[bug #62694] Radial profile script overestimates the surface brightness error

[Raul Infante-Sainz]

Follow-up Comment #2, bug #62694 (project gnuastro):

Thanks a lot Mohammad. In addition to the description of the commit, here I am
attaching two plots to show the check and tests I am currently doing. The goal
is basically to understand and ensure that the error in the surface brightness
measurements are correct. 

In short. I am simulating a bunch (333) of Sersic profiles (sersic index 0.5).
I compute the surface brightness radial profile for all of them. At each
radius, the measured error ('--sberror') should be equal to the measured
standard deviation (STD) of the simulated profiles. This is what I plot in the
attached figures.

X-axis is radius in pixels. Y-axis is surface brightness.
The square red points are the STD of the simulations at each radius. I.e., the
real error at each radius. The circle blue points  are the averaged value of
measured error ('--sberror') of the simulated profiles. One plot is with
'--spatialresolution=0' and other is with '--spatialresolution=2'. 

Results. With '--spatialresolution=2' (default value) the results only match
at intermediate radius. For the core (very high signal-to-noise) and the outer
part (noise) the don't match. With '--spatialresolution=0', the match is good
for the region where the signal-to-noise is high. However, the result don't
match for larger radius. Eventhough for larger radius the region is pure
noise, they should match. The question is, why they don't match?

More test are needed. 



(file #53391, file #53392)

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Additional Item Attachment:

File name: sersic-0.5_m-12_zp-25_back-22_nsims-333_spatialresolution-0.png
Size:46 KB
   
<https://file.savannah.gnu.org/file/sersic-0.5_m-12_zp-25_back-22_nsims-333_spatialresolution-0.png?file_id=53391>

File name: sersic-0.5_m-12_zp-25_back-22_nsims-333_spatialresolution-2.png
Size:45 KB
   
<https://file.savannah.gnu.org/file/sersic-0.5_m-12_zp-25_back-22_nsims-333_spatialresolution-2.png?file_id=53392>



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