Calibration of the 3pi Survey

The discussion below was part of a conversation with Eric Bell about the utility of the calibration fields

The calibration fields are effectively internal standard star fields. Consider the goal to re-calibrating the survey after all data have been taken. Let's say we have a target photometric accuracy for the calibrated catalog of dM (the current goal is 1%), where dM is not the stability within a field for relative photometry, but the accuracy across the sky of any random patch.

How well can we achieve this goal, and what are the drivers?

First, there are 2 classes of observations : those that have been taken in "photometric weather" and those which have not. For our purposes, "photometric weather" means that the sky transparency (dF) is stable to < dM, both for long periods of time and for large spatial scales. Let's defer the definition of "long periods of time" for now, but accept that "large spatial scales" means >> GPC1 FOV. Also, note the it is acceptable for dF to have coherent trends in both spacial and temporal scales smaller than the above; it is merely necessary that dF(x,t) not be decoupled from dF(x+dx,t+dt).

Exposures which have NOT been taken in such conditions cannot be used to constrain the calibration of the catalog and must be (a) identified and (b) excluded from the initial analysis. The remaining exposures can then be used to determine an internal photometric system.

Now imagine the full sky tiled with a grid of these photometric exposures. For most of the sky, the coverage is sparse. We don't know the fraction of time which will be photometric on Haleakala, but on Mauna Kea, depending on your choice of dM, the fraction is probably something in the range of 50-75% of good weather conditions. If that holds, that means there will be on average something like 6 - 8 exposures per field that are photometric. In reality the distribution will be complex and non-Gaussian because of choices at the observatory and the correlated nature of weather.

There are two ways we can pin down the full system. Observations of fields with external standards provide one pin. Obviously, the SDSS area is a big help in this regard, especially the Stripe 82 region which is better characterized than the rest of the survey (with only a single visit per filter). The 2 downsides of this calibration are (a) the internal to external color terms (especially for z and y in our case), and (b) more than 1/2 the sky is very far from SDSS (or the few other fields with high-accuracy photometric calibrators).

The other way to pin down the system is to use fields with many observations and determine the photometric data from the internal consistency of the zero points. If you examine a histogram of the zero points in a field which has been observed many times, the photometric data is seen as a well-defined peak in that distribution. The MD fields and the other calibration fields provide this measurement and act as a set of hard points on the sky.

To tie together the full system, and to calibrate both spatial and temporal variations in the transparency, we can use both the spatial overlaps of neighboring images and the temporal information in sequences of observations. Since the hard points are the calibration fields, the quality of the calibration is partly determined by the distance (number of overlaps) to the calibration fields. The other determining factor is the time-scale between visits to a calibration field. It is the timescale of these visits (and to a lesser extent the spatial distance between the calibration fields) which sets the necessary constraints on the definition of "photometric weather" above.

The choice of calibration field re-visit timescale was set by observations from Mauna Kea of the temporal coherence of the sky transparency in photometric weather, which seems to be about 45 minutes for 1%. To be sure, this is not a very well determined number: it could be too large for Haleakala (with probably worse weather); it could be overly conservative if we can better detrend the transparency variations than in that analysis.

Note that bad fields are not part of this calculus. The calibration fields are used to constrain only the true zero points of the photometric observations. If all of the exposures for a field are bad and the field cannot be calibrated, more or less calibration information will not help.