What is a uniform survey?

On the flight home, I wrote this paragraph (subject to further revision) for my self-calibration paper with Holmes and Rix. For context, strategy A is the traditional uniform, aligned, square-grid survey strategy with small marginal overlaps; strategy D is a quasi-random strategy where no two fields are precisely aligned in any respect.

Ultimately, survey design requires trade-offs between calibration requirements and other requirements related to cadence, telescope overheads, and observing constraints (like alt, az, airmass, and field-rotation constraints). One requirement that is often over-emphasized, however, is conceptual or apparent ``uniformity''; these different survey strategies have different uniformities of coverage, each with possibly non-obvious consequences. Many astronomers will see survey strategy A as being ``more uniform'' in its coverage (especially relative to survey D). This is not true, if uniformity is defined by the variance or skewness or any other simple statistic in exposure times; strategy D is extremely uniform (more uniform than Poisson, for example). In any survey, past and future, variations in exposure time have been valuable for checking systematic and random errors, and don't---in themselves---make it difficult to obtain a uniform survey in properties like brightness (since samples can be cut on any well-measured property). In general, in the presence of real astronomical variations in distributions of luminosity, distance, metallicity, and (more importantly) extinction by dust, there is no way to make a survey uniformly sensitive to the objects of interest. As a community we should be prepared to adjust our analysis for the non-uniformity of the survey rather than adjust (cut) our data to match the uniformity of unrealistically simplified analyses. This is already standard practice in the precise cosmological measurement experiments, and will be required practice for the next generation of massively-multiple-epoch imaging surveys.