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 an improved signal-to-noise ratio 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 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 Cosmic Evolution Survey (COSMOS), Lockman Hole, Subaru XMM–Newton Deep Field, Great Observatories Origins Deep Survey (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.