[AstroPy] Re : surface computing on the sphere for projected maps

[Jerome Caron]

Hello,

I am new on the forum since a few days. I am a French amateur astronomer, living 
in Netherlands, with imaging and photometry as main interests. A few months ago, 
I started developing my own CCD image processing routines in Python (see 
http://astrosurf.com/caron/python_scripts.html), starting from Pyfits. I find 
the discussions here very interesting.

Maybe I could help about your question to compute area distorsion induced by a 
projection. If you know the mapping (alpha, delta) on sky --> (x,y) on map, then 
you could calculate it analytically, following the method explained there: 
http://www.uni-stuttgart.de/gi/geoengine/mappro/lecturenotes.pdf
All equations simplify due to the spherical sky (instead of ellipsoidal Earth). 
The idea is that you calculate a matrix called C (see slide 19), and the shape 
distorsions in the two principal (orthogonal) directions = lambda1, lambda2, are 
the square roots of the eigenvalues of C (see slide 24). Area distorsion is just 
the product of the two shape distorsions = lambda1 * lamdba2 = sqrt(det(C)).

In practice:
An arc element on the sky is
   ds^2 = ddelta^2 + cos(delta)^2 * dalpha^2
An arc element on the map is
   dl^2 = dx^2 + dy^2
Then relative area distorsion induced by map projection is
    area_distorsion = cos(delta) * abs(dx/dalpha * dy/ddelta - dx/ddelta * 
dy/dalpha)
 
I hope this helps
Kind regards
Jerome
 
Hello, I have a 2D skymap resulting from a given projection (say 'CAR' 
for instance, but not necessarily), and I would like to compute the 
corresponding surface on the sphere of a pixel.
What is the best way to do that, with pywcs if possible, but any 
suggestion of other tools welcome.
thanks in advance,
Johann
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________________________________

De : Johann Cohen-Tanugi <johann.cohentanugi at gmail.com>
À : "astropy at scipy.org" <astropy at scipy.org>
Envoyé le : Lun 11 avril 2011, 15h 25min 48s
Objet : [AstroPy] surface computing on the sphere for projected maps
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