From: 	Frank Masci <fmasci@ipac.caltech.edu>
Subject: 	empirical maglimit
Date: 	January 29, 2013 11:32:33 AM PST

Hi all,

I forgot to mention this earlier. It's something I've used (with caution!) on other projects. A good semi-empirical estimate of the point-source magnitude limit can be obtained from:

mlim = zp - 2.5 * log10[ snr * sigmapix * sqrt(Np) ],

where:
 * zp = photometric zeropoint.

 * snr = desired signal-to-noise limit, e.g., 5.

 * sigmapix = a _robust_ estimate of the background RMS per pixel (tricky in confused regions and/or w/ large background gradients but possible if computed over a grid).

 * Np = the "number of noise pixels" defining the observed PSF, i.e., the "effective footprint" of a point source. For a Gaussian-like profile with FWHM in pixels, Np = 2.226*FWHM^2.

The above assumes that close to mlim you're background dominated (i.e., not source-photon dominated) and that the pixel noise is not significantly correlated. Both these approximations hold well for PTF (both frames and reference images). This agrees well with the classic histogram-turnover method where typically mlim ~19.4 - 21.3 (5-sigma) for single frames.

Regards, Frank