4-Detector Skymap With 8 Arcminute Pixels

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Here are some notes on the MAXIMA pixelization to allow people familiar with FITS jargon to display MAXIMA maps quickly:-

MAXIMA-1 data maps are projected according to the pseudo-cylindrical Sanson-Flamsteed projection, an equal-area projection with projection law:

x=(alpha-alpha0) cos(delta)

where x and y are the projected native coordinates (Calabretta & Greisen 2002).

1) To pass from celestial coordinates to pixel coordinates

x=(alpha-alpha0) cos(delta)

ix= x/ CDELT1 + CRPIX1
iy= y/ CDELT2 + CRPIX2

alpha = right ascension
delta = declination
alpha0 = right ascension of the meridian center of the map = CRVAL1

CRPIX1, CRPIX2 = central reference pixels of the map
CDELT1, CDELT2 = angular pixel sizes (increments)
ix, iy = pixel coordinates of the map

2) To pass from pixel coordinates to celestial coordinates

x= (ix-CRPIX1)* CDELT1
y= (iy-CRPIX2)* CDELT2
alpha= x /cos(y) + alpha0

Note : since the reference point for the projection has alpha_p=alpha0, delta_p=0, the rotation of the reference frame is equivalent to adding alpha0 to the alpha coordinates (a consequence of setting up CRVAL2=0).

For these maps:
CDELT1, CDELT1 = 8 arcmin
alpha0 = 14.8 hours
(don't forget to put everything in the same angular units).

CRPIX1, CRPIX2 = you choose, but it should correspond to the center point of your displayed array image.

"Representations of celestial coordinates in FITS", Calabretta. M.R., & Greisen, E.W. (2002), Astronomy & Astrophysics, 375, 1077-1122. (see also http://www.atnf.csiro.au/people/mcalabre/index.html)

[adapted from a document written by Domingos Barbosa, dated 02/25/02]

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