LSST Scheduler

The LSST is a the nation's top priority next-gen ground-based astronomy project, with the objective of
conducting observations of the entire accessible sky, with about 800 visits per field. The scheduler for the project
will determine the order in which these fields are observed, with the goal of maximizing some scientific merit function.
A portion of that merit function has to do with Fourier coverage in the time domain.
The variability in sky conditions (cloud cover, sky brightness and atmospheric seeing) makes the scheduling
problem non-trivial. It's a traveling salesman problem with a stochastic component, subject to certain constraints.
Our goals are to
1. devise a sensible quantitative framework that would accommodate various merit functions.
2. assess whether an instantaneous (nightly) sequence of observations optimization will achieve a global optimum,
3. build some numerical tools to make a toy model and try out some implementation schemes.

Oct 18 2013, C. Stubbs

Observations obtained at angles z from zenith suffer from two effects:

1) additional optical attenuation due to increased atmospheric path length

2) degraded "seeing".

band	central wavelength	extinction (mag per airmass)	seeing degradation compared to r band at zenith
u	350 nm	0.40*a	(1.1)*a^0.6
g	450 nm	0.18*a	(1.07)*a^0.6
r	650 nm	0.10*a	(1.0)*a^0.6
i	750 nm	0.08*a	(0.97)*a^0.6
z	850 nm	0.05*a	(0.94)*a^0.6
y	1000 nm	0.04*a	(0.91)*a^0.6

plot of seeing degradation vs. airmass, and polynomial fit:

airmass	seeing degradation	SNR_u	SNR_g	SNR_r	SNR_i	SNR_z	SNR_y
1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
1.1	1.06	0.91	0.93	0.94	0.94	0.94	0.94
1.2	1.11	0.83	0.87	0.88	0.88	0.89	0.89
1.3	1.17	0.77	0.81	0.83	0.84	0.84	0.85
1.4	1.22	0.71	0.77	0.79	0.79	0.80	0.81
1.5	1.27	0.65	0.72	0.75	0.76	0.77	0.77
1.6	1.32	0.61	0.68	0.71	0.72	0.73	0.74
1.7	1.37	0.56	0.65	0.68	0.69	0.71	0.71
1.8	1.42	0.53	0.62	0.65	0.66	0.68	0.68
1.9	1.46	0.49	0.59	0.62	0.64	0.65	0.66
2.0	1.52	0.46	0.56	0.60	0.61	0.63	0.64
fits	Seeing=0.35+0.72a^2-0.07a	SNR_u=2.1-1.4a+0.30a^2	SNR_g=1.9-1.1a+0.23a^2	SNR_r=1.8-a+0.21*a^2	SNR_i=1.8-0.98a+0.20a^2	SNR_z=1.7-0.94a+0.19a^2	SNR_y=1.7-0.93a+0.19a^2

Decent approximation to seeing degradation vs. airmass a is

S=0.35+0.72a^2-0.07a

Signal to Noise degradation vs. airmass:

SNR scales as source flux in the numerator and (for unresolved objects) as seeing in the denominator. Flux at an airmass "a" is reduced by a factor f(a)=10^(x*(a-1)/2.5) where x is the extinction coefficient listed in the table above. So SNR vs. airmass at fixed exposure time for unresolved point sources scales as SNR(a)~10^(x*(a-1)/2.5)/(0.35+0.72a^2-0.07a)

Some references

LSST science book

lucent paper, 1965, on TSP

SPIE_2006

Hubble Space Telescope scheduler

genetic_edge_recombination_operator

genetic_algorithms_review

kubanek_MS_thesis

genetic_alg_scheduler_SPIE2012