[alma-config] Re: dynamic range and fidelity

[Min Yun]

Dave Woody has some interesting suggestions.  I will try to summarize
everyone's suggestions together later.  


					-- Min
					
					
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From: "David Woody" <dwoody at ovro.caltech.edu>
To: "Min Yun" <myun at zia.aoc.NRAO.EDU>
Subject: Re: dynamic range and fidelity
Date: Wed, 23 Aug 2000 14:15:28 -0700
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Min

I haven't been keeping up on the details of the image simulations
that are being done, but I assume that the simulations are 
ignoring additive noise, i.e. no receiver noise. Then the noise
in the images as given by the difference maps will scale with the
total or peak flux.  So the diff maps should be turned into
dimensionless fractions by dividing by either the total or 
peak flux (probably the peak flux).  We don't know the 
flux of the sources we will be looking at, 
so the diff maps in Jy are not very useful.

The rms of the diff map is composed of roughly 
two parts, the on-source part and the off-source part.  The
various definitions of dynamic range and fidelity try to get
at these two components of the errors.  Using masks and thresholds
can be misleading, because the threshold that an astronomer
might want to use to decide which statistic to apply for 
determining whether a feature in an image is real will depend 
on the amount of additive noise, which is not known and is
not included in the simulations.  

There should be a simple method to separate out the two error 
components that does not require masks or thresholds.

What about doing a simple linear fit of the (diff-map)^2 to
A + B*(original simulation image)^2.  
1/sqrt(B) would be interpreted as the fidelity, 
i.e. the errors in the map that are proportional to the image. 
1/sqrt(A) would be the "off-source" dynamic range.
This fit is not computationally time consuming or difficult.

This gives two simple and mathematically well defined imaging 
quality measures that should contain most of the information
we need to evaluate the images.  Anything more complicated
risks the danger of applying a particular slant to the results
that depends upon "what one expects to see".

Note: pointing and other calibration type errors are multiplicative
and can be included in the simulation studies and the above
type of image quality analysis can be applied.

Cheers
David
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