{"id":11250,"date":"2020-06-01T05:46:39","date_gmt":"2020-06-01T15:46:39","guid":{"rendered":"http:\/\/www.eaobservatory.org\/jcmt\/?p=11250"},"modified":"2020-12-29T10:55:29","modified_gmt":"2020-12-29T20:55:29","slug":"re-modelling-the-error-estimates-in-a-pol2-vector-catalogue","status":"publish","type":"post","link":"https:\/\/www.eaobservatory.org\/jcmt\/2020\/06\/re-modelling-the-error-estimates-in-a-pol2-vector-catalogue\/","title":{"rendered":"Re-modelling the error estimates in a POL2 vector catalogue"},"content":{"rendered":"

If the MAPVAR=YES<\/span> option is used when running the SMURF pol2map<\/span>\u00a0 script, the I, Q and U error estimates in the resulting vector catalogue will be based on the spread of pixel values at each point on the sky in the I, Q and U maps made from individual observations. Thus if 20 observations are processed by pol2map<\/span> to create a vector catalogue, then each I, Q or U error estimate in the vector catalogue will be based on the spread of 20 independent measurements of I, Q or U.\u00a0 Even though 20 observations is a lot of POL2 data, 20 is still a fairly small number from which to produce an accurate estimate of the error. Consequently, it is usual to see a large level of random “noise” on the error estimates, as in the following example which shows the total intensity (I) error estimates taken from a 12″ vector catalogue near Ophiuchus L 1688 (the noise level increases towards the edge of the map due to there being fewer bolometer samples per pixel near the edge):<\/p>\n

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The uncertainty on the error estimate can cause some vectors that are clearly wrong (e.g. because they are very different to nearby vectors) to have anomalously low error estimates and so to be included in the set of “good” vectors (i.e. vectors that pass some suitable selection criterion based on the noise estimates).<\/p>\n

One simple solution to this could be to apply some spatial smoothing to the error estimates. This would be a reasonable thing to do if there were no compact sources in the map. The errors close to a compact source are generally higher than those in a background region because of things like pointing errors, calibration errors, etc. These things cause a compact source to look slightly different in each observation and so cause higher error estimates in the vector catalogue. The above error estimates map shows this effect in the higher values at the very centre. Simply smoothing this map would spread that central feature out, artificially decreasing the peak error and increasing the errors in the neighbouring background pixels.<\/p>\n

An alternative to smoothing is to split the total noise up into several different components, create a model of each component , and then add the models together. The pol2noise<\/span> script in SMURF has been modified to include\u00a0 a facility to re-model the noise estimates in a vector catalogue using such an approach. This facility is used by setting MODE=REMODEL<\/span>\u00a0on the pol2noise<\/span> command line:<\/p>\n

% pol2noise mycat.FIT mode=remodel out=newcat.FIT exptime=iext debiastype=mas<\/pre>\n
This\u00a0 creates an output catalogue (newcat.FIT) holding a copy of the input catalogue (mycat.FIT), and then calculates new values for all the error columns in the output catalogue. The new I, Q and U error values are first derived from a three component model of the noise in each quantity, and then errors for the derived quantities (PI, P and ANG) are found. New values of PI and P are also found using the specified de-biasing algorithm. The file iext.sdf<\/span> holds the total intensity coadd map created by pol2map and is used to define the total exposure time in each pixel<\/span><\/span>. The re-modelled total intensity error estimates look like this :<\/span><\/span><\/p>\n
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Most of the noise has gone without reducing the resolution. The script displays the original and re-modelled error estimates for each Stokes parameter (I, Q and U), the residuals between the two and a scatter plot. The best fitting straight line through the scatter plot is also displayed:<\/p>\n
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The three components used to model the error on each Stokes parameter (I, Q or U) are described below:<\/p>\n