Power spectrum model of visual masking: simulations and empirical data

In the study of the spatial characteristics of the visual channels, the power spectrum model of visual masking is one of the most widely used. When the task is to detect a signal masked by visual noise, this classical model assumes that the signal and the noise are previously processed by a bank of linear channels and that the power of the signal at threshold is proportional to the power of the noise passing through the visual channel that mediates detection. The model also assumes that this visual channel will have the highest ratio of signal power to noise power at its output. According to this, there are masking conditions where the highest signal-to-noise ratio (SNR) occurs in a channel centered in a spatial frequency different from the spatial frequency of the signal (off-frequency looking). Under these conditions the channel mediating detection could vary with the type of noise used in the masking experiment and this could affect the estimation of the shape and the bandwidth of the visual channels. It is generally believed that notched noise, white noise and double bandpass noise prevent off-frequency looking, and high-pass, low-pass and bandpass noises can promote it independently of the channel's shape. In this study, by means of a procedure that finds the channel that maximizes the SNR at its output, we performed numerical simulations using the power spectrum model to study the characteristics of masking caused by six types of one-dimensional noise (white, high-pass, low-pass, bandpass, notched, and double bandpass) for two types of channel's shape (symmetric and asymmetric). Our simulations confirm that (1) high-pass, low-pass, and bandpass noises do not prevent the off-frequency looking, (2) white noise satisfactorily prevents the off-frequency looking independently of the shape and bandwidth of the visual channel, and interestingly we proved for the first time that (3) notched and double bandpass noises prevent off-frequency looking only when the noise cutoffs around the spatial frequency of the signal match the shape of the visual channel (symmetric or asymmetric) involved in the detection. In order to test the explanatory power of the model with empirical data, we performed six visual masking experiments. We show that this model, with only two free parameters, fits the empirical masking data with high precision. Finally, we provide equations of the power spectrum model for six masking noises used in the simulations and in the experiments.

The SCUBA HAlf degree extragalactic survey - III. Identification of radio and mid-infrared counterparts to submillimetre galaxies

Determining an accurate position for a submillimetre (submm) galaxy (SMG) is the crucial step that enables us to move from the basic properties of an SMG sample - source counts and 2D clustering - to an assessment of their detailed, multiwavelength properties, their contribution to the history of cosmic star formation and their links with present-day galaxy populations. In this paper, we identify robust radio and/or infrared (IR) counterparts, and hence accurate positions, for over two-thirds of the SCUBA HAlf-Degree Extragalactic Survey (SHADES) Source Catalogue, presenting optical, 24-μm and radio images of each SMG. Observed trends in identification rate have given no strong rationale for pruning the sample. Uncertainties in submm position are found to be consistent with theoretical expectations, with no evidence for significant additional sources of error. Employing the submm/radio redshift indicator, via a parametrization appropriate for radio-identified SMGs with spectroscopic redshifts, yields a median redshift of 2.8 for the radio-identified subset of SHADES, somewhat higher than the median spectroscopic redshift. We present a diagnostic colour-colour plot, exploiting Spitzer photometry, in which we identify regions commensurate with SMGs at very high redshift. Finally, we find that significantly more SMGs have multiple robust counterparts than would be expected by chance, indicative of physical associations. These multiple systems are most common amongst the brightest SMGs and are typically separated by 2-6 arcsec, similar to 15-20/sin i kpc at z~ 2, consistent with early bursts seen in merger simulations.