. Fsys already corrected with (divided by) the gain curve (Poly) evaluated at the proper elevation.

EVN practice

The present EVN calibration scheme may be summarized in the following steps (considerably simplified here for clarity):

    Calibration experiments of CL... type
1) Using observations of a source of known flux density Fso, determine the power of noise diode signal in units of Jansky (Jy)

  Fcal = Fso × Poly × (tpical - tpi)/(tponso - tpi),   (6)  

where the quantities txxx are the signal power levels of the diode (tpical), background (tpi) and source (tponso), as measured by the Field System.

2) Convert this to the noise temperature:

  Tcal = Fcal × DPFU,   (7)  

    User experiments
3) Use this Tcal for 'continuous' monitoring of the system noise temperature:

  Tsys = Tcal × (tpi - tpzero) / (tpical - tpi').   (8)  

For the VLBA racks, the AGC gain level, tpgain, is used as proxy for tpi (tpi becoming a function of tpi', tpgain and tpgain'). So obtained Tsys data constitute the ANTAB files (along with DPFU and Poly).

4) Convert the correlation coefficient to the correlated flux density using the station determined Tsys of two stations (see Eq. (4) above):

  rFlux = robs { [ Tsys / (DPFU × Poly) ]1 ×
×  [ Tsys / (DPFU × Poly) ]2 } 1/2  

or, same as Eq. (5) above,

  rFlux = robs { [Fsys/Poly]1 × [Fsys/Poly]2 }1/2   (9)  

or simply

  rFlux = robs { SEFD1  × SEFD2 }1/2   (10)  

Conclusion: The DPFU parameter is just a scaling factor not essential for the calibration process. It is being introduced at the beginning of the process (in Tcal) and is removed (from Tsys) at the end. Thus we are free to ascribe virtually ANY nonzero value to it, not affecting the correlated flux at all.

What do recent EVN
station data tell us?

Here are actual DPFU in LCP and Poly values at L-band taken from pipelined N07L2 (and N06L1, for DPFU only). In the following table the antenna efficiencies in the two rightmost columns have been calculated as 2760×DPFU×Poly/(π×D2/4), where the polynomial Poly has been evaluated for two extreme elevations, 0 (horizon) and 90° (zenith).

Sta-   DPFU (LCP)     Poly       D  Efficiency 
tion  2006   2007   0°    90°    m   0°    90°
 Cm  0.0047 0.0047 1.0    1.0    32 0.016 0.016
 Ef  1.5516 1.55   1.0    1.0   100 0.545 0.545
 Hh  0.0973 0.0954 0.9638 1.0    26 0.478 0.496
 Jb  1.1849 1.1849 0.7373 0.9117 76 0.532 0.657
 Mc  0.1080 0.1080 0.8869 0.9831 32 0.329 0.365
 Nt  0.11   0.1102 1.0    0.9239 32 0.378 0.349
 On  0.0800 0.0900 0.9099 0.9887 20 0.720 0.782
 Sh  0.0653 0.0765 0.5009 0.4434 25 0.215 0.191
 Tr  0.1400 0.1400 1.0    1.0    32 0.480 0.480
 Ur  0.0880 0.0880 1.0    1.0    25 0.495 0.495
 Wb* 1.0    1.0    1.0    1.0 14×25 0.402 0.402    

   *Tsys values for Wb are really SEFD of the array

Note on passing that at Nt and Sh the efficiency is higher at the horizon which may be indicative of their Poly being a function of the zenith distance rather then the elevation.

The table above shows that some efficiencies are clearly unrealistic (which implies unrealistic DPFUs). In about half of the stations these values were different in 2006. Those unrealistic, however, apparently were not at all harmful for calibration of EVN experiments (otherwise Cormac would complain). Thus we see that:

  • Stations do fit DPFU to measurements,
  • DPFU lost its pristine meaning and the name is now misleading
    (unless we agree for it to mean 'Degrees Per Fake Unit').

    Pros and cons of the DPFU use

    Arguments for:

  • Long tradition
  • Incorporated in the FS, GNPLT, ANTABFS, and AIPS

    Arguments against:

  • Complicates the overall picture of calibration process. Presently, due to misleading nature of DPFU a newcomer has little chance to acquire in reasonable time (if at all) a feel of the EVN calibration idea, although in fact it is quite simple.
  • Is almost sure cause for the loss of Tcal and Tsys scaling. This will happen when fitting DPFU to data within the GaiN PLoT (GNPLT) application. It is so just because there is no way to determine the absolute value of DPFU with this kind of observations (the CL experiments).

    Note: In the GNPLT for checking the gain curve and DPFU we have a cascade submenu 'Fit to' with fitting options of 'New DPFU' and 'Gain Curve and DPFU'.

    Possible actions to take

  • First and foremost, stations should definitely 
    stop updating the value of DPFU with the GNPLT program,
    since  doing so only modifies the unit of noise temperature (that supposedly once was Kelvin), whereas one is cheated to believe one has made some improvement. Therefore, it would be best if the next release of GNPLT had the option to fit DPFU disabled or outright removed.

  • It would be beneficial to 
    set DPFU = 1 in every rxg file of each station.
    This  way we would work only with the equivalent flux densities instead of temperatures. It would be an intermediate step preparing grounds for more concrete future solutions.

  • In a more remote future, releases of FS, GNPLT and ABTABFS might completely do away with the DPFU quantity.

    Last modified: Nov. 2, 2007