Fix Version/s: None
Implement well-motivated theoretical fits to the astrometric and photometric performance measurements based on derivations from LSST Overview paper.
Photometric errors described by
sigma_rand^2 = (0.039 - gamma) * x + gamma * x^2 [mag^2]
where x = 10^(0.4*(m-m_5))
sigma_1^2 = sigma_sys^2 + sigma_rand^2
error = C * theta / SNR
Based on helpful comments from Zeljko Ivezic
I think eq. 5 from the overview paper (with gamma = 0.039 and m5 = 24.35; the former I assumed and the latter I got from the value of your analytic fit that gives err=0.2 mag) would be a much better fit than the adopted function for mag < 21 (and it is derived from first principles). Actually, if you fit for the systematic term (eq. 4) and gamma and m5, it would be a nice check whether there is any “weird” behavior in analyzed data (and you get the limiting depth, m5, even if you don’t go all the way to the faint end).
Similarly, for the astrometric random errors, we’d expect
error = C * theta / SNR,
where theta is the seeing (or a fit parameter), SNR is the photometric SNR (i.e. 1/err in mag), and C ~ 1 (empirically, and 0.6 for the idealized maximum likelihood solution and gaussian seeing).