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Jaimal and I have agreed that weighted sum and a product figure of merit amount to the same thing. So we'll stick with the weighted sum, and compute a Figure of Merit accordingly:
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where the weights w and merits M are drawn from multiple considerations, including
- maximum tolerable unobserved gap in time, tau ,for each field
- desired co-added depth, m_tot
- homogeneity of coverage, m/m_bar
- seeing-dependence, for galaxy shape measurements
This FOM is computed per field, per passband, for each potential observation. We can also introduce a couple of penalties:
- penalize an observation if a better opportunity will come up within the characteristic time tau
- penalize observations as a function of hour angle, favoring observations towards the East, since we can follow transients for a longer time for those fields.
- We also need to compute a penalty that connects pairs of fields, namely the slew time between them.
We can adopt the 5 or 10 sigma point source limiting magnitude as a good indicator of quality of an observation.
Apart from atmospheric variation in cloud transparency and seeing, the observing conditions as a function of time are deterministic. The zenith angle and sky brightness can be computed, and so the ten sigma point source magnitude depends upon
- sky brightness, which is a function of moon phase, distance from the moon, lunar elevation, solar cycle.
- zenith angle, which affects both atmospheric attenuation and seeing degradation.
We can compute all of this in advance, for each field
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Some references
LSST science book
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