The source counts of galaxies discovered at submillimetre and millimetre wavelengths provide important information on the evolution of infrared-bright galaxies. We combine the data from six blank-field surveys carried out at 1.1 mm with AzTEC, totalling 1.6 deg 2 in area with root-mean-square depths ranging from 0.4 to 1.7 mJy, and derive the strongest constraints to date on the 1.1 mm source counts at flux densities S 1100 = 1-12 mJy. Using additional data from the AzTEC Cluster Environment Survey to extend the counts to S 1100 ∼ 20 mJy, we see tentative evidence for an enhancement relative to the exponential drop in the counts at S 1100 ∼ 13 mJy and a smooth connection to the bright source counts at >20 mJy measured by the South Pole Telescope; this excess may be due to strong-lensing effects. We compare these counts to predictions from several semi-analytical and phenomenological models and find that for most the agreement is quite good at flux densities 4 mJy; however, we find significant discrepancies ( 3σ ) between the models and the observed 1.1-mm counts at lower flux densities, and none of them is consistent with the observed turnover in the Euclideannormalized counts at S 1100 2 mJy. Our new results therefore may require modifications to existing evolutionary models for low-luminosity galaxies. Alternatively, the discrepancy between the measured counts at the faint end and predictions from phenomenological models could arise from limited knowledge of the spectral energy distributions of faint galaxies in the local Universe.

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.

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