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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 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
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Oct 18 2013, C. Stubbs
Observations obtained at angles z from zenith suffer from two effects:
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| band | central wavelength | extinction (mag per airmass) | seeing degradation compared to r band at zenith |
|---|---|---|---|
| u | 350 nm | 0.40*a | (1.1)*a0.6 |
| g | 450 nm | 0.18*a | (1.07)*a0.6 |
| r | 650 nm | 0.10*a | (1.0)*a0.6 |
| i | 750 nm | 0.08*a | (0.97)*a0.6 |
| z | 850 nm | 0.05*a | (0.94)*a0.6 |
| y | 1000 nm | 0.04*a | (0.91)*a0.6 |
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plot of seeing degradation vs. airmass, and polynomial fit:
Decent approximation to seeing degradation vs. airmass a is
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| 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 |
Some references
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