[daip] RMS flux density per pixel

[Eric Greisen]

Modhurita Mitra wrote:
> I have a question about this again. I read the explain files you 
> mentioned and also the Condon (1997) paper, but they talk about Gaussian 
> fits. I am not fitting Gaussians, I am calculating the total integrated 
> flux density by placing a rectangular bounding box around the object. I 
> could not understand how to calculate the error in this flux density 
> from either the explain files or the paper, these talk about errors in 
> the parameters when you are fitting a Gaussian to the object. Can you 
> please explain how I can apply their results to my problem?
> 
> You said:
> 
> /It would be more accurate to use off-source rms in Jy/beam times the 
> sqrt of the number of beams in the area./
> 
> Is this valid even in the case of correlated noise? Isn't this exactly 
> equivalent to what I was doing:
> 
> /Off-source RMS flux density per pixel = (Off-source RMS flux density in 
> Jy/beam)/(Number of pixels/beam)
> Error in source flux density = (Off-source RMS flux density per 
> pixel)*sqrt(Number of pixels in bounding box around the source)
> /
> If I understood everything correctly, you are doing the calculations in 
> units/multiples of beams and I was doing it in units/multiples of pixels 
> - aren't these are equivalent?
> 
> Thanks,
> Modhurita
> 
> 
> On Mon, Jun 13, 2011 at 6:11 PM, Eric Greisen <egreisen at nrao.edu 
> <mailto:egreisen at nrao.edu>> wrote:
> 
>     Modhurita Mitra wrote:
> 
>         Thank you Eric. I need the RMS flux density per pixel to
>         calculate the error in the source flux density obtained by
>         placing a bounding box around the source and computing the
>         integrated flux inside the box using IMSTAT. The expressions I
>         am using are:
> 
>         Off-source RMS flux density per pixel = (Off-source RMS flux
>         density in Jy/beam)/(Number of pixels/beam)
>         Error in source flux density = (Off-source RMS flux density per
>         pixel)*sqrt(Number of pixels in bounding box around the source)
> 
>         Are these correct? Yes, I am aware that the errors in adjacent
>         pixels are correlated but I am neglecting that for the moment.
> 
> 
>     Given that a beam is usually 20 pixels, I do not thin you can ignore
>     the correlation.  It would be more accurate to use off-source rms in
>     Jy beam times the sqrt of the number of beams in the area.  The
>     explain files for IMFIT (JMFIT or SAD) have a discussion of these
>     uncertainties also.
> 
>     Eric Greisen
> 
> 
I suspect that the two methods are equivalent roughly.  I would take one 
source that can be fit with a Gaussian and run JMFIT on it to make sure 
that your rms is about the same as the rms estimated by JMFIT for the 
total flux.  Note however that your estimate of noise increases in an 
unbounded way depending on the size of your rectangular area.

ERic Greisen