Calculating the transfer function of noise removal by principal
  component analysis and application to AzTEC observations
  Instruments using arrays of many bolometers have become increasingly common
in the past decade. The maps produced by such instruments typically include the
filtering effects of the instrument as well as those from subsequent steps
performed in the reduction of the data. Therefore interpretation of the maps is
dependent upon accurately calculating the transfer function of the chosen
reduction technique on the signal of interest. Many of these instruments use
non-linear and iterative techniques to reduce their data because such methods
can offer improved signal-to-noise over those that are purely linear,
particularly for signals at scales comparable to that subtended by the array.
We discuss a general approach for measuring the transfer function of principal
component analysis (PCA) on point sources that are small compared to the
spatial extent seen by any single bolometer within the array. The results are
applied to previously released AzTEC catalogues of the COSMOS, Lockman Hole,
Subaru XMM-Newton Deep Field, GOODS-North and GOODS-South fields. Source flux
density and noise estimates increase by roughly +10 per cent for fields
observed while AzTEC was installed at the Atacama Submillimeter Telescope
Experiment and +15-25 per cent while AzTEC was installed at the James Clerk
Maxwell Telescope. Detection significance is, on average, unaffected by the
revised technique. The revised photometry technique will be used in subsequent
AzTEC releases.
