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where the weights w and merits M are drawn from multiple considerations. We'll tune values of M to range from 0 to 1, where they saturate. Some candidate elements for the merit by field:
For the atan() function, tau_1 determines the 50% point and tau_2 the slope of the merit function at that point.
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Here is an example of FWHM-based merit, driving a field higher if seeing is really excellent. This is for FWHM_1= 0.5 and FWHM_2=0.1. Depth uniformity would look the same as this.
This FOM is computed per field, per passband, for each potential observation. We can also introduce a couple of penalties:
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This includes the zenith-depedence of FWHM, which scales as airmass^0.6, and extinction in the various bands. The coefficient of the final term comes from the airmass dependence of seeing, a^0.6, and the 2.5 factor for magnitudes, so that 2.5*0.6=1.5.
Have each science program fill out this table, for each field center. Constrain field weights so they sum to one, for each program. Examples from SN, weak lensing, and static sky are illustrated
| program | program weight | field ID | filter | field weight | tau 1 (days) | tau 2 (days) | FWHM 1 | FWHM 2 | depth 1 |
|---|---|---|---|---|---|---|---|---|---|
| WL | 0.3 | 100 | r | epsilon | 365 | 100 | 0.5 | 0.1 | 27 |
| 101 | r | epsilon | 365 | 100 | 0.5 | 0.1 | 27 | ||
| SN | 0.2 | 205 | g | epsilon2 | 5 | 2 | 0.1 | 0.1 | 25 |
| static sky | 0.2 | 205 | g | epsilon3 | 365 | 100 | 0.8 | 0.2 | 27 |
A high value for tau1,2 de-emphasizes that aspect. A low value for FWHM1,2 de-emphasizes seeing.
A prescription for a (single-band, for now) optimization strategy would be
- allocate weights to different science programs, based on fashion and merit
- have those science programs determine merit attributes for all fields
- pre-calculate zenith angle and sky background dependent m5 values for all fields, for all potential observations.
- Construct a nominal m5 value for zero clouds and median FWHM, for all fields for all observation slots.
Then, before the start of each night
- trim list of candidate fields to the ones that are above some cutoff airmass
- estimate the co-added depth for each one, compute their depth merit functions
- determine the (partial-credit) time since last observed for each one, compute the temporal merit function for each field
- compute merit function for each field, and calculate nominal sky merit function vs. t by looking forward until temporal merit hits 0.9. Store best merit within that interval.
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Some references
LSST science book
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