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Bias correction of visibilities

Since Wittkowski et al. (2001), the importance of improved bias corrections of the amplitudes has been recognized. A good fraction of the non-Poisson bias was removed from the 3-station data through the use of Dave's ``$z^2$'' correction in CONSTRICTOR. For the new 6-station data, CONSTRICTOR allows one to specify one, two, or three fringe modulation values ($k$-values) at which the amplitude is measured and then used in a polynomial fit of order zero, one, or two, respectively, to compute a bias at other modulations through interpolation. In the case of zero-order bias correction in CONSTRICTOR, a remaining bias can be studied by plotting the visibilities of incoherent scans (i.e. fringe-less data) versus the photon rate. Here is how.

After all editing of the point data has been done, one should set the default back ground rate (which is zero) using defaultbg or REDUCEBG DATADEFAULT BGi, and zero bias coefficients (genconfig.bias=0, only needed when starting over) before averaging the data. Then use (use CALIBRATESYSTEM) to bring up the system calibration widget. Both squared visibilities (V2Bias) and triple amplitudes (TABias, if two or more baselines are on the same detector) need to be plotted, but only for spectrometers without interpolated bias corrections from CONSTRICTOR. Plot all fits for all channels for every configuration. The fit coefficients are stored in the genconfig.v2bias and genconfig.tabias variables. (If scan selection directive ``All'' is selected, the fit coefficients will not be stored!) Then re-load the back ground data (get_bgdata) and re-average. The bias coefficients will be written into the output file with the averaged data, when done after the calibration.

Note that the triple amplitude bias correction currently is not handled in a strict fashion. This is because it is the complex triple product which is biased. CONSTRICTOR applies a correction to the complex triple product based on Poisson noise if all three baselines are from the same detector. The remaining biases studied as mentioned above in the amplitude are due to non-Poisson detector statistics. If the amplitudes require additional bias compensation, so would of course the closure phases. But this is not currently done for lack of an analytical expression for the bias.

Another issue with the bias correction using incoherent scans is that they are currently combined in a single fit, whereas ideally each coherent scan would be corrected with the incoherent scan immeadiately following it. Implementation has been delayed however because of the new possibility to do bias correction with unused fringe frequencies.


next up previous contents
Next: Photometry Up: Discussion of reduction issues Previous: Sub-arrays   Contents
Christian Hummel 2009-10-20