From dey@noao.edu Fri Dec 22 23:16:43 2000
Date: Mon, 18 Dec 2000 15:41:29 -0700 (MST)
From: Arjun Dey <dey@noao.edu>
To: sdawson@astron.Berkeley.EDU
Subject: limits



Hi Steve

I forgot to comment on one of your previous questions regarding th e
limiting depth of your data. Once you have determined the rms noise
per pixel (using iterstat, say), you can then compute the 1 sigma limiting 
magnitude in a fixed aperture using: 

	mlim = -2.5*log10[rms*sqrt(N)]

where N = number of pixels in your fixed aperture (i.e., for a fixed 
circular aperture of diameter D arcseconds, N = (PI/4) * (D/0.258)^2 ).
I generally compute a 5-sigma limit by replacing rms in the eqn above 
with 5*rms. 

Esther Hu and Len Cowie have made the case that this is an artificial way
in which to measure the limiting magnitude since the noise is really 
dominated by the unresolved faint galaxies and not by the Poissonian sky 
noise. This is true, and in some sense it is better to look at the 
distribution of the noise estimates made in the aperture of interest by 
measuring the noise in a fixed aperture at many different locations in 
the frame and studying their distribution. This will in general result 
in a more conservative estimate (i.e., a brighter limiting magnitude), 
but may be more appropriate. 

You can also quote a surface brightness (i.e., in magnitudes per sq arcsecond).
Just remember, whether you quote limits in magnitudes or surface 
brightnesses, you need to also quote the aperture to which your
limit corresponds.

Cheers

Arjun