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DR: Weaksource

When reducing data of weak sources (F_corr << 1 Jy, e.g. 200 mJy), there are a number of effects that need to be taken into account with respect to the standard EWS data reduction (midivispipe / midipipe) in order to not get biased results. Walter has written a routine weaksource.pro that contains the procedures / functions meddelay, ph11 and procmed that takes care of this. It is not part of the standard MIA+EWS distribution (neither release nor snapshot as of June 2010), but can be requested from Walter Jaffe.

Effects to consider when reducing fringe tracks from weak sources:

• Dependence of tracking accuracy on correlated flux amplitude (meddelay): Another effect in weak sources is that the tracking precision of weak sources isn't as good as for stronger sources (e.g. a brighter calibrator). Since in weak tracks it is more likely that oirGroupDelay picks a wrong (noise) peak as true zero OPD (and not all of them will be flagged by oirAutoFlag due to excessive OPD or excessive differential OPD), you will at the end sum up some frames that are derotated by a wrong groupdelay (namely the one that corresponds to the noise peak in that respective frame and not to the true, maybe very weak, zero OPD peak). This will effectively decrease your signal, leading to a too low correlated flux. This bias can be partly removed by running a median filter over the delays found by oirGroupDelay. On the one hand, this improves the tracking for the weak sources by being less sensitive to individual noise peaks found by oirGroupDelay. On the other hand, by applying the same method to the calibrator, it will effectively deteriorate the tracking for the calibrator leading to the same effect as described above in the calibrator, thereby making the data better calibratable. The median filtering routine calls oirAutoFlag after it did the median filtering and produced a new groupdelay.fits file, see the Processings steps and Diagnosis of Fringe Tracking pages for more details. Taking care of this effect should effectively increase the reduced correlated flux.
• Phases are biased towards 0 (i.e. cos / real part doesn't average to zero; similar to water vapour delay problem, see below). The procedure ph11 does the following: after de-rotating with a crude groupdelay (found by standard data reduction) and med-delaying, runs groupdelay again with larger value of gsmooth.

Other effects that might be relevant in very weak sources:

• In the groupdelay file, only the high signal-to-noise data remains in a weak source fringe track due to flagging of bad points. If during frames where the fringe amplitude is stronger, the transmission has been stronger (but this correlation is unknown...?), this could lead to too high correlated fluxes.

Already implemented in the MIA+EWS distribution:

1. Water vapour phase bias: In the delay line tunnels there is water vapour; in the universe (where the OPD occurs), there isn't. This water vapour has a chromatic index of refraction, i.e. it affects 13 micron radiation different than 8 micron radiation. While this was always been taken care of, a bug in the way it was treated led to differential phases that tended to be too small. This had an implication on the correlated flux, or the real part of the visibility, which is Real(V) = V_amplitude * cos(V_phase). If V_phase is biased towards zero, cos(V_phase) will be biased towards 1 and, on average, lead to correlated fluxes that are higher than they should be. This effect can be very significant for very weak sources (ca. 100 mJy) and is taken care of in oirRotateGroupDelay.c in all distributed versions of EWS since the end of 2008.