[mmaimcal] Re: 4 pol postscript files

[Al Wootten]

Hi Dick

I looked at these images and compared them with what I have seen of others.
I don't have the original image so I can't say much about how well it is
reproduced; but I can compare the four cases the IRAM group ran.

I am not very familiar with Q and U images but my impression is that the
difference between them as observed with ACA and with ALMA, both with SD,
is larger than other differences for other test images.  However, I agree that
your .ps analyses of these images don't show that much in variation.
The general sense of the vectors doesn't seem to have been affected much
but their magnitude might be; I'm not sure the scales are the same in the
various .ps images.  The greyscale looks quite a bit different in the two
images, I thought, with the central 'blob' tending to be enhanced relative
to the E and W outliers in the ALMA reconstructions as opposed to the ACA
reconstructions.  Anyway, gotta go home and make dinner...here are my
thoughts at the end of the day...

Thanks,
Al

A Study of the Polarization Test Image
'science' investigation of SG's simulations of the Crutcher test image
Fetched gunzipped and untarred the images, from 
ftp://iram.fr/pub/alma/fits/polar/Fits.tar.gz   

Stephane had said:
"They are astonishing:
 ALMA+SD completely fails.
     The "hybrid" technique does a decent job without errors, but has more
 limited success in the "typical" error case produced. Errors are dominated 
by the pointing  error in this case (just by accident, we don't control 
the random numbers)."

They have names like
i19-aca.fits
i-aca.fits
i-alma.fits
i19-alma.fits
q19-aca.fits
q-aca.fits
q-alma.fits
q19-alma.fits
u19-aca.fits
u-aca.fits
u-alma.fits
u19-alma.fits

I will assume that these are I,Q,U images of the simulated test image with 
pointing and phase errors superposed.  I will assume that the '19' refers 
to a 19-field mosaic whereas I will assume that those not so labeled are a 
7-field mosaic.  I will assume that those labeled aca were simulated 
assuming ALMA + ACA + TP12m and those labeled alma were simulated assuming 
ALMA + TP12m.

To determine the fidelity index of these images I could do the simple task
                                     Model
                         Fidelity = ----------------
                               Max(difference, 0.7 x rms(difference))
and      
                             Max(abs(model))
          Fidelity range = ------------------------------
                             Rms(difference)
but I don't have the model.  So perhaps a deviant index might be defined:
        Deviant index =          ALMA - ACA
                               ------------------
                                    ALMA
For the intensity images, first that with 7? Fields:
The difference image ranges from -.6 to .7 whereas the input ALMA image ranged 
from -.5 to 8.7, so the differences are less than ten per cent here.

The deviant index shows some deviation near the edges of the image but in 
the central regions tends to be somewhat negative on the W and somewhat 
positive on the E, with values like
1.7 to the SE near pixel (227,223) and -.06 to the W near pixels (275,257), 
in an image clipped at the roughly 1 sigma level.  The peak is near where 
the peak of the difference image lies, of course.  

For the Q image, also 7? Fields.  The difference image shows stripes 
oriented at pa about 40 degrees with a bright band in the nw and a dark 
band in the se, with two bright and two dark bands overall.  The difference 
image ranges between -.077 and .043, following the stripes, while the Q 
images themselves ranged between -.13 and .055 for ALMA and -.10 and .065 
for ACA.
The difference image has its highest positivity where the Q image is most 
negative.  The deviant index image ranges between -1 and 1; much of the 
image is blanked since I used a 1 sigma mask in forming the ratio.  The 
ACA image differs quite visibly from the ALMA+SD image, being fairly 
smooth with lower values toward the SE and higher values toward the NW 
while the latter has a sort of yin/yang character with more variation 
in the center of the image.

For the U image, also 7? Fields.  The difference image shows a dark 
doughnut structure, with a strong central peak surrounded by a dark 
halo.  The range is -.04 to .06 while for the U images themselves the 
range lay between -.03 and .2 for the ACA and for ALMA both.  The 
image appearance of the U images is clearly different to the eye, with 
the ACA structure possessing a broad centrally condensed aspect while 
the ALMA structure seems more clearly divided into three regions to 
the E, W and S of center.

In my opinion, the Q and U images show greater variation between the 
ACA and ALMA cases than other images I have seen in these simulations.

Dick Crutcher sent .ps copies of polarization images for the four cases.  
Comparing ACA and ALMA, it is very hard to see a difference qualitatively, 
by eyeball.