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.

LSST synopsis

The telescope feeds a focal plane that spans a field of view of 9.6 square degrees, so it's 3.1 degrees on a side. 

The default plan calls for a pair of 15 second exposures at each pointing of the telescope, and this pair is termed a "visit" to a field. 

The LSST will be situated in Chile at a latitude of -30 degrees. From there it can usefully access the sky up to a declination of +30 degrees. The full sky is 41,253 square degrees, and LSST plans to conduct a survey over 20,000 square degrees in addition to a few "deeper" fields that will receive longer and more frequent observations.

This implies that we need to schedule observations in 6 bands, spread across 20,000/9.6~2100 fields over the course of 10 years. 

Images are obtained in 6 different optical passbands, designated u,g,r,i,z and y, that span the atmospheric cutoff at 340 nm up to the longest wavelength that can be detected in silicon CCDs, about one micron.  

The time it takes the telescope to slew from one place to another on the sky is determined by two upper limits, one is the maximum angular acceleration (about 3 deg/s^2) and the other is the maximum angular rate (3 deg/s). 

Merit Function Ingredients. 

Observational effectiveness is impacted by both deterministic and stochastic factors. A reasonable initial merit function is the signal to noise ratio for flux determination of an "unresolved" source (i.e. a star). The numerator contains the flux from the source. For the LSST case, the denominator (noise) is dominated by the Poisson noise from the sky background, within the footprint of the source. This footprint is turn dominated by time-variable turbulence in the atmosphere, which produces a Gaussian flux distribution with a FWHM that astronomers term "seeing". The surface brightness of the night sky depends on time of day, on the phase of the moon and distance to the moon, and on the optical filter. 

The signal to noise ratio for measuring the flux phi (at the telescope input aperture) from an unresolved point source for an integration time t scales as

SNR~ (phi)(sqrt(t)) / (FWHM)(sqrt(sky)). 

Both phi and FWHM depend on the "airmass" a of the observation. Looking straight up corresponds to a=1. Looking at an angle of 60 degrees from the zenith has a=2. The atmosphere attenuates the light by an amount that depends on the airmass as well as the passband. So the SNR as a function of airmass and exposure time is a sensible merit function that we seek to optimize, summed over all fields and over the 10 year duration of the survey. This is subject to some science-driven constraints, such as the desire to achieve a uniform survey-integrated SNR across the survey area. 

The FWHM varies depending on atmospheric conditions, and is usually expressed in units of arcseconds. LSST expects to achieve a median seeing of 0.6 arcsec, with a long term distribution as shown in the Figure below.

The deterministic factors that influence the merit function are

• sky brightness, as a function of optical filter, phase of the moon and distance to the moon. 
• time lost during telescope slews and focal plane readout (~3 seconds per image)
• zenith angle dependence of the signal to noise ratio
• exposure time spent on each field

Stochastic factors are

• seeing
• cloud cover

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". 

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

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