Notes on CCB Data Calibration


Intended to inform efforts to organize the calibration data products and GFMs processing of it.

One Cal Calibration

The calibrated data c for integration i port j, in terms of the raw data d for the same port, are:

c_{ij} = \frac{d_{ij}}{<d_{ij}^{AcalOn} - d_{ij}>} \, \times T_{calA}

T_{calA} should be determined by a standard y-factor measurement against a cold load from data with only cal A firing, as:

y_{calA} = \frac{<d_{ij}^{AcalOn}>}{<d_{ij}>}

and then

T_{calA} = (y_{calA} - 1) \times (T_{cold}+T_{rx})

with all these data collected against a cold load. This is an approximation to the real single-cal Tcal value! What you really in principle want to do is to apply a known power difference to the receiver (eg a hot load to one horn and a cold load to the other horn) and measure the cal relative to that. The above approximation should be valid to about the level of the cross talk (a few to 10 percent). Real astronomical calibration will trump this anyway so probably that level of accuracy is sufficient, also, systematic errors in the measurement probably matter more (things like condensation on the cold load)

  • Unless otherwise specified the raw data "d" are cal off integrations only

  • All averages are over one scans' data

  • You could in principle figure out the two-cal information from each of the one-cal Tcal values plus the individual channel leakages (crosstalks) but it seems easier and more reliable to measure equivalent Tcals directly.

  • One could get fancier and instead of averaging all the CAL OFF integrations in the numerator include only those immediately before and after tha cal ON integrations.

Two Cal Calibration

c_{ij} = \frac{d_{ij}}{<d_{ij}^{ABcalOn} - d_{ij}>}  \, \times T_{calAB}

T_{calAB} should be determined by a standard y-factor measurement against a cold load from data with both cal A and cal B firing.

y_{calAB} = \frac{<d_{ij}^{ABcalOn}>}{<d_{ij}>} and then as above.

Recommendations for the Measurement and Analysis Procedure

As a check on the sanity of your Tsys and Tcal values one should compare

<d_{ij}^{ABcalOn} - d_{ij}>

with the background of the cold load to the same quantity with the background of the hot load. If these are more than a few percent difference (a measure of differential linearity) your Trx value is probably off by a lot more than a few percent (since it depends on the integral linearity, ie, overall power response curve).


How to represent all this stuff in the calibration database and get it all out

  • We already have continuum Tcal tables. We should use them. Up to now I (bsm) have just done my own thing (ie taken the data in the lab, analyzed the results, and put the analyzed Tcal results straight into my own IDL software)
  • Maybe we should extend the Tcal table scheme to include separate tables or columns for one-cal and two-cal measurements.

GFM data fitting

  • Works great, but should we allow each beam height to be fitted separately? There are a few to 10 percent differences in the beam 1 vs beam 2 height for a given channel. It's pretty stable and I calibrate it out celestially. If done, we'd need to constrain the amplitudes of the individual beams to be nonnegative, perhaps even more strict (like [0.5,1.5]), to avoid possible beamswapping confusion.

Bits that need to get Mapped or Associated

  • AisXL -- determines if CCB cal A corresponds to XL or YR polarization in the receiver. This value is set in the CCB26_40.conf file and recorded in the CCB FITS file main header.

  • There are per-CCB-channel approximate counts to kelvins conversions in the CCB .conf file which are used to produce sampler values in Kelvin. I haven't updated these recently.

-- BrianMason - 12 Oct 2007
Topic revision: r1 - 2007-10-12, BrianMason
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