Chapter 3
POL-2 Data Reduction – The Theory

 3.1 The Data Flow
 3.2 MAKEMAP
 3.3 CALCQU
 3.4 PCA
 3.5 Masking
 3.6 Tailoring a reduction

3.1 The Data Flow

POL-2 data reduction is an involved process for which a broad overview is first presented here before the specific details are discussed. It is noted that this same procedure is used irrespective of whether a single or multiple observations are to be reduced.

The data reduction process can be broken down into three main stages – referred to as “Run 1”, “Run 2” and “Run 3” in Figure 3.1.


pict
Figure 3.1: The data flow of the POL-2 data reduction method is presented. In this example, three POL-2 observations are reduced and combined in various stages and combination to produce I, Q and U maps and a vector catalogue.


Step 1

The initial step of the process (see Run 1 in Figure 3.1) creates a preliminary co-added total intensity (I) map from the raw data files for all observations provided to the reduction routine (see Chapter 4).

The process

The analysed intensity values in the raw data time-streams are first converted into Q, U and I time-streams using the SMURF:calcqu command (these are stored for future use in the directory qudata, specified by the QUDIR parameter in the example command below).

The SMURF:makemap command is then used to create a separate map from the I time-stream for each observation, using SNR-based “auto-masking” to define the background regions that are to be set to zero at the end of each iteration.

These maps are stored for future use in the directory maps, specified by the MAPDIR parameter. Each map has a name of the form:

<UT_DATE>_<OBS_NUM>_<CHUNK_NUM>_imap.sdf

where <CHUNK_NUM> indicates the raw data file at the start of the contiguous chunk of data used to create the map, and is usually 0003. Each of these maps is compared to the specified reference map (if any) to determine a pointing correction to be applied to the observation in future. If no reference map is supplied, the I map created from the first observation defines the expected source position, and is compared with later maps to determine their pointing corrections.

This step uses a PCA threshold of 50 (see Section 3.4 for more details).

pca.pcathresh = -50

Step 2

In the second step of the process (see Run 2 in Figure 3.1) an improved I map is produced. These improvements come from

(1)
applied relative pointing corrections
(2)
the use of an increased number of PCA components (pca.pcathresh=-150)
(3)
using a single fixed mask for all observations. The mask is determined from the preliminary co-add I map and thus includes fainter structure than would be used if the mask was based on only one observation.

Step 3

In the third step of the reduction process (see Run 3 in Figure 3.1), both the Q and U maps are produced. The production of the Q and U maps requires the Q and U time-series data (produced in Step 1), the final I map (produced in Step 2) and the output masks (also produced in Step 2). Once the Q and U maps are produced a final vector catalogue is created.

3.2 MAKEMAP

The POL-2 data reduction builds upon the existing SCUBA-2 Dynamic Iterative Map-Maker, hereafter just referred to as the map-maker. This is the tool used to produce SCUBA-2 maps, and is invoked by the Smurf makemap command. It performs some pre-processing steps to clean the data, solves for multiple signal components using an iterative algorithm, and bins the resulting time-series data to produce a final science map.

In pol2map the map-maker is used in conjunction with calcqu (see Section 3.3) to produce maps of Q and U, as well as I.

3.3 CALCQU

In addition to the POL-2 data reduction building on the existing SCUBA-2 map-maker, pol2map also relies on the Smurf command CALQU.

This calcqu tool creates time series holding Q and U values from a set of POL-2 time series holding raw data values. The supplied time-series data files are first flat-fielded, cleaned and concatenated, before being used to create the Q and U values. The Q and U time-series are down-sampled to 2Hz (i.e. they contain two Q or U samples per second), and are chosen to minimise the sum of the squared residuals between the measured raw data values and the expected values given by Equation 2.9.

3.4 PCA

One difference between the reduction of SCUBA-2 data and POL-2 data is the method used to remove the sky background. The sky background is usually very large compared with the astronomical signal, and both are subject to the same form of instrumental polarisation (IP – see Section 2.2). This IP acting on the high sky background values causes high background values in the Q and U maps. However, there is evidence that the IP is not constant across the focal plane, resulting in spatial variations in the background of the Q and U maps.

For non-POL-2 data, the background is removing using a simple common-mode model, in which the mean of the bolometer values is found at each time slice and is then removed from the individual bolometer values. This ignores any spatial variations in the background and so fails to remove the background properly in POL-2 Q and U maps.

To fix this, a second stage of background removal is used when processing POL-2 data, following the initial common-mode removal. This second stage is based upon a Principal Component Analysis (PCA) of the 1280 time-streams in each sub-array (the Q and U data are processed separately). The PCA process identifies the strongest time-dependent components that are present within multiple bolometers. These components are assumed to represent the spatially varying background signal and are removed, leaving just the astronomical signal. You may specify the number of components to remove, via a makemap configuration parameter called pca.pcathresh although pol2map, the reduction command for POL-2 data, provides suitable defaults for this parameter.

On each makemap iteration, the PCA process removes the background (thus reducing the noise in the map) but also removes some of the astronomical signal. The amount of astronomical signal removed will be greater for larger values of pca.pcathresh. However, this astronomical signal is still present in the original time-series data and so can be recovered if sufficient makemap iterations are performed. In other words, using larger values of pca.pcathresh slows down the rate at which astronomical signal is transferred from the time-series data to the map, thus increasing the number of iterations required to recover the full astronomical signal in the map.

Spatial variations in the sky background may also be present in non-POL-2 data, but at a lower level. For a discussion of why PCA is not routinely run on non-polarimetric SCUBA-2 data, see Appendix A.

3.5 Masking

A mask is a two-dimensional array which has the same shape and size as the final map, and which is used to indicate where the source is expected to fall within the map. ‘Bad’ pixel values within a mask indicate background pixels, and ‘good’ pixel values indicate source pixels. Masks are used for two main purposes.

(1)
They prevent the growth of gradients and other artificial large scale structures within the map. For this purpose, the astronomical signal at all background pixels defined by the mask is forced to zero at the end of each iteration within makemap (except for the final iteration).
(2)
They prevent bright sources polluting the evaluation of the various noise models (PCA, COM, FLT) used within makemap. Source pixels are excluded from the calculation of these models.

The pol2map script uses different masks for these two purposes – the “AST” mask and the “PCA” mask. The PCA mask is in general less extensive than the AST mask, with the source areas being restricted to the brighter inner regions. Each of these two masks can either be generated automatically within pol2map, or be specified by a fixed external NDF.

3.6 Tailoring a reduction

Variances between POL-2 maps

MAPVAR is a pol2map parameter that controls how the variances in the coadded I, Q and U maps are formed.

If MAPVAR is set TRUE, the variances in the coadded I, Q and U maps are formed from the spread of pixel data values between the individual observation maps. If MAPVAR is FALSE (the default), the variances in the coadded maps are formed by propagating the pixel variance values created by makemap from the individual observation maps (these are based on the spread of I, Q or U values that fall in each pixel).

Use MAPVAR=TRUE only if enough observations are available to make the variances between them meaningful. A general lower limit on its value is difficult to define, but is advised a minimum of 10 observations.

If a test of the effect of this option is required on a field for which the I, Q and U maps from a set of individual observations are already available, the following may be done:

  % pol2map in=maps/\* iout=imapvar qout=qmapvar uout=umapvar mapvar=yes \
                     ipcor=no cat=cat_mapvar debias=yes

assuming that the I, Q and U maps are in directory maps. The variances in imapvar.sdf, qmapvar.sdf and umapvar.sdf will be calculated using the new method, and these variances will then be used to form the errors in the cat_mapvar.FIT catalogue.