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Solid angle Omega subtended in an angle A from zenith celestial pole is Omega=2pi*(1-cos(A)). 

So within 2 airmasses we can get to 3/4 of the entire sky. A six-band, annual 3pi survey would require 6*3222 = 19K visits. At 50 seconds per visit, this is essentially 16K minutes ~ 270 hours = 30 nights per year. But of course it's only the marginal investment that should count. 

Cadence, coverage, and passband trades.

Assume about 70% of workable weather. Only considering time between astronomical twilight, using skycalc:

  average duration is 9 hours. Obstime=9.2+2*cos(2pi t/yr). 

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Sky Brightness from LSST ETC

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footprint is 26.82 pixels, Gaussian weighted. Units are electrons in 15 sec exposure. Moon is 90 deg from boresight

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SDSS cumulative DR1 sky brightness distribution (no bright time imaging...)

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 The 10% to 90% range in r is 20.6-21.1=0.5 mag=factor of 1.6. The 10% to 90% range in z (OH dominated) is 19.4-18.6=0.8 mag=factor of 2.

y band sky brightness varies over a night, from High, Stubbs et al PASP paper on y band variability:

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Some observations:

• Sky brightness contribution from OH typically varies by a factor of two over the course of a single night, darkest at midnight. This corresponds to 0.25 mag change in m5. 

• For the OH contribution from slab of emission in the upper atmosphere, we'd expect sky darkest at zenith, getting brighter proportional to airmass

• Clouds produce scattered moonlight, so in grey time the night sky brightness doesn't have lunar angle dependence that's built into current version of opsim

• We definitely want a real-time adaptive scheduler, that optimizes based on both cloud transparency and sky brightness. 

• Can we expect to slew during readout? if so, that saves us 2 seconds of slew time, during which we can move by half a field width. 

Merit Function Ingredients. 

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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.

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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

Point Source Photometric Merit Function

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Not all science goals are equal. We should assign pre-factors to the photometric and weak lensing merit functions, and any others that might be useful, such that the sum of all weights is 1. 

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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". 

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

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Decent approximation to seeing degradation vs. airmass a is

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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).

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=2.1-1.4*a+0.30*a^2	SNR_g=1.9-1.1*a+0.23*a^2	SNR_r=1.8-a+0.21*a^2	SNR_i=1.8-0.98*a+0.20*a^2	SNR_z=1.7-0.94*a+0.19*a^2	SNR_y=1.7-0.93*a+0.19*a^2

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Slew times. 

Oct 19 2013, CWS. 

angular distance moved is limited by both the maximum angular rate and the maximum angular acceleration. If we imagine the max angular rate is 3 deg/s and max angular acceleration is 3 deg/s/s, then to move one field width requires a slew of 3 degrees in angle (gives small overlap). For no coast phase this takes a time given by t=2*sqrt(2*1.5deg/alpha)=2 seconds. The maximum angular rate achieved is omega=alpha(1)=3 deg/sec. So for these parameters for any slew larger than a field width, we are angular-rate-limited, and the slew requires a time t_slew~2+dtheta/3 seconds. IF we can slew during readout, the overhead between images separated by an angle theta then is approximately (2+theta/3) seconds.

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At 35 seconds per visit and 9.6 square degrees per field, we cover the sky at a rate of 7900 square degrees in an 8 hour night. That means that on average we revisit interval (no weather) is 3 days for 18,000 square degrees. In the longest night in the year, 10 hours, we'd get about 1000 images.  

Sky rotation.

The position of objects on the sky changes in right ascension direction at an angular rate of 15 degrees per hour times cos(declination).  

One potential approach:

1. determine the rank-ordered priority of all fields on the meridian, in each passband, for different potential values of seeing. 

2. reject the fields that never appear in the top 1000. These have such low priority we'd never get to them. 

3. For each parametric value of seeing, compute the sequence of observations that maximizes the merit function, including the slew overhead contribution. 

A merit function we'd seek to maximize therefore might look something like this:

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subject to these constraints:

• sum of time used = total time available

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Some references

LSST science book

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