Thus both positive and negative Q and U values give a positive PI value, pushing the mean PI value upwards. A correction for this effect is applied if the parameter setting “debias=yes<\/span>” is specified when running the SMURF<\/span> pol2map<\/span> command (note, the default is “debias=no<\/span>“). To date, this correction has used the so-called “asymptotic estimator” (AS):<\/p>\n PIAS<\/sub> = \u221a( Q2<\/sup> + U2 <\/sup> – \u03c32 <\/sup>)<\/p>\n where \u03c32 <\/sup>is the weighted mean of the variances on Q and U:<\/p>\n \u03c32<\/sup> = ( Q2<\/sup>*\u03c3Q<\/sub>2<\/sup> + U2<\/sup>*\u03c3U<\/sub>2<\/sup> ) \/ ( Q2<\/sup> + U2<\/sup> )<\/p>\n However, this estimator has the problem that it becomes undefined when<\/p>\n Q2<\/sup> + U2 <\/sup>< \u03c32\u00a0<\/sup><\/p>\n The usual practice is to use an exact value of zero for the PI at such points. However, this can upset the PI noise statistics in very low SNR regions.<\/p>\n However, there are other forms of de-biasing that avoid this problem, such as the “modified asymptotic estimator” (MAS) described by\u00a0Plaszczynski et al\u00a0 (MNRAS 2014).<\/a>\u00a0 \u00a0The de-biased MAS estimate of PI is defined by<\/p>\n PIMAS<\/sub> = PI – 0.5*\u03c32<\/sup>*( 1 – e-(PI\/\u03c3)2<\/sup><\/sup>)\/PI<\/p>\n where PI is \u221a( Q2<\/sup> + U2 <\/sup>). The PIMAS <\/sub>value is defined for all non-zero PI. The following figure shows PIAS <\/sub>\u00a0(blue) and PIMAS<\/sub> (green) plotted against uncorrected PI, assuming \u03c32\u00a0<\/sup>= 1:<\/p>\n The MAS estimator may now be used in pol2map<\/span> by adding “debiastype=mas<\/span>” to the pol2map<\/span> command line. Note, the default de-biasing method is still the asymptotic estimator. Using the MAS estimator may facilitate investigation of PI noise statistics in low SNR areas.<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Calculation of the polarised intensity (PI) and percentage polarisation (P) values from measurements of I, Q and U usually need to be corrected to take account of the bias towards larger values caused by the presence of noise (particularly noticeable\u00a0 in areas of low signal-to-noise). This bias occurs because of\u2026 Continue reading<\/a><\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[36],"tags":[37],"_links":{"self":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/posts\/11051"}],"collection":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/comments?post=11051"}],"version-history":[{"count":4,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/posts\/11051\/revisions"}],"predecessor-version":[{"id":11056,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/posts\/11051\/revisions\/11056"}],"wp:attachment":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/media?parent=11051"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/categories?post=11051"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/tags?post=11051"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"http:\/\/www.eaobservatory.org\/jcmt\/wp-content\/uploads\/sites\/2\/2020\/04\/mas-300x224.png\")
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