[daip] [Fwd: Re: [Fwd: Re: IMEAN and noise]]

[Eric Greisen]

Glenn Morrison writes:
 >   Further question Eric....
 > 
 > --Glenn
 > 
 > 
 > >  > 2) Does it assume that all the pixel are independent, that there 
 > > exists
 > >  > no correlation between individual pixels?
 > >
 > >     The shape of the histogram is unaffected by independence of
 > > pixels so the fit width is independent of that.  The independent part
 > > comes in when you integrate.
 > 
 > This makes me think that part of the issue comes down to the
 > units of the image.  In the headers, the flux unit is given as follows:
 > 
 > BUNIT   = 'JY/BEAM '           /Units of flux
 > 
 > Can you tell me what this means?  What is assumed (or known)
 > about the beam, and how is this used when one measures the
 > flux density of a source?  I suspect that if I understand this, I may
 > then understand why the pixel correlations don't matter.
 > 
 > 	Thanks,
 > 
 > 		Mark

Be careful - I said they don't matter in plotting a histogram and
measuring its width.  They do matter when estimating a source's
parameters.

On a dirty image nothing is really known about the "beam" except that
its integral to infinity (that is important) is equal to whatever was
put in for the observation at (u,v) = (0,0).  The beam and image are
computed by identical means and then the peak of the beam is divided
into both images.  Thus the beam is the source image of a point
source at the origin, i.e. with complex visibility = (1.0, 0.0) Jy.
The beam area is often taken to be the Gaussian that best fits the
center part of the beam and this is not bad for estimating the flux of
point objects.

After Cleaning things are even worse - the units of the residual
portion of the image are unchanged and much of the source flux may
still be in the residual image if it is extended.  The Cleaned
portions are returned to the image with a well-defined Gaussian
convolving function so the beam area of this is known
(1.1331 * Major * Minor).

Eric Greisen